{ "checkpoint": "RMO95", "fixed_upstream_global_normalized": { "rho": "1.0", "p": "0.04056", "u": [ "-1.0", "-0.0", "0.0" ], "B": [ "0.05618818561896245", "0.6422339004220036", "0.0" ] }, "gamma_exact": "5/3", "velocity_unit_km_s": 600, "density_unit": "arbitrary fixed normalization", "frame": "all planes stationary; original axes fixed; u1=(-600,0,0) km/s", "angle_domain_phi_degrees": [ -4, 4 ], "step_degrees": 0.025, "summary": { "status": "PASS", "checkpoint": "RMO95", "coverage": "321 computed points; no continuum or all-family completeness certificate", "root_selection": "one unique root in [1.3,1.9] at each sampled normal; anchored to R94", "number_of_points": 321, "classification_counts": { "SUPPORTED_LOCAL_CLASS:fast_shock": 321 }, "max_scaled_flux_residual": "9.42528391286795761039980288682224398056393935349885254226809363729516273827931634347384527E-67", "R94_anchor_scaled_error": "9.51058685342338207641135368681252882795850838312511106666053114752387844294871794871794872E-17", "full_flux_reference_controls": 3, "max_reference_state_error": 1.7913266788665354e-66, "max_jacobian_eigenvalue_error": 6.217248937900877e-15, "coarse_0p1_midpoint_error_km_s": "0.000192415602929358267506494349143128135830118938831008764890407030721462634315343875541356121", "fine_0p05_midpoint_error_km_s": "0.0000481090320861795233087567493873549505467935928735088631311364717556076693253321260403052928", "refinement_improvement_factor": "3.99957335630192979609296081676082077638723284108941963595694556802894735630073584574529188", "sampled_ranges": { "compression": [ 1.554878051330473, 1.560202952778077 ], "u2x_km_s": [ -387.0931165171392, -384.2882560500542 ], "u2y_km_s": [ -17.31473486570809, -6.899012551770272 ], "speed2_km_s": [ 384.40109204164565, 387.48016839371445 ], "signed_deflection_degrees": [ 1.0277403949255857, 2.5611418744505925 ], "entropy_over_cv": [ 0.17769606542840166, 0.1823162633083594 ], "upstream_fast_Mach": [ 1.4350783949137533, 1.4393044892030291 ], "downstream_fast_Mach": [ 0.7369096211914559, 0.7385718435248592 ], "downstream_alfven_margin": [ 0.5594049819360838, 0.632547495895375 ] }, "negative_normal_only_control": { "flux_residuals": [ "-0.002209935531797517538973262196036187106420139751628641956996380362657208950239414650943462", "-8.06670761709675925406242372819093418577199577122005619325104892679824916361790467239322993E-90", "-0.0164109950074238774119309359904309224665323450604274538430010359722025039870861166126166022", "0E-181", "-1E-90", "0E-181", "-0.000808243025729269067732516819452703028209261572161824356521851374439030499479274889791231330", "0.025212156706796391910001519178016133496403267844255119985177980527586715931501868214938188" ], "diagnosis": { "case_id": "wrong_normal_only", "status": "INCONSISTENT_BN", "family": null, "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "NOT_ASSESSED", "reason": "Required checks not completed." }, "slow_shock": { "status": "NOT_ASSESSED", "reason": "Required checks not completed." }, "rotational_discontinuity": { "status": "NOT_ASSESSED", "reason": "Required checks not completed." }, "contact": { "status": "NOT_ASSESSED", "reason": "Required checks not completed." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": {}, "result_sentence": "The two normal magnetic fields disagree beyond the declared tolerance.", "next_action": "The two normal magnetic fields disagree beyond the declared tolerance." } }, "external_solver_checked": false, "new_solar_identification": false, "native_browser_checked": false, "source_sha256": { "results/upstream_flow/RMO_upstream_flow.json": "fe91637db391258e748b6806100c40fd58a289f7313125bf6e9fa4727f477f83", "shock_polar/PROTOCOL.md": "dca875461f34f178aa79d09064ad678ea999a65d3a85f216f67570ed1c95c334", "shock_polar/audit.py": "c33e3b44ba90a88c7c9ffc36a324bf26daef1b8183c84235c07af2d36e110b1a", "local_diagnosis/diagnose.py": "d89a9402476765d9e923b000eeb69c9a431704d86e64abb52d8c819db4e90f3f" }, "runtime": { "python": "3.12.13", "numpy": "2.3.5", "decimal_precision": 90 } }, "controls": [ { "phi_degrees": -4.0, "reference_global_state": { "rho": "1.55487805133047286895916763245468287035510767769419396856491566212291976205733813901859465", "p": "0.101103049590192654402247631334078734376206135334246340824820283584253643283412094714521801", "u": [ "-0.645155194195232053691856812167116656912641826495044466809771285556628869011342742120988092", "-0.0288578914428468176168770238179983658844192722151043737799909411967667403819977759199447978", "0" ], "B": [ "0.0811427978666834796659319888416390700326212424300498691473595309468973861788633935560312201", "0.999101481742317926790744502167751340458665150455749795129909077906839497248184169239822811", "0" ] }, "reference_iterations": 6, "reference_residuals": [ "1.568800E-84", "-1.1604E-85", "-1.114038E-85", "1.014905E-84", "9.6848E-85", "-1E-91" ], "reference_state_error": "9.89966905871434389299809E-67", "characteristic_matrix": { "upstream": { "matrix_eigenvalues": [ -1.692692660512354, -1.0088153920702527, -1.0017724065662157, -0.997564050259828, -0.9933556939534279, -0.9863127084493961, -0.3024354400072966 ], "formula_eigenvalues": [ -1.6926926605123511, -1.0088153920702525, -1.0017724065662186, -0.9975640502598242, -0.9933556939534299, -0.9863127084493959, -0.30243544000729733 ], "max_absolute_error": 3.774758283725532e-15, "jacobian": [ [ 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], [ -0.6618007010374518, -1.3300854003464322, 0.04650431582941687, 0.0, 0.6666666666666667, 0.2148629802046659, 0.0 ], [ -0.06958655048003272, -0.0697564737441253, -0.9975640502598243, -0.0, -0.0, -0.011251341810428315, -0.0 ], [ 0.0, 0.0, 0.0, -0.9975640502598243, 0.0, 0.0, -0.011251341810428315 ], [ 0.6813905392390653, 0.35347221278135244, -0.053643524151425113, 0.0, -1.6626067504330406, -0.21355473085427762, 0.0 ], [ 0.6422339004220036, 0.6445889406139977, -0.011251341810428315, 0.0, 0.0, -0.9975640502598243, 0.0 ], [ 0.0, 0.0, 0.0, -0.011251341810428315, 0.0, 0.0, -0.9975640502598243 ] ] }, "downstream": { "matrix_eigenvalues": [ -1.5102343762696788, -0.650593711746256, -0.644990105161383, -0.6415706038208165, -0.6381511024802466, -0.632547495895375, 0.22709316862804746 ], "formula_eigenvalues": [ -1.5102343762696782, -0.6505937117462558, -0.644990105161384, -0.6415706038208154, -0.6381511024802468, -0.632547495895375, 0.2270931686280475 ], "max_absolute_error": 1.1102230246251565e-15, "jacobian": [ [ 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], [ -0.2725935055218008, -0.8554274717610872, 0.049194230956300246, 0.0, 0.6666666666666667, 0.3341093187321235, 0.0 ], [ -0.0473423586887013, -0.07379134643445036, -0.6415706038208155, -0.0, -0.0, -0.011251341810428315, -0.0 ], [ 0.0, 0.0, 0.0, -0.6415706038208155, 0.0, 0.0, -0.011251341810428315 ], [ 0.5628937899808238, 0.7428134155918574, -0.038814574989887954, 0.0, -1.0692843397013594, -0.21352446569974406, 0.0 ], [ 0.41304454704499755, 0.6446344492024324, -0.007236157074055297, 0.0, 0.0, -0.6415706038208155, 0.0 ], [ 0.0, 0.0, 0.0, -0.007236157074055297, 0.0, 0.0, -0.6415706038208155 ] ] } }, "rotation_state_error": "1E-90", "rotation_flux_residuals": [ "-1E-90", "9.91242246058387604549683066828709441741096514407662995727653160086589209141443003726726280E-90", "2E-90", "0E-182", "-5E-90", "0E-182", "5.01115643509179579080765722716406986873561883424417549861838705334474044852865445091778034E-67", "-1.0E-90" ], "boost_state_error": "1E-90", "moving_front_flux_residuals": [ "-1E-90", "0E-90", "0E-90", "0E-182", "-5E-90", "0E-181", "5.08087108881042855018994E-67", "0E-91" ], "rotation_diagnosis": { "case_id": "rotation", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.07177391008928782, 0.0 ], "rh_scaled_inf": 4.3882011991206896e-16, "rh_components": { "mass": 2.220446049250313e-16, "normal_momentum": -3.571634227666843e-16, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 4.3882011991206896e-16 }, "characteristics": { "left": { "slow": 0.0034195013405686186, "alfven_n": 0.009023107925440378, "fast": 0.8686637724488628 }, "right": { "slow": 0.004208356306394351, "alfven_n": 0.011251341810428315, "fast": 0.6951286102525269 } }, "front_relative_normal_velocity": { "left": -0.6415706038208154, "right": -0.9975640502598242 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.554878051330473, "pressure_ratio": 2.4926787374307855, "entropy_over_cv": 0.17769606542840155, "tangential_field_ratio": 1.5549878271904753 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "boost_diagnosis": { "case_id": "boost", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.3837475580824013, "evaluation_boost": [ 0.3837475580824013, -0.25545246535852456, 0.0 ], "rh_scaled_inf": 3.8163916471489756e-17, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -3.8163916471489756e-17, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.0034195013405686186, "alfven_n": 0.009023107925440378, "fast": 0.8686637724488628 }, "right": { "slow": 0.004208356306394351, "alfven_n": 0.011251341810428315, "fast": 0.6951286102525269 } }, "front_relative_normal_velocity": { "left": -0.6415706038208153, "right": -0.9975640502598242 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.554878051330473, "pressure_ratio": 2.4926787374307855, "entropy_over_cv": 0.17769606542840155, "tangential_field_ratio": 1.5549878271904753 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.0, "reference_global_state": { "rho": "1.55999999999999985163484508659523960798288248572455028384726922324901003634904914880784301", "p": "0.102094867397826711600962155469156982968501619921040585108040740505159305505016578119147866", "u": [ "-0.641025641025641086606325983483224236692158025059558580018431779045251678769630272641841806", "-0.0203081558579378307300780023639536378481354426228758558857113591580030112557139862522328293", "0" ], "B": [ "0.0561881856189624500000000000000000000000000000000000000000000000000000000000000000000000000", "1.00366496701056794405751091592429512407082944759545601036732719011686840764408621366307769", "0" ] }, "reference_iterations": 6, "reference_residuals": [ "3.909E-87", "-3.8E-88", "-1.178E-88", "2.424E-87", "2.91E-87", "0E-91" ], "reference_state_error": "4.78430838717898811801320168842878452639485143355828089439804693227861868828119102731087997E-67", "characteristic_matrix": { "upstream": { "matrix_eigenvalues": [ -1.6948233071770147, -1.0561881856189625, -1.0210253860370384, -1.0000000000000062, -0.9789746139629569, -0.943811814381038, -0.30517669282298465 ], "formula_eigenvalues": [ -1.694823307177015, -1.0561881856189625, -1.021025386037041, -1.0, -0.978974613962959, -0.9438118143810376, -0.3051766928229851 ], "max_absolute_error": 6.217248937900877e-15, "jacobian": [ [ 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], [ -0.6666666666666666, -1.3333333333333333, 0.0, 0.0, 0.6666666666666667, 0.21407796680733449, 0.0 ], [ 0.0, 0.0, -1.0, 0.0, 0.0, -0.05618818561896245, 0.0 ], [ 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, -0.05618818561896245 ], [ 0.6805310495179265, 0.3471977161845932, -0.03608595760770178, 0.0, -1.6666666666666667, -0.21407796680733449, 0.0 ], [ 0.6422339004220036, 0.6422339004220036, -0.05618818561896245, 0.0, 0.0, -1.0, 0.0 ], [ 0.0, 0.0, 0.0, -0.05618818561896245, 0.0, 0.0, -1.0 ] ] }, "downstream": { "matrix_eigenvalues": [ -1.5108190912231358, -0.6860121931697507, -0.6581073220047025, -0.6410256410256422, -0.6239439600465811, -0.5960390888815311, 0.22876780917185224 ], "formula_eigenvalues": [ -1.5108190912231345, -0.6860121931697511, -0.6581073220047022, -0.6410256410256411, -0.6239439600465799, -0.596039088881531, 0.22876780917185235 ], "max_absolute_error": 1.3322676295501878e-15, "jacobian": [ [ 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], [ -0.2738051079034393, -0.8547008547008548, 0.013538770571958555, 0.0, 0.6666666666666667, 0.33455498900352254, 0.0 ], [ -0.013018048626883228, -0.02030815585793783, -0.6410256410256411, -0.0, -0.0, -0.05618818561896245, -0.0 ], [ 0.0, 0.0, 0.0, -0.6410256410256411, 0.0, 0.0, -0.05618818561896245 ], [ 0.5620228322451061, 0.7410670616621011, -0.04482877181897319, 0.0, -1.0683760683760686, -0.21331724785338474, 0.0 ], [ 0.4116883977064127, 0.6433749788529283, -0.036018067704463114, 0.0, 0.0, -0.6410256410256411, 0.0 ], [ 0.0, 0.0, 0.0, -0.036018067704463114, 0.0, 0.0, -0.6410256410256411 ] ] } }, "rotation_state_error": "1E-90", "rotation_flux_residuals": [ "0E-89", "-9.84069007044813275294040414504395052129413512656366167777105270536929169253329641727307803E-90", "1E-90", "0E-180", "-1E-90", "0E-181", "-2.44472176952271555555107043410610778492391897003132426061389778086390958548403362213422952E-67", "-1E-90" ], "boost_state_error": "0", "moving_front_flux_residuals": [ "0E-89", "0E-90", "0E-90", "0E-179", "-2E-90", "0E-179", "-2.47861632810018838288749E-67", "0E-89" ], "rotation_diagnosis": { "case_id": "rotation", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.010154077928968915, 0.0 ], "rh_scaled_inf": 4.3783588229215367e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 4.3783588229215367e-16 }, "characteristics": { "left": { "slow": 0.017081680979061195, "alfven_n": 0.04498655214411002, "fast": 0.8697934501974935 }, "right": { "slow": 0.02102538603704097, "alfven_n": 0.05618818561896245, "fast": 0.6948233071770148 } }, "front_relative_normal_velocity": { "left": -0.6410256410256411, "right": -1.0 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599999999999998, "pressure_ratio": 2.517131839196911, "entropy_over_cv": 0.18197705884385496, "tangential_field_ratio": 1.5627717041269118 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "boost_diagnosis": { "case_id": "boost", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.37, "evaluation_boost": [ 0.37, -0.2201540779289689, 0.0 ], "rh_scaled_inf": 4.3783588229215367e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 4.3783588229215367e-16 }, "characteristics": { "left": { "slow": 0.017081680979061195, "alfven_n": 0.04498655214411002, "fast": 0.8697934501974935 }, "right": { "slow": 0.02102538603704097, "alfven_n": 0.05618818561896245, "fast": 0.6948233071770148 } }, "front_relative_normal_velocity": { "left": -0.6410256410256411, "right": -1.0 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599999999999998, "pressure_ratio": 2.517131839196911, "entropy_over_cv": 0.18197705884385496, "tangential_field_ratio": 1.5627717041269118 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 4.0, "reference_global_state": { "rho": "1.55821447702299972446479056310832331355787950590556964668794966167383768159379048285972789", "p": "0.101834354285681130727752695588898563620809228160442656590547102156795343603880514299096459", "u": [ "-0.640956134656921265031145596655350252063000945666980209200521217014387571927085146012238457", "-0.0114983542529504531221556510725481140305218945050908804787913819628435205668844016699421325", "0" ], "B": [ "0.0309924633099337921414489394062749481360803583314656288369176720577434629093978769170078398", "1.00254951626021366950238391639156570346520667220959932763808549821000746632032299573440814", "0" ] }, "reference_iterations": 6, "reference_residuals": [ "1.1659414723471E-77", "-7.1762949151E-79", "8.56037999651E-80", "7.413836932418E-78", "8.63182781214E-78", "0E-90" ], "reference_state_error": "1.79132667886653525209842142925932378419959058493712261387132914665337063842166484536424961E-66", "characteristic_matrix": { "upstream": { "matrix_eigenvalues": [ -1.6916781739523314, -1.098415336495002, -1.0353407407580033, -0.9975640502598251, -0.9597873597616459, -0.8967127640246466, -0.30344992656731806 ], "formula_eigenvalues": [ -1.6916781739523306, -1.098415336495002, -1.0353407407580026, -0.9975640502598242, -0.9597873597616458, -0.8967127640246466, -0.303449926567318 ], "max_absolute_error": 8.881784197001252e-16, "jacobian": [ [ 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], [ -0.6618007010374518, -1.3300854003464322, -0.04650431582941687, 0.0, 0.6666666666666667, 0.2122499870747597, 0.0 ], [ 0.06958655048003272, 0.0697564737441253, -0.9975640502598243, 0.0, 0.0, -0.10085128623517765, 0.0 ], [ 0.0, 0.0, 0.0, -0.9975640502598243, 0.0, 0.0, -0.10085128623517765 ], [ 0.6763560809302788, 0.3434278235385978, -0.017826018946312926, 0.0, -1.6626067504330406, -0.21876798687421803, 0.0 ], [ 0.6422339004220037, 0.6367499612242794, -0.10085128623517765, 0.0, 0.0, -0.9975640502598243, 0.0 ], [ 0.0, 0.0, 0.0, -0.10085128623517765, 0.0, 0.0, -0.9975640502598243 ] ] }, "downstream": { "matrix_eigenvalues": [ -1.5083165748503455, -0.7209887828114894, -0.6709115719505098, -0.6401968823737868, -0.6094821927970624, -0.5594049819360838, 0.22792281010277526 ], "formula_eigenvalues": [ -1.5083165748503475, -0.7209887828114887, -0.6709115719505101, -0.6401968823737862, -0.6094821927970624, -0.5594049819360838, 0.22792281010277504 ], "max_absolute_error": 1.9984014443252818e-15, "jacobian": [ [ 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], [ -0.27286638863282625, -0.8535958431650482, -0.022160329958957364, 0.0, 0.6666666666666667, 0.3326484770244736, 0.0 ], [ 0.021280461228148372, 0.03324049493843604, -0.6401968823737862, 0.0, 0.0, -0.10085128623517765, 0.0 ], [ 0.0, 0.0, 0.0, -0.6401968823737862, 0.0, 0.0, -0.10085128623517765 ], [ 0.5597595674356942, 0.7347526797667282, -0.050402388737505285, 0.0, -1.0669948039563104, -0.21631286458709126, 0.0 ], [ 0.412160142196217, 0.6404416373925726, -0.06472233939698474, 0.0, 0.0, -0.6401968823737862, 0.0 ], [ 0.0, 0.0, 0.0, -0.06472233939698474, 0.0, 0.0, -0.6401968823737862 ] ] } }, "rotation_state_error": "3E-90", "rotation_flux_residuals": [ "-2E-90", "9.81747453103826251428646697026239302340640105961675426407323991693309031885549893387847548E-90", "2E-90", "0E-181", "0E-90", "0E-181", "9.17711496942211151408090995415769611266078100343871032753431481008898174861562265937429119E-67", "-1E-90" ], "boost_state_error": "1E-90", "moving_front_flux_residuals": [ "-2E-90", "2E-90", "1E-90", "0E-180", "0E-90", "0E-180", "9.25858417449719544350430E-67", "0E-90" ], "rotation_diagnosis": { "case_id": "rotation", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.05149848434128067, 0.0 ], "rh_scaled_inf": 2.2131215794860735e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.2131215794860735e-16 }, "characteristics": { "left": { "slow": 0.03071468957672387, "alfven_n": 0.08079190043770244, "fast": 0.8681196924765614 }, "right": { "slow": 0.03777669049817849, "alfven_n": 0.10085128623517767, "fast": 0.6941141236925062 } }, "front_relative_normal_velocity": { "left": -0.6401968823737862, "right": -0.9975640502598242 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5582144770229998, "pressure_ratio": 2.5107089320927303, "entropy_over_cv": 0.1813308234379314, "tangential_field_ratio": 1.567248514871789 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "boost_diagnosis": { "case_id": "boost", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.35444983910986866, "evaluation_boost": [ 0.35444983910986866, -0.18379986149860877, 0.0 ], "rh_scaled_inf": 2.2131215794860735e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.2131215794860735e-16 }, "characteristics": { "left": { "slow": 0.03071468957672387, "alfven_n": 0.08079190043770244, "fast": 0.8681196924765614 }, "right": { "slow": 0.03777669049817849, "alfven_n": 0.10085128623517767, "fast": 0.6941141236925062 } }, "front_relative_normal_velocity": { "left": -0.6401968823737862, "right": -0.9975640502598242 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5582144770229998, "pressure_ratio": 2.5107089320927303, "entropy_over_cv": 0.1813308234379314, "tangential_field_ratio": 1.567248514871789 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } } ], "points": [ { "phi_degrees": -4.0, "theta_Bn_degrees": 89.0, "compression": 1.554878051330473, "u2x_km_s": -387.0931165171392, "u2y_km_s": -17.31473486570809, "speed2_km_s": 387.48016839371445, "signed_deflection_degrees": 2.5611418744505925, "p2_over_p1": 2.4926787374307855, "B2_over_B1": 1.5548489453909184, "entropy_over_cv": 0.17769606542840166, "upstream_fast_Mach": 1.4350783949137533, "downstream_fast_Mach": 0.7385718435248592, "downstream_alfven_margin": 0.632547495895375, "state_global_normalized": { "rho": "1.55487805133047286895916763245468287035510767769419396856491566212445891034995701320663511", "p": "0.101103049590192654402247631334078734376206135334246340824820283583892481951487001410278838", "u": [ "-0.645155194195232053691856812167116656912641826495044466809771285555996116590576829171674441", "-0.0288578914428468176168770238179983658844192722151043737799909411968222069939072871128656715", "-0E-91" ], "B": [ "0.0811427978666834796659319888416390700326212424300498691473595309469666114085205642237460072", "0.999101481742317926790744502167751340458665150455749795129909077907829464154055603629122620", "0E-91" ] }, "root_record": { "r": "1.55487805133047286895916763245468287035510767769419396856491566212445891034995701320663511", "b": "0.0407583286261993293450062640059285114452396814918781484749496743528741521715304825277677253", "h": "0.000127211700296368408331121637981023380422594722007953375509236393652110531877977952767858245", "A": "0.417526572312030146433399373331796654345940388502576227810505894913668549828969463794681899", "denominator": "0.999802201319336746551314018761612555564450560332826757773697529563033402231597602609562785", "polynomial_residual": "-8.91659611083598235622135E-66", "bracket_initial_signs": [ "1.44947315317554997572595550239136012699279534390068517635770359436968349276948915769274331", "-2.04903203463373723853270988469178310276802246684509929622197250000422364359682578572178140" ], "bracket_derivative_max": "-5.58066166753348508207107596629354379494093114712324900316641730908624207872151082554163964", "iterations": 216 }, "flux_residuals": [ "-4E-90", "8.03408001050129357436819573593770011896027347768429165190071099281510582812342021702982115E-90", "1E-91", "0E-182", "-7E-90", "0E-182", "5.01115643509179579080755859926449320293350105112817491878806159574308007733210758389648116E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-4", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.07177391008928782, 0.0 ], "rh_scaled_inf": 4.3882011991206896e-16, "rh_components": { "mass": 2.220446049250313e-16, "normal_momentum": -3.571634227666843e-16, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 4.3882011991206896e-16 }, "characteristics": { "left": { "slow": 0.0034195013405686186, "alfven_n": 0.009023107925440378, "fast": 0.8686637724488628 }, "right": { "slow": 0.004208356306394351, "alfven_n": 0.011251341810428315, "fast": 0.6951286102525269 } }, "front_relative_normal_velocity": { "left": -0.6415706038208154, "right": -0.9975640502598242 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.554878051330473, "pressure_ratio": 2.4926787374307855, "entropy_over_cv": 0.17769606542840155, "tangential_field_ratio": 1.5549878271904753 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.975, "theta_Bn_degrees": 88.975, "compression": 1.5549314963696181, "u2x_km_s": -387.07010794275203, "u2y_km_s": -17.283742601487443, "speed2_km_s": 387.4557990547156, "signed_deflection_degrees": 2.556715450638875, "p2_over_p1": 2.4929257647820156, "B2_over_B1": 1.554900912632828, "entropy_over_cv": 0.17773787516862824, "upstream_fast_Mach": 1.4351233757918045, "downstream_fast_Mach": 0.7385555090319533, "downstream_alfven_margin": 0.632319562716133, "state_global_normalized": { "rho": "1.55493149636961821598746439844293391332426214793371050777303786764989753581294500844063729", "p": "0.101113069019558549649975129716311693202646127750885268925033324024349936336137152264974461", "u": [ "-0.645116846571253298932489100192539500164630150470899363694290669924324192140598202095626767", "-0.0288062376691457362647645379881397887994074016436324460052610665890828664884052595771158338", "-0E-91" ], "B": [ "0.0809895282155287859075452869089658702562787405457779894454204899810875082730282573699257232", "0.999147530321547027091985161895084104939398008473759548885643196261196427429531057951015623", "0E-91" ] }, "root_record": { "r": "1.55493149636961821598746439844293391332426214793371050777303786764989753581294500844063729", "b": "0.0407558493177717753296538222251461278801222798796686183923577955206338793387975278056755677", "h": "0.000133642975656257617543595039137488174961559760452388468898167628964675790347808315791080032", "A": "0.417494735369131771012625213355772426319515690873654460898845458484520126625885487246047337", "denominator": "0.999792194327883526882750219845836620589939533018478587670605597222135152013165594747310781", "polynomial_residual": "-3.9420183765663414010232E-67", "bracket_initial_signs": [ "1.44970916274318184895006938934242585408865661046850315143365865334708013260814594412577359", "-2.04861061721521774438780207260259565531755313503564437219776034669957552136797722748049884" ], "bracket_derivative_max": "-5.58038872179987173924328662615027272525365512348684246546637183708885722524798487910705439", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "2E-91", "0E-182", "-2E-90", "0E-182", "2.21570203456492431622956526990510804564523808167737131664758973189878579789815430477706837E-68", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.975", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.07138920565169565, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7857393736238017e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": -0.0, "energy": -2.1939804330747907e-16 }, "characteristics": { "left": { "slow": 0.0035049694061084153, "alfven_n": 0.009248502906355106, "fast": 0.868679547815452 }, "right": { "slow": 0.004313558128692508, "alfven_n": 0.0115325957138469, "fast": 0.6951279653924747 } }, "front_relative_normal_velocity": { "left": -0.6415680656224881, "right": -0.997594392301337 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5549314963696181, "pressure_ratio": 2.4929257647820156, "entropy_over_cv": 0.17773787516862827, "tangential_field_ratio": 1.5550468382508968 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.95, "theta_Bn_degrees": 88.95, "compression": 1.5549846712855675, "u2x_km_s": -387.04719376647876, "u2y_km_s": -17.25273327303553, "speed2_km_s": 387.4315255730962, "signed_deflection_degrees": 2.5522853272883923, "p2_over_p1": 2.49317162372696, "B2_over_B1": 1.5549525729664726, "entropy_over_cv": 0.17777949794024808, "upstream_fast_Mach": 1.4351681163917533, "downstream_fast_Mach": 0.7385392561914262, "downstream_alfven_margin": 0.632091627701334, "state_global_normalized": { "rho": "1.55498467128556742120904926928171783001694586404379669366391904391247151027261022290371957", "p": "0.101123041058365503648892087008385668054468752433967804991690411087089390491738502316738474", "u": [ "-0.645078656277464668852459599295118685456168508489903852751285359979031877031541276230917511", "-0.0287545554550592202920867322749672811957518788007244141946743855913048716673829294831504407", "-0E-91" ], "B": [ "0.0808362125325483249924667525679686457494108386644229605441230865738629361607600378129983165", "0.999193359609168124924049875686591245936062942329734781840587647319793927300934162941585282", "0E-91" ] }, "root_record": { "r": "1.55498467128556742120904926928171783001694586404379669366391904391247151027261022290371957", "b": "0.0407533857528252847710221555280443012219636095522759756838378384392732108974359428536285245", "h": "0.000140232431424172179037666078201827828332401368870533036016124994219638520500576052437695042", "A": "0.417462901570508234014000753388322623774123772605459489755374271527741915270848213722590559", "denominator": "0.999781940718718307748920086023232912119713836915707493173058844746429939791042202969318759", "polynomial_residual": "1.44134325343358739351891E-66", "bracket_initial_signs": [ "1.44994353786882378566378915935219207831366567084459812536414934632226406126181297684787442", "-2.04819060483367157861231023591241650288104231200191815734597016708785881469515666619501090" ], "bracket_derivative_max": "-5.58011580888034015974149173786422154998798842842006122597573183002423593800970108764620272", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.03379657794427811844979427122923272839299833954824237801491754336340533511119788259099831E-90", "2E-91", "0E-182", "1E-90", "0E-182", "-8.10240527885089829735350681324238377242729912033192233105188332934108320103811028922638273E-68", "-4E-91" ], "diagnosis": { "case_id": "R95_phi_-3.95", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.07100449398478956, 0.0 ], "rh_scaled_inf": 2.1938613986408622e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 1.7856624088337213e-16, "t1_momentum": -1.0408340855860843e-17, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1938613986408622e-16 }, "characteristics": { "left": { "slow": 0.0035904365173571326, "alfven_n": 0.009473889205133847, "fast": 0.8686952135963057 }, "right": { "slow": 0.004418759426129263, "alfven_n": 0.01181384742162205, "fast": 0.6951273046137268 } }, "front_relative_normal_velocity": { "left": -0.6415655169064678, "right": -0.997624544414959 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5549846712855675, "pressure_ratio": 2.49317162372696, "entropy_over_cv": 0.17777949794024805, "tangential_field_ratio": 1.555105717239304 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.925, "theta_Bn_degrees": 88.925, "compression": 1.5550375760942654, "u2x_km_s": -387.0243739922542, "u2y_km_s": -17.221706948598555, "speed2_km_s": 387.4073479611863, "signed_deflection_degrees": 2.547851517023282, "p2_over_p1": 2.4934163138989063, "B2_over_B1": 1.555003926395729, "entropy_over_cv": 0.17782093368983734, "upstream_fast_Mach": 1.4352126167071595, "downstream_fast_Mach": 0.738523084981877, "downstream_alfven_margin": 0.631863690824118, "state_global_normalized": { "rho": "1.55503757609426539956021827593703815447962198332322347081597888250053617751829228609710481", "p": "0.101132965691739629967276222510449697694070903490206259392225372423642516083025789922504159", "u": [ "-0.645040623320423654660540260847771872426832858666620551237137572252158466328480135436990344", "-0.0287028449143309239740494539792431832970929308926909770971495168696591051462764390890594048", "-0E-91" ], "B": [ "0.0806828510475284726869746051349430164212774374640480723960549893485089706202179352340728140", "0.999238969578334711444549420481251194406845731974834569916182805816587498918950916252766172", "0E-91" ] }, "root_record": { "r": "1.55503757609426539956021827593703815447962198332322347081597888250053617751829228609710481", "b": "0.0407509379275806264178742133265477211910929115946607353731322428117587463979150180071672625", "h": "0.000146980041390031751436655048883714818686928779063949770991433644607049032451853396380122389", "A": "0.417431070903643537307613339521897533944472157275264908344799418444969895479177459212543214", "denominator": "0.999771440512702610222353900652179183394350885417950338011255401047361613349108038816587766", "polynomial_residual": "1.607645134817187907280706E-65", "bracket_initial_signs": [ "1.45017627882125824752491471587791085889320334825234573608066596765850075520895419724015916", "-2.04777199729069801623530117418128278626591487272696170236487550572845497919968506800966830" ], "bracket_derivative_max": "-5.57984292881867583362242520810523010912348793587228567483487195758686200215461262419250693", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "2E-91", "0E-182", "-1E-90", "0E-182", "-9.03837901352480813003953158686580879436711195610009446850091393948503440290081372283656635E-67", "3E-91" ], "diagnosis": { "case_id": "R95_phi_-3.925", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.07061977512508204, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -1.214306433183765e-17, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.0036759026738489103, "alfven_n": 0.009699266838117067, "fast": 0.868710769789923 }, "right": { "slow": 0.004523960185900701, "alfven_n": 0.012095096880207412, "fast": 0.6951266279165599 } }, "front_relative_normal_velocity": { "left": -0.6415629576622351, "right": -0.9976545065949499 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5550375760942654, "pressure_ratio": 2.4934163138989063, "entropy_over_cv": 0.17782093368983742, "tangential_field_ratio": 1.5551644641995686 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.9, "theta_Bn_degrees": 88.9, "compression": 1.5550902108115072, "u2x_km_s": -387.0016486240237, "u2y_km_s": -17.19066369643407, "speed2_km_s": 387.38326623130774, "signed_deflection_degrees": 2.5434140324783616, "p2_over_p1": 2.493659834932515, "B2_over_B1": 1.5550549729244791, "entropy_over_cv": 0.177862182364185, "upstream_fast_Mach": 1.435256876731588, "downstream_fast_Mach": 0.7385069953820375, "downstream_alfven_margin": 0.6316357520577146, "state_global_normalized": { "rho": "1.55509021081150712161426710700991876111009188057645347831417273347305517989932777462972869", "p": "0.101142842904862811784060985628706660976613442206386961468643756679707624515045049602920657", "u": [ "-0.645002747706706189279205496718974543359121402408356086806463196377654246912407093183021420", "-0.0286511061607234481669929787473535438028110415293051853404378988184902467088773517413614253", "-0E-91" ], "B": [ "0.0805294439902593963268988287503355564695588515217739616539795578074012779657012513608127437", "0.999284360202317266478021090969540637693060775881173838980070466572692160486823646746253939", "0E-91" ] }, "root_record": { "r": "1.55509021081150712161426710700991876111009188057645347831417273347305517989932777462972869", "b": "0.0407485058382830530942862251478214288900575230020371654010458652390653018097230699731585051", "h": "0.000153885779589815732507711917493325092692815585891233061945334743592403696887171054365506783", "A": "0.417399243356026513260765715943306995608855996245111979406572723563748067438990674510194795", "denominator": "0.999760693730576780332620979548959360886587072472455076569631584415612881153248609417269148", "polynomial_residual": "1.162706992531159857359062E-65", "bracket_initial_signs": [ "1.45040738586852156642334886669387703797270278520206417058655082567409067041953124434130525", "-2.04735479438704728650311109002048545624071017954989302973334882065850310321312496703489602" ], "bracket_derivative_max": "-5.57957008165657793929429391276389092802857500184160312014322088852931587200032782679329404", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "1E-91", "0E-182", "-5E-90", "0E-182", "-6.53769179202086365253523187529304914112348687156928348328334141181397028716459644182518575E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_-3.9", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.07023504910910364, 0.0 ], "rh_scaled_inf": 1.7855108049494552e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7855108049494552e-16, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.0037613678751059355, "alfven_n": 0.00992463582163199, "fast": 0.8687262163948232 }, "right": { "slow": 0.004629160395202735, "alfven_n": 0.012376344036057058, "fast": 0.6951259353012564 } }, "front_relative_normal_velocity": { "left": -0.6415603878793465, "right": -0.9976842788356053 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5550902108115072, "pressure_ratio": 2.493659834932515, "entropy_over_cv": 0.17786218236418483, "tangential_field_ratio": 1.5552230791752821 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.875, "theta_Bn_degrees": 88.875, "compression": 1.5551425754529375, "u2x_km_s": -386.9790176657439, "u2y_km_s": -17.159603584810956, "speed2_km_s": 387.35928039577425, "signed_deflection_degrees": 2.5389728862990912, "p2_over_p1": 2.4939021864638247, "B2_over_B1": 1.5551057125566121, "entropy_over_cv": 0.17790324391029283, "upstream_fast_Mach": 1.4353008964586096, "downstream_fast_Mach": 0.7384909873707721, "downstream_alfven_margin": 0.6314078113754416, "state_global_normalized": { "rho": "1.55514257545293757343787521412615204602561667161120307431498660046885472637790168498031653", "p": "0.101152672682972721228345991002048558315384822439731415317492224492251932528833067984022986", "u": [ "-0.644965029442906571952537244843709303015364980738756187525541454000003484912019863685309844", "-0.0285993393080182582378428243480420189250157828804515692000683691924754870869512653399437661", "-0E-91" ], "B": [ "0.0803759915905350790930383528446081514298048637898366990506647491482889070133794298109631467", "0.999329531454503276370323089819384893938450304572724009260175340219081418118538117918666535", "0E-91" ] }, "root_record": { "r": "1.55514257545293757343787521412615204602561667161120307431498660046885472637790168498031653", "b": "0.0407460894812022894304389559751844267363451351114475259692246425139191154472704836505564746", "h": "0.000160949620305457495392181574542127855845793077394499574004295021684918924462942363396639829", "A": "0.417367418915150804778203214172680600284812739286033882098030067150246280419777644152398354", "denominator": "0.999749700392959998413595850825226632364660979450962493071080992096071701258894040602860096", "polynomial_residual": "1.459184902269423360964519E-65", "bracket_initial_signs": [ "1.45063685927790372569082312566919929365328919023461870413352032833076173487320735482317234", "-2.04693899592262191032732061963999035195586713902068378702502263094204628266670545783315335" ], "bracket_derivative_max": "-5.57929726743366096364291221580909017523237795814892199986530096341743066037445842241486440", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-1E-91", "0E-182", "-4E-90", "0E-182", "-8.20574978973884241131901226670546753956217120590890327753401501862025422042894816405907888E-67", "-4E-91" ], "diagnosis": { "case_id": "R95_phi_-3.875", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06985031597340274, 0.0 ], "rh_scaled_inf": 2.1935110854208846e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7854361655774874e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1935110854208846e-16 }, "characteristics": { "left": { "slow": 0.0038468321206385167, "alfven_n": 0.010149996171992701, "fast": 0.8687415534095463 }, "right": { "slow": 0.004734360041231102, "alfven_n": 0.0126575888356255, "fast": 0.6951252267681062 } }, "front_relative_normal_velocity": { "left": -0.6415578075474343, "right": -0.9977138611312569 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5551425754529375, "pressure_ratio": 2.4939021864638247, "entropy_over_cv": 0.177903243910293, "tangential_field_ratio": 1.555281562209755 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.85, "theta_Bn_degrees": 88.85000000000001, "compression": 1.5551946700340518, "u2x_km_s": -386.95648112138247, "u2y_km_s": -17.128526682009362, "speed2_km_s": 387.3353904668912, "signed_deflection_degrees": 2.5345280911415426, "p2_over_p1": 2.4941433681302474, "B2_over_B1": 1.5551561452960234, "entropy_over_cv": 0.1779441182753752, "upstream_fast_Mach": 1.435344675881799, "downstream_fast_Mach": 0.7384750609270783, "downstream_alfven_margin": 0.6311798687507058, "state_global_normalized": { "rho": "1.55519467003405171660758524219077921733420948448175187595492326792708131318966879149528250", "p": "0.101162455011362838672687895444275790272213723679026031946081690130495008980131561958500302", "u": [ "-0.644927468535637393360187061852337434424557341503384784170644676617722683115652658704647511", "-0.0285475444700156019930116159109452278527444562972714462745365743139533797832480633467625744", "-0E-91" ], "B": [ "0.0802224940781533442061644614411993524681004741051490725920258461676544959739608977584764252", "0.999374483308397251658077929530604595800804391838629739857628975208474036727994819771174662", "0E-91" ] }, "root_record": { "r": "1.55519467003405171660758524219077921733420948448175187595492326792708131318966879149528250", "b": "0.0407436888526325196748455714202551387888264812102420597324814584129905176935380861645006382", "h": "0.000168171538064739443490174044860402998054992168107975781982522971748298121767223955378141186", "A": "0.417335597568514845358174053177721025604115313417167164774740721632355106113555477067375169", "denominator": "0.999738460520350288572989672886232374347156894179683597088469891448888225748428961712396885", "polynomial_residual": "-4.09973523678442095370493E-66", "bracket_initial_signs": [ "1.45086469931594814620586648518792369558507967387110470342778006179069710513403014980149352", "-2.04652460169647802357903484841844758272936795358872112826192455726048706547286324148996614" ], "bracket_derivative_max": "-5.57902448618745630732362571825416417852211286929241626321249120221546695988616040335164046", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.03324812474095220344493864999565096815644127270760238186428262706246804501915314775039801E-90", "1E-91", "0E-182", "-2E-90", "0E-182", "2.30577816622995138408697110350129504167047927149776622565289473281918659237309676754355747E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-3.85", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06946557575454551, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.0039322954099451435, "alfven_n": 0.01037534790550025, "fast": 0.8687567808326534 }, "right": { "slow": 0.004839559111181352, "alfven_n": 0.012938831225367698, "fast": 0.6951245023174053 } }, "front_relative_normal_velocity": { "left": -0.6415552166562061, "right": -0.9977432534762729 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5551946700340518, "pressure_ratio": 2.4941433681302474, "entropy_over_cv": 0.17794411827537515, "tangential_field_ratio": 1.5553399133460168 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.825, "theta_Bn_degrees": 88.825, "compression": 1.5552464945701945, "u2x_km_s": -386.93403899491767, "u2y_km_s": -17.097433056320657, "speed2_km_s": 387.3115964569559, "signed_deflection_degrees": 2.5300796596723623, "p2_over_p1": 2.4943833795705737, "B2_over_B1": 1.5552062711466146, "entropy_over_cv": 0.1779848054068588, "upstream_fast_Mach": 1.435388214994737, "downstream_fast_Mach": 0.7384592160300855, "downstream_alfven_margin": 0.6309519241570025, "state_global_normalized": { "rho": "1.55524649457019444838606765920928074257030461791589059348525884956417659068984300137077088", "p": "0.101172189875382471980218828635280602116127714917567350766499473949316971785317836400266201", "u": [ "-0.644890064991529461237050359343594113567185621958633815053003427871436815343120512298236862", "-0.0284957217605344276065631322031249392140687113903550506113469134778359016090300029747798129", "-0E-91" ], "B": [ "0.0800689516829158790423973944174418999785771866095094690565503845933064179359740991914093620", "0.999419215737620744553148197844570598215293112014858150831042855852069606446364526054142875", "0E-91" ] }, "root_record": { "r": "1.55524649457019444838606765920928074257030461791589059348525884956417659068984300137077088", "b": "0.0407413039488923755879476014005676623566817582928347806732892086685404813200691927834275116", "h": "0.000175551507641188883365832595549285185052063409048289722773272817679846510467118163668926658", "A": "0.417303779303621839164254216505762801162542247018241925894157997128325563127042011965028353", "denominator": "0.999726974133124528284090703699340842958805649707214194357543246245489991089039581286053720", "polynomial_residual": "7.09009817927587665128849E-66", "bracket_initial_signs": [ "1.45109090624845147738550371194087142546077752599720403827885979586915739200569952244944037", "-2.04611161150682668624798650718962714907855127917893282063990151462324003427461163531235955" ], "bracket_derivative_max": "-5.57875173795341387523590684869820213555219408541973995487903189437855389160479347234199797", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.03311484648993104571334727559926612191009060463493147954509971472309765835212271312654080E-90", "0E-91", "0E-182", "-4E-90", "0E-182", "-3.98811538151221794379940149841719945255465439741224619635439910107472760970382806882456786E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-3.825", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06908082848911576, 0.0 ], "rh_scaled_inf": 1.7852892112901473e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7852892112901473e-16, "t1_momentum": -8.673617379884035e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.004017757742512559, "alfven_n": 0.010600691038442762, "fast": 0.8687718986627258 }, "right": { "slow": 0.004944757592248851, "alfven_n": 0.01322007115173907, "fast": 0.6951237619494567 } }, "front_relative_normal_velocity": { "left": -0.6415526151954453, "right": -0.9977724558650571 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5552464945701945, "pressure_ratio": 2.4943833795705737, "entropy_over_cv": 0.17798480540685868, "tangential_field_ratio": 1.5553981326268158 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.8, "theta_Bn_degrees": 88.8, "compression": 1.5552980490765607, "u2x_km_s": -386.9116912903391, "u2y_km_s": -17.06632277604738, "speed2_km_s": 387.28789837825667, "signed_deflection_degrees": 2.525627604568739, "p2_over_p1": 2.49462222042497, "B2_over_B1": 1.5552560901122945, "entropy_over_cv": 0.1780253052523825, "upstream_fast_Mach": 1.4354315137910096, "downstream_fast_Mach": 0.738443452659056, "downstream_alfven_margin": 0.6307239775679155, "state_global_normalized": { "rho": "1.55529804907656056205786268224628834013274150662169159653800196919044637991420685505686194", "p": "0.101181877260436775705639299843374515855060048340141696325733628485092635974565745131544642", "u": [ "-0.644852818817231726498311017440978289215547030153434705869114229305404257575126357770021219", "-0.0284438712934123015474499426747684042053081094035153366687008975937770812452515117356793228", "-0E-91" ], "B": [ "0.0799153646346282591697426953986295211731875657307697830600445272691354198458355367732732718", "0.999463728715912366242127637939874236943931148930117808117373329661469687257441976293711478", "0E-91" ] }, "root_record": { "r": "1.55529804907656056205786268224628834013274150662169159653800196919044637991420685505686194", "b": "0.0407389347663249244170109586550963536822896090835636331620015020065460255703795679068950188", "h": "0.000183089504053974715044495398771335434393010463038682350182362789105888127253115451256961362", "A": "0.417271964107979741112868461988632165890932704364107667718946426610726636201400306318016208", "denominator": "0.999715241251538458099658697725788162919205795244557114033406276039556881975690268603188327", "polynomial_residual": "-3.8181265647152088429554E-67", "bracket_initial_signs": [ "1.45131548034046339305524462753550188830306796926925137471128758570013899996522017691024672", "-2.04570002515103517748483900297463398673173706030503910223433854864020485840680958669682023" ], "bracket_derivative_max": "-5.57847902276490365219737869478500323905846708301823858072027449725606047212866991333595406", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.03298310200244880306755518606988599685831658192418551613130691124417825080104880836080510E-90", "0E-91", "0E-182", "2E-90", "0E-182", "2.14792703477009952355154900459580279531435117565644783260789834202410334402090445296440112E-68", "2E-91" ], "diagnosis": { "case_id": "R95_phi_-3.8", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06869607421371479, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.004103219117815821, "alfven_n": 0.010826025587095538, "fast": 0.8687869068983658 }, "right": { "slow": 0.005049955471628771, "alfven_n": 0.013501308561195505, "fast": 0.6951230056645699 } }, "front_relative_normal_velocity": { "left": -0.6415500031550111, "right": -0.99780146829205 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5552980490765607, "pressure_ratio": 2.49462222042497, "entropy_over_cv": 0.17802530525238236, "tangential_field_ratio": 1.5554562200946198 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.775, "theta_Bn_degrees": 88.775, "compression": 1.5553493335681947, "u2x_km_s": -386.8894380116467, "u2y_km_s": -17.035195909503198, "speed2_km_s": 387.2642962430735, "signed_deflection_degrees": 2.5211719385183717, "p2_over_p1": 2.4948598903349795, "B2_over_B1": 1.5553056021969776, "entropy_over_cv": 0.17806561775979726, "upstream_fast_Mach": 1.4354745722642075, "downstream_fast_Mach": 0.7384277707933845, "downstream_alfven_margin": 0.6304960289571169, "state_global_normalized": { "rho": "1.55534933356819470742429381688174544328293530070854524525625708603609144514811997458935833", "p": "0.101191517151986770250132313638640027244965931392181558319675819535427751929817934545608241", "u": [ "-0.644815730019411209869517722726569138364791317517309712382764258533022125487437449847343675", "-0.0283919931825053265056363215063473573639472180280607373487337744705652123403072869535760120", "-0E-91" ], "B": [ "0.0797617331630999723065734580713038046692140972275059450200632926537913586167611131513765724", "0.999508022217127804000830094416530329749594471827599295071261201114712996226714178451250196", "0E-91" ] }, "root_record": { "r": "1.55534933356819470742429381688174544328293530070854524525625708603609144514811997458935833", "b": "0.0407365813012976569522544355025607386763840464237530667511040839913195926330962950293821222", "h": "0.000190785502567804939077643530157405365547311052687226803100839902619182479344031986000020070", "A": "0.417240151969101236976439108579328335163592674875565573268414058030293253599503564307563879", "denominator": "0.999703261895726691487919170716075343659938628317919357405368578728717229442442518835096692", "polynomial_residual": "1.373644016303446554653301E-65", "bracket_initial_signs": [ "1.45153842185628639218900060722399871388786555358996371741308700258571489647621183592074358", "-2.04528984242562827654492462846065266158337476073916126865657139079525780774400606597318444" ], "bracket_derivative_max": "-5.57820634065321726383389745744413599302071849459632988413571598380374430892623243324332707", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.03285289115288137616438604454961967472373858222416713874986356277293885927526198119031472E-90", "-2E-91", "0E-182", "0E-90", "0E-182", "-7.72853406573351191830456681589900690865640275668247380165812396012484301857814122304261681E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_-3.775", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06831131296496133, 0.0 ], "rh_scaled_inf": 2.1930598365137778e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 1.214306433183765e-17, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1930598365137778e-16 }, "characteristics": { "left": { "slow": 0.004188679535318379, "alfven_n": 0.011051351567721161, "fast": 0.8688018055381966 }, "right": { "slow": 0.0051551527365160926, "alfven_n": 0.013782543400193371, "fast": 0.6951222334630609 } }, "front_relative_normal_velocity": { "left": -0.6415473805248381, "right": -0.9978302907517279 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5553493335681947, "pressure_ratio": 2.4948598903349795, "entropy_over_cv": 0.17806561775979712, "tangential_field_ratio": 1.555514175791616 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.75, "theta_Bn_degrees": 88.75, "compression": 1.5554003480599914, "u2x_km_s": -386.8672791628518, "u2y_km_s": -17.004052525012835, "speed2_km_s": 387.24079006367765, "signed_deflection_degrees": 2.516712674219431, "p2_over_p1": 2.4950963889435247, "B2_over_B1": 1.555354807404585, "entropy_over_cv": 0.17810574287716574, "upstream_fast_Mach": 1.4355173904079266, "downstream_fast_Mach": 0.738412170412598, "downstream_alfven_margin": 0.630268078298367, "state_global_normalized": { "rho": "1.55540034805999135145724954724644441605134886976359874827922304206821696672981749134989257", "p": "0.101201109535549360970245238561603361706623769395426044049311281285213865204512452377859182", "u": [ "-0.644778798604752929021356487538260111266962968502935077653898871025383731481291435784886478", "-0.0283400875416880593169183977423353964896877632851010699467578408520475217422884400456157975", "-0E-91" ], "B": [ "0.0796080574981444422028442253626328612421880265480371745132278625006482303724951191494396372", "0.999552096215239838123758476302940246824393457795487604656821744732590829838733504339322157", "0E-91" ] }, "root_record": { "r": "1.55540034805999135145724954724644441605134886976359874827922304206821696672981749134989257", "b": "0.0407342435502024756641435687381785670115966195058087684390602580195928506683989029471627191", "h": "0.000198639478692824979756219654969233354600746770576807513514970106953010809156567344987550099", "A": "0.417208342874503723502094333475886766493261268398600673095929843919972852468905358719663670", "denominator": "0.999691036085702724790604536897256727278731419683693477924394806696044045443616124519317788", "polynomial_residual": "-7.01791401735955775115023E-66", "bracket_initial_signs": [ "1.45175973105947560451063916610981436887443472879137199163893069585861453258944202544962060", "-2.04488106312628952965151221603499954665043937982411578403289513929152422018372768545922452" ], "bracket_derivative_max": "-5.57793369164756952270219808561179143855243759150759540773528536087235519298396537798736661", "iterations": 216 }, "flux_residuals": [ "-2E-90", "-1.60654484276341438267290184290701287777171393383187553136595297663862136015510751837702997E-89", "3E-91", "0E-182", "1E-90", "0E-182", "3.94897766754720547844298525248236672885565084908771471763984002578176532583592096909466607E-67", "3E-91" ], "diagnosis": { "case_id": "R95_phi_-3.75", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06792654477949137, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7850745889923042e-16, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 2.220446049250313e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.004274138994472128, "alfven_n": 0.0112766689965696, "fast": 0.8688165945808621 }, "right": { "slow": 0.005260349374105593, "alfven_n": 0.014063775615189521, "fast": 0.6951214453452529 } }, "front_relative_normal_velocity": { "left": -0.6415447472949366, "right": -0.9978589232386035 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5554003480599914, "pressure_ratio": 2.4950963889435247, "entropy_over_cv": 0.17810574287716563, "tangential_field_ratio": 1.5555719997597113 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.725, "theta_Bn_degrees": 88.72500000000001, "compression": 1.5554510925666947, "u2x_km_s": -386.8452147479759, "u2y_km_s": -16.972892690912058, "speed2_km_s": 387.21737985233153, "signed_deflection_degrees": 2.512249824380528, "p2_over_p1": 2.4953317158949053, "B2_over_B1": 1.5554037057390453, "entropy_over_cv": 0.1781456805527624, "upstream_fast_Mach": 1.435559968215768, "downstream_fast_Mach": 0.7383966514963558, "downstream_alfven_margin": 0.630040125565514, "state_global_normalized": { "rho": "1.55545109256669473911153193238636540106073177105544305680574232912738083730218978882760724", "p": "0.101210654396697357240785784040474811996744311333773807858562996627372918387335316137682784", "u": [ "-0.644742024579959826208786913981008654664619057381812721315487505996955440948245056431210281", "-0.0282881544848534288862537698065608944192597812390100948919565836841100936224728156341448609", "-0E-91" ], "B": [ "0.0794543378695790524448219041369406368389001982627380582312968562253975603492050984749869953", "0.999595950684338358668535489003949843920519910360095323831047176790549092449382976583822070", "0E-91" ] }, "root_record": { "r": "1.55545109256669473911153193238636540106073177105544305680574232912738083730218978882760724", "b": "0.0407319215094556829217832284778104506515755697321416345543078308948209907248833343244811617", "h": "0.000206651408184516823857587814537972983506933430879148781308868077369104810933960770799636534", "A": "0.417176536811709288545867800877211451551353189153960442199713352477061938813435618180084299", "denominator": "0.999678563841358947302990187925168749019554149107424000478454081046854091017819656647688441", "polynomial_residual": "4.81118847409602525562160E-66", "bracket_initial_signs": [ "1.45197940821283860094896200352594891879469464717867338821941979082566943429671045269111887", "-2.04447368704786250279655765303186508952448574225475918930908959688996651019023359716152087" ], "bracket_derivative_max": "-5.57766107577509995966148201694158245306772634953501373181369843863740739087035253656690582", "iterations": 216 }, "flux_residuals": [ "2E-90", "-1.60651941397446610433108535279045813147889562490892641351317714050305787358080339592572343E-89", "3E-91", "0E-182", "-1E-90", "0E-182", "-2.70758872994708187644012169551252093205944709379396161646810591593117855381308499265104360E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.725", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.067541769693958, 0.0 ], "rh_scaled_inf": 1.7850045968029783e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7850045968029783e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.0043595974947174924, "alfven_n": 0.011501977889878315, "fast": 0.8688312740250265 }, "right": { "slow": 0.005365545371591847, "alfven_n": 0.014345005152641315, "fast": 0.6951206413114751 } }, "front_relative_normal_velocity": { "left": -0.6415421034553923, "right": -0.9978873657472256 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5554510925666947, "pressure_ratio": 2.4953317158949053, "entropy_over_cv": 0.17814568055276248, "tangential_field_ratio": 1.555629692040531 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.7, "theta_Bn_degrees": 88.7, "compression": 1.5555015671028989, "u2x_km_s": -386.82324477105163, "u2y_km_s": -16.941716475547594, "speed2_km_s": 387.19406562128864, "signed_deflection_degrees": 2.507783401720681, "p2_over_p1": 2.4955658708348003, "B2_over_B1": 1.555452297204292, "entropy_over_cv": 0.17818543073507298, "upstream_fast_Mach": 1.4356023056813385, "downstream_fast_Mach": 0.7383812140244495, "downstream_alfven_margin": 0.6298121707324945, "state_global_normalized": { "rho": "1.55550156710289885429547308233084883002946320767214956325530663264082240401535367731423702", "p": "0.101220151721059491471778252501505145385771586380859707648168305798093790156883965451025849", "u": [ "-0.644705407951752696414212868875347999026406736691979939954699004398020078261956732125765507", "-0.0282361941259126541094130782668282437036717327503381777739588232807888555176584120150665926", "-0E-91" ], "B": [ "0.0793005745072251701841186718015656306086332291630292431436894089962664392604051691993222205", "0.999639585598630382015277488237252985177330824244613655862027131345316556181553143084290973", "0E-91" ] }, "root_record": { "r": "1.55550156710289885429547308233084883002946320767214956325530663264082240401535367731423702", "b": "0.0407296151754979692923427520983062977140581675729540482665522887189720883049774871202463531", "h": "0.000214821267043598974316085316261232123100081802637481467059830443090172521311128811949109158", "A": "0.417144733768244691222321531498942681480327638245742547354657870164626369412169526168766077", "denominator": "0.999665845182466651475874648332833671656177543334258599795235761503703740354289507263710175", "polynomial_residual": "-9.9216294596379273553330E-67", "bracket_initial_signs": [ "1.45219745357843520893796624394878179400909247437291474091155180793105086961338784990205508", "-2.04406771398435202049675005344543510985653343798817544922560724626273415457898957678413704" ], "bracket_derivative_max": "-5.57738849306087434051020050847758384870920340826297355791057030363711028888092545399405642", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "0E-91", "0E-182", "-1E-90", "0E-182", "5.58427771694732942229591768453995143846352263482430974402174950733574513226648269827371283E-68", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-3.7", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06715698774503145, 0.0 ], "rh_scaled_inf": 2.1927332689493412e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.784935378687144e-16, "t1_momentum": -5.204170427930421e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1927332689493412e-16 }, "characteristics": { "left": { "slow": 0.004445055035483469, "alfven_n": 0.011727278263872362, "fast": 0.8688458438693758 }, "right": { "slow": 0.0054707407161692255, "alfven_n": 0.014626231959006617, "fast": 0.6951198213620637 } }, "front_relative_normal_velocity": { "left": -0.641539448996367, "right": -0.997915618272179 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5555015671028989, "pressure_ratio": 2.4955658708348003, "entropy_over_cv": 0.17818543073507298, "tangential_field_ratio": 1.5556872526754224 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.675, "theta_Bn_degrees": 88.67500000000001, "compression": 1.5555517716830474, "u2x_km_s": -386.80136923612207, "u2y_km_s": -16.910523947277095, "speed2_km_s": 387.1708473827934, "signed_deflection_degrees": 2.503313418969278, "p2_over_p1": 2.495798853410267, "B2_over_B1": 1.5555005818042662, "entropy_over_cv": 0.17822499337279468, "upstream_fast_Mach": 1.4356444027982493, "downstream_fast_Mach": 0.7383658579768028, "downstream_alfven_margin": 0.6295842137733327, "state_global_normalized": { "rho": "1.55555177168304738099952270383597251280489229766882879646021613043135020436004912401008206", "p": "0.101229601494320438079526045588481640419427654998957969717108404081578708290168673728494579", "u": [ "-0.644668948726870115994361335282434252604661482225064611387712761974805739501540159490395433", "-0.0281842065787951617927662926569158830170133730865814721404965601514132118975156073181127155", "-0E-91" ], "B": [ "0.0791467676409081697918114704859101393948415784573824896936993113042499629052417602087947889", "0.999683000932440067240892410571539616927567326942248906812097314342948934104230465012195365", "0E-91" ] }, "root_record": { "r": "1.55555177168304738099952270383597251280489229766882879646021613043135020436004912401008206", "b": "0.0407273245447944019214479091934260080915496603292584332690491630320404022278974240861112762", "h": "0.000223149031515927218211792892879598340752493803175148786032309918017233597536788207193730362", "A": "0.417112933731641342069524009355322208896044330141111807623684047148219944273598686580191349", "denominator": "0.999652880128676043239454008074386495873385096649616714973254996131775487667488394631185556", "polynomial_residual": "-1.437251639455930532672136E-65", "bracket_initial_signs": [ "1.45241386741757733255432284788149416401821235498229629884893319823471052742208273976504618", "-2.04366314372892539052252598611737004935415050181462859643841418107302755674485513118860115" ], "bracket_derivative_max": "-5.57711594352788616790416178904673562235464761749544194478575805434074441646354838539168960", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.03234738167262546215204549325399079583029508976900932805259181187717073896839729234888251E-90", "1E-91", "0E-182", "2E-90", "0E-182", "8.09040905156425629173402716582698264064543631772294601236941827783069386181476730895421256E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.675", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06677219896939873, 0.0 ], "rh_scaled_inf": 2.192626672778578e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.192626672778578e-16 }, "characteristics": { "left": { "slow": 0.0045305116161877225, "alfven_n": 0.0119525701347645, "fast": 0.8688603041126156 }, "right": { "slow": 0.005575935395031879, "alfven_n": 0.01490745598074381, "fast": 0.6951189854973617 } }, "front_relative_normal_velocity": { "left": -0.6415367839080972, "right": -0.9979436808080849 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5555517716830474, "pressure_ratio": 2.495798853410267, "entropy_over_cv": 0.17822499337279452, "tangential_field_ratio": 1.5557446817054499 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.65, "theta_Bn_degrees": 88.65, "compression": 1.5556017063214336, "u2x_km_s": -386.779588147241, "u2y_km_s": -16.879315174469102, "speed2_km_s": 387.1477251490811, "signed_deflection_degrees": 2.4988398888660455, "p2_over_p1": 2.496030663269744, "B2_over_B1": 1.555548559542915, "entropy_over_cv": 0.1782643684148357, "upstream_fast_Mach": 1.4356862595601172, "downstream_fast_Mach": 0.7383505833334715, "downstream_alfven_margin": 0.6293562546621404, "state_global_normalized": { "rho": "1.55560170632143366458251212135420193306971841430545628546219760574829582327034657997224776", "p": "0.101239003702220832411826215696858188976157249075020884802131359666313427081580675378402015", "u": [ "-0.644632646912068371830546302239589488956900035537912352436639768282311612682026434019419906", "-0.0281321919574485045710167264777289725198418179115745242576752150244914103774793779157145164", "-0E-91" ], "B": [ "0.0789929175004574564384323092534988656666698560644996054756347149129614321573473609865479676", "0.999726196660208732308282337175604449455112595597582317517931394036816679278671053036491797", "0E-91" ] }, "root_record": { "r": "1.55560170632143366458251212135420193306971841430545628546219760574829582327034657997224776", "b": "0.0407250496138344129944744476700620158105942147633849884234528307079437580988477813654427518", "h": "0.000231634678092396208476819072094838212122807374182015611139303511363633207187684274538978376", "A": "0.417081136689435283229315609286288614701458006973330647171548937904713481073521642825006035", "denominator": "0.999639668699516252449041899138450721469900748216084899869951807675528466096927905525693890", "polynomial_residual": "1.46945602071590348768838E-66", "bracket_initial_signs": [ "1.45262864999082877748408026967087343256702232200413019757733043912939800901412287620551167", "-2.04325997607391361461758398873231454841069433802956147155455862661887367525674450905609504" ], "bracket_derivative_max": "-5.57684342719705816857196520091076854331024606049471830649972702028237567638327783475183458", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.03222483717961424780947136866427171140802852597017870400326707912086805793948200805716071E-90", "-2E-91", "0E-182", "-2E-90", "0E-182", "-8.27271204002557131441436324536716264179550370727259802302435819504167207841464912827642593E-68", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.65", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06638740340376373, 0.0 ], "rh_scaled_inf": 2.1925212061141071e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1925212061141071e-16 }, "characteristics": { "left": { "slow": 0.004615967236236628, "alfven_n": 0.0121778535187553, "fast": 0.8688746547534734 }, "right": { "slow": 0.005681129395373751, "alfven_n": 0.015188677164311817, "fast": 0.6951181337177186 } }, "front_relative_normal_velocity": { "left": -0.6415341081808957, "right": -0.9979715533496006 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5556017063214336, "pressure_ratio": 2.496030663269744, "entropy_over_cv": 0.17826436841483573, "tangential_field_ratio": 1.5558019791713997 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.625, "theta_Bn_degrees": 88.62500000000001, "compression": 1.5556513710322006, "u2x_km_s": -386.7579015084728, "u2y_km_s": -16.84809022550297, "speed2_km_s": 387.12469893237795, "signed_deflection_degrees": 2.4943628241610116, "p2_over_p1": 2.4962613000630496, "B2_over_B1": 1.5555962304241926, "entropy_over_cv": 0.1783035558103152, "upstream_fast_Mach": 1.4357278759605636, "downstream_fast_Mach": 0.7383353900746437, "downstream_alfven_margin": 0.6291282933731174, "state_global_normalized": { "rho": "1.55565137103220067321530239335707194453933341225379642207421605862055733951882362982533635", "p": "0.101248358330557289627381666633305075198688280671941635978857207965557966541593670047194771", "u": [ "-0.644596502514121390981997646948876864890067600789228646111976325148232992688020920738972322", "-0.0280801503758382788226960491914536657649043270888921692181383036196716273051413153401136916", "-0E-91" ], "B": [ "0.0788390243157064896006132251208946068450158154142997712444668229321575268009379296151168704", "0.999769172756494870070430849805567375754141543217933593476023069440225449593591854452952507", "0E-91" ] }, "root_record": { "r": "1.55565137103220067321530239335707194453933341225379642207421605862055733951882362982533635", "b": "0.0407227903791317882786784347537297122139521589068335623873783095643576870068468885109650222", "h": "0.000240278183508841858723059126995690651485062312204107209827176445496733624573457290191738801", "A": "0.417049342629167168642793515278437615558323080030500575983122933075305701843050242076209386", "denominator": "0.999626210914395343452587350082492693915359802410314176398135137452962854907301187174041355", "polynomial_residual": "8.35273572314060806333039E-66", "bracket_initial_signs": [ "1.45284180155800508081067541226814563469618650116475873434925281025610391188714643133834386", "-2.04285821081081258522629164926874422261380184713752391447853444820997619450412810332338789" ], "bracket_derivative_max": "-5.57657094408724376584364062067708654783445937060098660115925660678859378494005749848898413", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-1E-91", "0E-182", "4E-90", "0E-182", "-4.70298602342128958926880567212511651818429983281382994964532772718537530694092884502387380E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-3.625", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06600260108484694, 0.0 ], "rh_scaled_inf": 2.1924168687576868e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7847323675202056e-16, "t1_momentum": 1.734723475976807e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1924168687576868e-16 }, "characteristics": { "left": { "slow": 0.004701421895025347, "alfven_n": 0.012403128432033226, "fast": 0.868888895790697 }, "right": { "slow": 0.005786322704388558, "alfven_n": 0.015469895456170087, "fast": 0.6951172660234902 } }, "front_relative_normal_velocity": { "left": -0.6415314218051507, "right": -0.9979992358914197 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5556513710322006, "pressure_ratio": 2.4962613000630496, "entropy_over_cv": 0.1783035558103152, "tangential_field_ratio": 1.5558591451137778 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.6, "theta_Bn_degrees": 88.6, "compression": 1.555700765829341, "u2x_km_s": -386.7363093238924, "u2y_km_s": -16.816849168768826, "speed2_km_s": 387.1017687449006, "signed_deflection_degrees": 2.489882237614473, "p2_over_p1": 2.4964907634413813, "B2_over_B1": 1.5556435944520586, "entropy_over_cv": 0.1783425555085631, "upstream_fast_Mach": 1.4357692519932157, "downstream_fast_Mach": 0.7383202781806391, "downstream_alfven_margin": 0.6289003298805507, "state_global_normalized": { "rho": "1.55570076582934095948152635772197846470062033830135581434238417774011126697644593201015720", "p": "0.101257665365182423529456420130401793526368351945990706902785641800677652744061830892022311", "u": [ "-0.644560515539820670841938052918880276571460685939873205500818268907217812034310599592175177", "-0.0280280819479480425832338150981668191595202145000144223693001001124339638519617074107695869", "-0E-91" ], "B": [ "0.0786850883164928064951693894832974058971840957145835893856651803267095366620813563005119472", "0.999811929195974164089354940889871302173095081952935239977968070620637384969796530518278935", "0E-91" ] }, "root_record": { "r": "1.55570076582934095948152635772197846470062033830135581434238417774011126697644593201015720", "b": "0.0407205468372246557460990697594971727972811465477626677699574959369219806613015360401639874", "h": "0.000249079524745944550600048102316561975453054288008144622101953318605400779721044977930896858", "A": "0.417017551538382244260948385794766946265394124075037581979685381051614433437583224162132006", "denominator": "0.999612506792600325779943919716899822261157544047757933628241867585142102367421235295894759", "polynomial_residual": "6.25324584151413475122556E-66", "bracket_initial_signs": [ "1.45305332237817334561640777256372448040169586875393484366835712979724759095555298788305891", "-2.04245784773028426824623781027366748704067646044993121636928379692521587243767464423897751" ], "bracket_derivative_max": "-5.57629849421522853750824675728407241718404945930889876925487650309697239541284547830627969", "iterations": 216 }, "flux_residuals": [ "-2E-90", "-8.03198434682314977470755591268084939030125390938565147214220747370229236576264805762426148E-90", "3E-91", "0E-182", "0E-90", "0E-182", "-3.52130844187115974988897929077335615407900371048986472566206469415338576061977150637418429E-67", "3E-91" ], "diagnosis": { "case_id": "R95_phi_-3.6", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06561779204938543, 0.0 ], "rh_scaled_inf": 1.7846662444450775e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7846662444450775e-16, "t1_momentum": -8.673617379884035e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.004786875591937902, "alfven_n": 0.012628394890774776, "fast": 0.8689030272230552 }, "right": { "slow": 0.005891515309269796, "alfven_n": 0.01575111080277863, "fast": 0.6951163824150397 } }, "front_relative_normal_velocity": { "left": -0.6415287247713255, "right": -0.9980267284282716 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.555700765829341, "pressure_ratio": 2.4964907634413813, "entropy_over_cv": 0.17834255550856315, "tangential_field_ratio": 1.555916179572809 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.575, "theta_Bn_degrees": 88.575, "compression": 1.5557498907266967, "u2x_km_s": -386.71481159758514, "u2y_km_s": -16.78559207266754, "speed2_km_s": 387.07893459885645, "signed_deflection_degrees": 2.4853981419969604, "p2_over_p1": 2.496719053057319, "B2_over_B1": 1.5556906516304803, "entropy_over_cv": 0.1783813674591199, "upstream_fast_Mach": 1.4358103876517057, "downstream_fast_Mach": 0.7383052476319095, "downstream_alfven_margin": 0.6286723641588148, "state_global_normalized": { "rho": "1.55574989072669662213513665249975497084909293680729102755460875665463059695363133675720053", "p": "0.101266924792004865353819178176608622304509600605310429883410307358149239280434889507134992", "u": [ "-0.644524685995975209796094093501678361342574588428378409285029585052896439487283248920924576", "-0.0279759867877792334554152764485702351212450896578995933003559562675095809921273215706411374", "-0E-91" ], "B": [ "0.0785311097326580454414034878785432434908631804698078678532046462848239967820783603039646968", "0.999854465953439504269900842811290793570245029446609091361458006776463882274641129314872144", "0E-91" ] }, "root_record": { "r": "1.55574989072669662213513665249975497084909293680729102755460875665463059695363133675720053", "b": "0.0407183189846754742771701080187747408900714731953644555992751551451110494435578272806768294", "h": "0.000258038679029133153096181272296552032439644679933148808943115474179846321365693613855748335", "A": "0.416985763404630328270385108092041550306800381104214666863948146781198423893895574369487019", "denominator": "0.999598556353297164953844579040961919579187415554372229844846975669403619795108590465126111", "polynomial_residual": "-1.440956770545398205888879E-65", "bracket_initial_signs": [ "1.45326321270965208038960638617042651806757355641714873118558987811405196100034018156671712", "-2.04205888662215787182304294488120113458048088786777043407439080660364941779328633607451198" ], "bracket_derivative_max": "-5.57602607759573165901605741673206322606763094597599910960258928741160713649593826475307961", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.03186640073044318019710013682979703655816623135727313990733580891584488303192361115630298E-90", "3E-91", "0E-182", "-1E-90", "0E-182", "8.11527272640676054310033380831853126707538679781772215328529874808971344783870567089624314E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_-3.575", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06523297633413266, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.004872328326347226, "alfven_n": 0.012853652911144556, "fast": 0.8689170490493376 }, "right": { "slow": 0.005996707197210731, "alfven_n": 0.016032323150598014, "fast": 0.6951154828927363 } }, "front_relative_normal_velocity": { "left": -0.6415260170699594, "right": -0.9980540309549222 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5557498907266967, "pressure_ratio": 2.496719053057319, "entropy_over_cv": 0.1783813674591198, "tangential_field_ratio": 1.5559730825884395 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.55, "theta_Bn_degrees": 88.55, "compression": 1.5557987457379592, "u2x_km_s": -386.6934083336469, "u2y_km_s": -16.75431900561065, "speed2_km_s": 387.0561965064431, "signed_deflection_degrees": 2.4809105500892037, "p2_over_p1": 2.4969461685648247, "B2_over_B1": 1.5557374019634307, "entropy_over_cv": 0.17841999161173644, "upstream_fast_Mach": 1.4358512829296703, "downstream_fast_Mach": 0.7382902984090388, "downstream_alfven_margin": 0.6284443961823715, "state_global_normalized": { "rho": "1.55579874573795926801447397001923158979642019299026593528865856174322414521879370026294936", "p": "0.101276136596989282511020224661369387054160940694228481475638888674268203155813128123426057", "u": [ "-0.644489013889411438383330692928067583677990398157459394659159597313459076760965336567676229", "-0.0279238650093510865170414920043452341286756185574805150186911783904310930061602345068638768", "-0E-91" ], "B": [ "0.0783770887940479691524141478530628375931436540073367494363694896185036888344297179778391525", "0.999896783003801002308362745124291592954450319470923117011629343825460327642223804741094188", "0E-91" ] }, "root_record": { "r": "1.55579874573795926801447397001923158979642019299026593528865856174322414521879370026294936", "b": "0.0407161068180710224449764973377479393482010582630072613793993053913410182585106213787842659", "h": "0.000267155623828489853201224023792634972441429117791602609373049538490021873178051214821446479", "A": "0.416953978215465791334060068866906652910343733156438198385961015245891186988679790929951904", "denominator": "0.999584359615530793422537878899216002957680672327160279346970018010291295718557533325476048", "polynomial_residual": "-3.81109554576929386515688E-66", "bracket_initial_signs": [ "1.45347147281001104322979276845056774997239354800748391777413237872069438244538657293852502", "-2.04166132727543100120440146530260067893672089265124449830012188487077429153527233751072957" ], "bracket_derivative_max": "-5.57575369424140733204084049781221834560710956884461125443147809576753320536449758943236622", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-1E-91", "0E-182", "-2E-90", "0E-182", "2.14662208076087524495473207863689949670102136331096213365866445850964776256844694657212769E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_-3.55", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06484815397585844, 0.0 ], "rh_scaled_inf": 2.192110630586248e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.784536318537149e-16, "t1_momentum": 1.734723475976807e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.192110630586248e-16 }, "characteristics": { "left": { "slow": 0.004957780097615243, "alfven_n": 0.0130789025092954, "fast": 0.868930961268355 }, "right": { "slow": 0.006101898355404395, "alfven_n": 0.01631353244608938, "fast": 0.6951145674569562 } }, "front_relative_normal_velocity": { "left": -0.6415232986916668, "right": -0.9980811434661735 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5557987457379592, "pressure_ratio": 2.4969461685648247, "entropy_over_cv": 0.1784199916117366, "tangential_field_ratio": 1.5560298542003352 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.525, "theta_Bn_degrees": 88.525, "compression": 1.55584733087667, "u2x_km_s": -386.6720995361839, "u2y_km_s": -16.72303003602033, "speed2_km_s": 387.0335544798489, "signed_deflection_degrees": 2.4764194746820962, "p2_over_p1": 2.4971721096192407, "B2_over_B1": 1.5557838454548893, "entropy_over_cv": 0.17845842791637387, "upstream_fast_Mach": 1.4358919378207524, "downstream_fast_Mach": 0.7382754304927426, "downstream_alfven_margin": 0.6282164259257695, "state_global_normalized": { "rho": "1.55584733087666997411257201297108134491670331495210792576858024886879016596911102962621649", "p": "0.101285300766156397283046523682050395848737319268138906568273991187532889882139700357922010", "u": [ "-0.644453499226973150958101256359416199156359669228395315551459560942107640877318706313781597", "-0.0278717167267005522256059825139972440743937092133213014314803061492646928896083761402629785", "-0E-91" ], "B": [ "0.0782230257305124879561908420192864720108737593632001004335119171411012486827295764602402875", "0.999938880322086006955902972477224278868456073518358949796305653434410801591720529135044443", "0E-91" ] }, "root_record": { "r": "1.55584733087666997411257201297108134491670331495210792576858024886879016596911102962621649", "b": "0.0407139103340223873800932898037772281341942659174492978889134332993062838007829132754719770", "h": "0.000276430336858655797352676614227997391646501758393753188339873929974421443536890983716600847", "A": "0.416922195958447536846967453533284736250577384807951495890935346008126710394711303234187155", "denominator": "0.999569916598225121614042009682393356984718223536028687524205606433278361705553589935699236", "polynomial_residual": "-3.23149126835143543329769E-66", "bracket_initial_signs": [ "1.45367810293607109084321651022799119715818608696934464634033126976046715051221520100479235", "-2.04126516947827079967019065300776015742898071858894593273052976203108750776314843379959662" ], "bracket_derivative_max": "-5.57548134416284619841761033907956469693011586082985883891518134240348496951403175729533989", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.03163510615393607021620157638294068230943827773450252166003936068879321292417804118246873E-90", "1E-91", "0E-182", "-1E-90", "0E-182", "1.82038108958465493483055976269730156098722707231145121787275770050298896171764179379624149E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_-3.525", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06446332501134869, 0.0 ], "rh_scaled_inf": 1.7844725154665149e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7844725154665149e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.00504323090509293, "alfven_n": 0.01330414370136847, "fast": 0.8689447638789388 }, "right": { "slow": 0.006207088771043587, "alfven_n": 0.01659473863571444, "fast": 0.6951136361080822 } }, "front_relative_normal_velocity": { "left": -0.641520569627138, "right": -0.9981080659568636 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.55584733087667, "pressure_ratio": 2.4971721096192407, "entropy_over_cv": 0.17845842791637379, "tangential_field_ratio": 1.5560864944478834 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.5, "theta_Bn_degrees": 88.5, "compression": 1.5558956461562192, "u2x_km_s": -386.65088520931283, "u2y_km_s": -16.69172523232933, "speed2_km_s": 387.011008531252, "signed_deflection_degrees": 2.471924928576662, "p2_over_p1": 2.497396875877293, "B2_over_B1": 1.5558299821088426, "entropy_over_cv": 0.17849667632320337, "upstream_fast_Mach": 1.4359323523185994, "downstream_fast_Mach": 0.7382606438638678, "downstream_alfven_margin": 0.6279884533636452, "state_global_normalized": { "rho": "1.55589564615621924980341783085861174614633044841572299329775355548767753069551031553265342", "p": "0.101294417285583005474399686011242060139769762453753548736194964895907268113884507019919570", "u": [ "-0.644418142015521437854408836679082851437909966569413303570024975218745661929303518036360564", "-0.0278195420538822143198024212318497334258589685960217323949511697969166703612117625132291555", "-0E-91" ], "B": [ "0.0780689207719056829472773512081952749607860837355601154630245982452909982473482466699007757", "0.999980757883439119096751800424524387405219596321929919688990410451599320905661694590347326", "0E-91" ] }, "root_record": { "r": "1.55589564615621924980341783085861174614633044841572299329775355548767753069551031553265342", "b": "0.0407117295291649537159443526558619882666618550436232906299651798265788297198054504278855139", "h": "0.000285862796078737543093197568756499588112248034441310576461944883847461452177679164420161889", "A": "0.416890416621138981206707170994854677966321157299549034075439192469566415100960679316015237", "denominator": "0.999555227320183049111974428739155095214944688189478804767983387920270262772294628233744978", "polynomial_residual": "2.68026503786218175926441E-66", "bracket_initial_signs": [ "1.45388310334390403232121352304283383590781570997732198048316366662959214372305505061699779", "-2.04087041301801507555534204342732971897349697179895925236627359716227160756443205140811512" ], "bracket_derivative_max": "-5.57520902736857673947111007341396592034309349481739825015577554003469267942441812904487707", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.03152175744967162750076937173730036890125407173553358113582407569669886839857255237241932E-90", "0E-91", "0E-182", "-3E-90", "0E-182", "-1.51004756817081610702146579238285281684559173243621025447497777067094068635030386204597508E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.5", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06407848947740541, 0.0 ], "rh_scaled_inf": 6.938893903907228e-18, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.005128680748120381, "alfven_n": 0.01352937650349336, "fast": 0.8689584568799413 }, "right": { "slow": 0.006312278431320857, "alfven_n": 0.01687594166593551, "fast": 0.6951126888465039 } }, "front_relative_normal_velocity": { "left": -0.6415178298671385, "right": -0.9981347984218669 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5558956461562192, "pressure_ratio": 2.497396875877293, "entropy_over_cv": 0.17849667632320343, "tangential_field_ratio": 1.5561430033701895 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.475, "theta_Bn_degrees": 88.47500000000001, "compression": 1.555943691589847, "u2x_km_s": -386.62976535716075, "u2y_km_s": -16.660404662980927, "speed2_km_s": 386.98855867282106, "signed_deflection_degrees": 2.4674269245840175, "p2_over_p1": 2.4976204669970907, "B2_over_B1": 1.5558758119292833, "entropy_over_cv": 0.178534736782606, "upstream_fast_Mach": 1.435972526416864, "downstream_fast_Mach": 0.7382459385033938, "downstream_alfven_margin": 0.627760478470721, "state_global_normalized": { "rho": "1.55594369158984699922388842402042952621462722317761329328285475852648591354057146572584330", "p": "0.101303486141401995017641289677575040728179474081170661520016009881611720402412852622305104", "u": [ "-0.644382942261934618050976778775022088273650604113447587757773113526501364942693240959272869", "-0.0277673411049682077176780806758536798852118343849862375132983153898244990915277890902005255", "-0E-91" ], "B": [ "0.0779147741480858290697855359175133283372767619437526649389323751274545827132291767142446371", "1.00002241566312220664116469110684709199600765516167551221084401994351426668244838201234337", "0E-91" ] }, "root_record": { "r": "1.55594369158984699922388842402042952621462722317761329328285475852648591354057146572584330", "b": "0.0407095644001583926146188622983238751832300373856723279603676093628582827933127961755097946", "h": "0.000295452979692214320370922695464969934387203945240931590865474943308314248243623004021552410", "A": "0.416858640191108034098867084938260882923701190451750258034561193962322477782649962237339181", "denominator": "0.999540291800086475952915800989611522566652653850068577973425210957769263638162358054872050", "polynomial_residual": "4.71257338854426997122284E-66", "bracket_initial_signs": [ "1.45408647428883248769391014103889217083915670142071819082283801152591371957973147213897117", "-2.04047705768117341538203245516526039906108018457239286151684655610980844083250788067788992" ], "bracket_derivative_max": "-5.57493674386506666075015686140634781111995103401051730032841369060645158107283616961035378", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "1E-91", "0E-182", "3E-90", "0E-182", "-2.65536702097547700439578648551059794519265536651558242092740873889230374931328276077283888E-67", "3E-91" ], "diagnosis": { "case_id": "R95_phi_-3.475", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06369364741084654, 0.0 ], "rh_scaled_inf": 2.1918145492549204e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -5.204170427930421e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1918145492549204e-16 }, "characteristics": { "left": { "slow": 0.0052141296260268775, "alfven_n": 0.01375460093178821, "fast": 0.8689720402702359 }, "right": { "slow": 0.006417467323428521, "alfven_n": 0.017157141483215503, "fast": 0.6951117256726171 } }, "front_relative_normal_velocity": { "left": -0.6415150794025092, "right": -0.998161340856094 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.555943691589847, "pressure_ratio": 2.4976204669970907, "entropy_over_cv": 0.178534736782606, "tangential_field_ratio": 1.5561993810060823 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.45, "theta_Bn_degrees": 88.45, "compression": 1.5559914671906425, "u2x_km_s": -386.6087399838649, "u2y_km_s": -16.62906839642888, "speed2_km_s": 386.9662049167147, "signed_deflection_degrees": 2.4629254755253425, "p2_over_p1": 2.497842882638125, "B2_over_B1": 1.5559213349202106, "entropy_over_cv": 0.17857260924517254, "upstream_fast_Mach": 1.4360124601092035, "downstream_fast_Mach": 0.738231314392431, "downstream_alfven_margin": 0.6275325012218069, "state_global_normalized": { "rho": "1.55599146719064248381108671033176719286541321349707769330734324169114077772872640464566815", "p": "0.101312507319802364533449855368468331265741700469695062948809953571857156514697524290320174", "u": [ "-0.644347899973108172337330351952885324740185215694621238769592893654487998452787288990256249", "-0.0277151139940481364112479863008374013037153957390062896946227717927376415487171821883783418", "-0E-91" ], "B": [ "0.0777605860889154181325408330297806208031046742428684138631728008889756664509537235603650647", "1.00006385363651441923311433593941920319551857090151290502639695574045776344902858509637964", "0E-91" ] }, "root_record": { "r": "1.55599146719064248381108671033176719286541321349707769330734324169114077772872640464566815", "b": "0.0407074149436866508730840253672498787699920300570410421154271860929961809429333190332443389", "h": "0.000305200866146846101919144852221074642367943638961533421042455969897252614561917581195599947", "A": "0.416826866655927078797152316435867013152991721756210641375811303082259970222233327207800893", "denominator": "0.999525110056496314045268068536004843602737753551264041800263604984420515544414326503429295", "polynomial_residual": "-1.561310767295281215963871E-65", "bracket_initial_signs": [ "1.45428821602542975125186937566278371240938081362363165577019065463762413789101980098641228", "-2.04008510325342828311761342286158078654014067342610727264586797493119697366684000275527167" ], "bracket_derivative_max": "-5.57466449365672426218285926719233879272519639154049780502909295597359542722288439334780495", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.03129965666894345713397621811159008487079432694851941851156140050264113229334348115274717E-90", "-2E-91", "0E-182", "4E-90", "0E-182", "8.79851369656587368931625107003873016308990358592787561704257214429423450145808552953643480E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.45", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06330879884850585, 0.0 ], "rh_scaled_inf": 4.3834362233657625e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 3.5685714887816225e-16, "t1_momentum": -5.204170427930421e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -4.3834362233657625e-16 }, "characteristics": { "left": { "slow": 0.00529957753813095, "alfven_n": 0.013979817002359788, "fast": 0.8689855140487169 }, "right": { "slow": 0.006522655434558638, "alfven_n": 0.017438338034017942, "fast": 0.6951107465868248 } }, "front_relative_normal_velocity": { "left": -0.6415123182241667, "right": -0.9981876932544915 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5559914671906425, "pressure_ratio": 2.497842882638125, "entropy_over_cv": 0.17857260924517238, "tangential_field_ratio": 1.5562556273941093 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.425, "theta_Bn_degrees": 88.42500000000001, "compression": 1.5560389729715443, "u2x_km_s": -386.5878090935728, "u2y_km_s": -16.597716501137395, "speed2_km_s": 386.9439472750812, "signed_deflection_degrees": 2.45842059423184, "p2_over_p1": 2.4980641224612734, "B2_over_B1": 1.5559665510856302, "entropy_over_cv": 0.17861029366170328, "upstream_fast_Mach": 1.4360521533892814, "downstream_fast_Mach": 0.7382167715122215, "downstream_alfven_margin": 0.6273045215917992, "state_global_normalized": { "rho": "1.55603897297154428499480215669039356726048030284222668584227136441261690136259192057801363", "p": "0.101321480807029241845233592416970576353500547645447144315204760823562511881090982891010856", "u": [ "-0.644313015155954676980493947900420946275924219627574859870525943953378671321115216280309715", "-0.0276628608352289913573849536623997113904605137556434481739020502842366007096096557412107221", "-0E-91" ], "B": [ "0.0776063568242611817571405690196981297134744062901092690988735209245345769154046043721816815", "1.00010507177911220277269449797338821122352237669845989620535544289496984169673662476398566", "0E-91" ] }, "root_record": { "r": "1.55603897297154428499480215669039356726048030284222668584227136441261690136259192057801363", "b": "0.0407052811564579401097329300609850831058887501399342108223072494900057439096403357279948019", "h": "0.000315106434134582482156442734547351248786825376399969447865718909191018244193496631517894877", "A": "0.416795096003172952478194466012079138159940348146235855868041877731986558577209223828613584", "denominator": "0.999509682107852498709567535846628344642454058822143125091341508923002808005044158601232317", "polynomial_residual": "-7.08818883073350258946040E-66", "bracket_initial_signs": [ "1.45448832880751965962834858634056745288624923022534549303705928191952561861932278905453542", "-2.03969454951963610557455957242530626449120806403286591499942684941777753009113920490020611" ], "bracket_derivative_max": "-5.57439227674589979366759260892904589482765914223097481180842878827239868346090793746117016", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "4E-91", "0E-182", "2E-90", "0E-182", "3.99492612710882252844323075388981681892994229852565156360977274802056459274092616877406410E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.425", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06292394382723276, 0.0 ], "rh_scaled_inf": 4.3832456038191326e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7842250330311808e-16, "t1_momentum": -5.204170427930421e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -4.3832456038191326e-16 }, "characteristics": { "left": { "slow": 0.005385024483740447, "alfven_n": 0.014205024731303618, "fast": 0.8689988782143001 }, "right": { "slow": 0.006627842751903013, "alfven_n": 0.01771953126480697, "fast": 0.6951097515895365 } }, "front_relative_normal_velocity": { "left": -0.6415095463231028, "right": -0.9982138556120422 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5560389729715443, "pressure_ratio": 2.4980641224612734, "entropy_over_cv": 0.17861029366170333, "tangential_field_ratio": 1.5563117425725392 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.4, "theta_Bn_degrees": 88.39999999999999, "compression": 1.5560862089453402, "u2x_km_s": -386.56697269044224, "u2y_km_s": -16.56634904558104, "speed2_km_s": 386.92178576005915, "signed_deflection_degrees": 2.4539122935447026, "p2_over_p1": 2.4982841861287945, "B2_over_B1": 1.556011460429554, "entropy_over_cv": 0.1786477899832079, "upstream_fast_Mach": 1.4360916062507654, "downstream_fast_Mach": 0.7382023098441393, "downstream_alfven_margin": 0.6270765395556808, "state_global_normalized": { "rho": "1.55608620894534026704482358350212415531238896773092743140325314911729166937095783596540990", "p": "0.101330406589383902448342846484917775288228360180695062545099374345061403496690671803572902", "u": [ "-0.644278287817403737892011485334043203218143595428975583519262377108557539629283305606061630", "-0.0276105817426350683648009079674480438777362155686783470933175749224576584978521632277026876", "-0E-91" ], "B": [ "0.0774520865839941142597058605812288071050604554526473836447994592303976465101640336938036233", "1.00014607006652931375321225247414175374924194947554217204096191132306466386724260140814731", "0E-91" ] }, "root_record": { "r": "1.55608620894534026704482358350212415531238896773092743140325314911729166937095783596540990", "b": "0.0407031630352047260312068897231098150630546608534707999206404834614805381120254103908239301", "h": "0.000325169662591472364052965111240707519233229853027132319388693544922616275943136527131478628", "A": "0.416763328220426926550973686295239389390216009175314848191823313950058906995937589558194180", "denominator": "0.999494007972474000340214928342812671621993009258609649614218065826790006627668937518397548", "polynomial_residual": "-5.49197102742597001604142E-66", "bracket_initial_signs": [ "1.45468681288817646463491067621878346266410613781569222747930702493743361130081678154808157", "-2.03930539626382834396857846581128470455800210342872453235995070863104681898755670780471194" ], "bracket_derivative_max": "-5.57412009313288679611449485957283994997814315935679839009349140183999343110948585866043997", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "1E-91", "0E-182", "3E-90", "0E-182", "3.09567394276595094895031344373873683090474588320440357400757090067403487027836082854149010E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.4", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06253908238389229, 0.0 ], "rh_scaled_inf": 2.1915286197558755e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7841650943180073e-16, "t1_momentum": 1.734723475976807e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1915286197558755e-16 }, "characteristics": { "left": { "slow": 0.005470470462152604, "alfven_n": 0.014430224134704076, "fast": 0.8690121327659212 }, "right": { "slow": 0.006733029262653197, "alfven_n": 0.018000721122047373, "fast": 0.695108740681168 } }, "front_relative_normal_velocity": { "left": -0.6415067636903848, "right": -0.9982398279237653 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5560862089453402, "pressure_ratio": 2.4982841861287945, "entropy_over_cv": 0.17864778998320807, "tangential_field_ratio": 1.556367726579362 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.375, "theta_Bn_degrees": 88.375, "compression": 1.5561331751246676, "u2x_km_s": -386.5462307786412, "u2y_km_s": -16.53496609824473, "speed2_km_s": 386.8997203837767, "signed_deflection_degrees": 2.4494005863150785, "p2_over_p1": 2.498503073304334, "B2_over_B1": 1.5560560629560014, "entropy_over_cv": 0.17868509816090533, "upstream_fast_Mach": 1.4361308186873287, "downstream_fast_Mach": 0.7381879293696894, "downstream_alfven_margin": 0.6268485550885211, "state_global_normalized": { "rho": "1.55613317512466754007283385561269477567359140647091084764853709395580543696782355893552951", "p": "0.101339284653223787933925995698851571647280807152101207814639803648141537872249068516536516", "u": [ "-0.644243717964401925295000723131789426821177080773730782735192614034351991718194572093022649", "-0.0275582768304078859769351036549368976937026254670081940956075658922379891853748103039932201", "-0E-91" ], "B": [ "0.0772977755979894954671075587765890054238096562147421617367155282676416056789379511028278260", "1.00018684847449683341294483048702650826785405511507207381660707427381027248573543733273693", "0E-91" ] }, "root_record": { "r": "1.55613317512466754007283385561269477567359140647091084764853709395580543696782355893552951", "b": "0.0407010605766837177794320989228997851858848402041908612753751659366074798190826317633944652", "h": "0.000335390530697574453413190153878357092209872599310369310118709007233256669239226471989619822", "A": "0.416731563295274687000786618948552485443462450075607651121381076281790670406379123961229709", "denominator": "0.999478087668558836188585453942405974381719049248937943366929673679323644476493900529802082", "polynomial_residual": "-4.93958506906600980479457E-66", "bracket_initial_signs": [ "1.45488366851972471084320364794858330113698389385523815471333790120556659516504245990877191", "-2.03891764326921255165088663828912002446763422351041722779970551769880000974574378653320974" ], "bracket_derivative_max": "-5.57384794281592342795212259066897075903438924041387967246688360937375138213059690226809677", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.03097799549073618150748054256280074878556653208579145872903694221871553057621651698498890E-90", "-1E-91", "0E-182", "-4E-90", "0E-182", "2.78465200005585766190219776820439706030704574438814812810536072889664398520571786773402691E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-3.375", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06215421455536489, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.005555915472654103, "alfven_n": 0.014655415228634486, "fast": 0.8690252777025378 }, "right": { "slow": 0.006838214954000477, "alfven_n": 0.018281907552204563, "fast": 0.6951077138621423 } }, "front_relative_normal_velocity": { "left": -0.6415039703171557, "right": -0.9982656101847159 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5561331751246676, "pressure_ratio": 2.498503073304334, "entropy_over_cv": 0.17868509816090528, "tangential_field_ratio": 1.5564235794522885 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.35, "theta_Bn_degrees": 88.35, "compression": 1.5561798715220123, "u2x_km_s": -386.5255833623477, "u2y_km_s": -16.50356772762366, "speed2_km_s": 386.8777511583516, "signed_deflection_degrees": 2.444885485404036, "p2_over_p1": 2.498720783652922, "B2_over_B1": 1.556100358668997, "entropy_over_cv": 0.17872221814622347, "upstream_fast_Mach": 1.43616979069265, "downstream_fast_Mach": 0.7381736300705083, "downstream_alfven_margin": 0.6266205681654761, "state_global_normalized": { "rho": "1.55617987152201242318861837749986327704404657736442798739262878872880722171865979213042187", "p": "0.101348114984962524367472357931365344519279095634671606093163497740357963842674069709555648", "u": [ "-0.644209305603912708890955241428183859744988719709349349782866181470405172855992013851684258", "-0.0275059462127061033505650768291387349035482553643507256863922589223349426897542300960885993", "-0E-91" ], "B": [ "0.0771434240961269134684463834361722967257790812332027462583797656508919667963121210403760321", "1.00022740697886318170153687672718902193512919350824475085825958698133841123891353462048839", "0E-91" ] }, "root_record": { "r": "1.55617987152201242318861837749986327704404657736442798739262878872880722171865979213042187", "b": "0.0406989737776758573588108800182687841214871042311782393479740782736664385768533568053377821", "h": "0.000345769017876868560030087828311420029163360129795908303572325215673846940743146302032972661", "A": "0.416699801215306314747693291749169159395301355733863086177752426846708617773233086024075066", "denominator": "0.999461921214184082267482969303404180963018658347238762483883150590108590817597352762818920", "polynomial_residual": "-8.90554980418727326485195E-66", "bracket_initial_signs": [ "1.45507889595373911790579596138722956848912087895790139062314008632470384960061404162007705", "-2.03853129031817341803051895269661507738705083810430918877248239568253283016797580584164311" ], "bracket_derivative_max": "-5.57357582579119377711378354121210627641353690353148134018859308736394604586417688550840006", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "2E-91", "0E-182", "-5E-90", "0E-182", "5.02105140223268218928013775169164299031955512000787009701631582612079730779372427482598193E-67", "-4E-91" ], "diagnosis": { "case_id": "R95_phi_-3.35", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06176934037854636, 0.0 ], "rh_scaled_inf": 2.1913436376015762e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1913436376015762e-16 }, "characteristics": { "left": { "slow": 0.0056413595145211465, "alfven_n": 0.014880598029157237, "fast": 0.8690383130231282 }, "right": { "slow": 0.006943399813135877, "alfven_n": 0.01856309050174462, "fast": 0.6951066711328887 } }, "front_relative_normal_velocity": { "left": -0.6415011661946333, "right": -0.9982912023899855 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5561798715220123, "pressure_ratio": 2.4987207836529226, "entropy_over_cv": 0.1787222181462238, "tangential_field_ratio": 1.5564793012287492 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.325, "theta_Bn_degrees": 88.325, "compression": 1.5562262981497104, "u2x_km_s": -386.5050304457498, "u2y_km_s": -16.472154002223263, "speed2_km_s": 386.8558780958911, "signed_deflection_degrees": 2.440367003682527, "p2_over_p1": 2.498937316840975, "B2_over_B1": 1.556144347572573, "entropy_over_cv": 0.17875914989079916, "upstream_fast_Mach": 1.4362085222604124, "downstream_fast_Mach": 0.7381594119283642, "downstream_alfven_margin": 0.6263925787617873, "state_global_normalized": { "rho": "1.55622629814971040781032151405476558227574019783874571085023389114866526754612759692520968", "p": "0.101356897571069940622085488146614593031868663962177621478209786084331474685656461540590811", "u": [ "-0.644175050742916393526010904850391436585587347323053443660863780249298597396922390804583970", "-0.0274535900037054381299563749821810360247660459315284965355346642621439258476176068997437959", "-0E-91" ], "B": [ "0.0769890323082902873025670906153913021179244708049835815419370393523444728847944314772596515", "1.00026774555559413106101354002897885466559314871176407048103792062988283895979832028002859", "0E-91" ] }, "root_record": { "r": "1.55622629814971040781032151405476558227574019783874571085023389114866526754612759692520968", "b": "0.0406969026349863091435082554136430303601891613232939156437568139464879699827209843895923413", "h": "0.000356305103797167705170216781140939098073757817590808157781306019375602331403322176152448700", "A": "0.416668041968116266019376153465124319584100762191939204105495296589582184168112657699036922", "denominator": "0.999445508627305885376903425165064909632335671394907692545848979227485379103473155445853227", "polynomial_residual": "-6.69066270381523120269717E-66", "bracket_initial_signs": [ "1.45527249544104446760902762402213946937809904148711441276488811123584715579149934951900182", "-2.03814633719227379870240100093684776040935945156866964427165620181287633931813615075321702" ], "bracket_derivative_max": "-5.57330374205282915851793965398733644381526652839644021815940386685514459526086766595441725", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "2E-91", "0E-182", "-3E-90", "0E-182", "3.77273693364196608401847528661295947097956140202034138793985848470706049809735525103006755E-67", "4E-91" ], "diagnosis": { "case_id": "R95_phi_-3.325", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06138445989034769, 0.0 ], "rh_scaled_inf": 1.7839899129675688e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7839899129675688e-16, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.0057268025870195124, "alfven_n": 0.01510577255232388, "fast": 0.8690512387266918 }, "right": { "slow": 0.007048583827250144, "alfven_n": 0.01884426991713427, "fast": 0.6951056124938435 } }, "front_relative_normal_velocity": { "left": -0.6414983513141113, "right": -0.9983166045347017 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5562262981497104, "pressure_ratio": 2.498937316840975, "entropy_over_cv": 0.17875914989079922, "tangential_field_ratio": 1.5565348919458974 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.3, "theta_Bn_degrees": 88.3, "compression": 1.556272455019946, "u2x_km_s": -386.48457203304605, "u2y_km_s": -16.44072499055915, "speed2_km_s": 386.8341012084922, "signed_deflection_degrees": 2.4358451540313535, "p2_over_p1": 2.4991526725362943, "B2_over_B1": 1.556188029670767, "entropy_over_cv": 0.17879589334647789, "upstream_fast_Mach": 1.4362470133843046, "downstream_fast_Mach": 0.7381452749251561, "downstream_alfven_margin": 0.6261645868527833, "state_global_normalized": { "rho": "1.55627245501994612112848726095748611897229605086043663528603029512527032893882668412561543", "p": "0.101365632398072086666530061242489435058531499014543905790758358371704055347998821843972201", "u": [ "-0.644140953388410055356396673846046583276889140717244999672171580930513181453287151310182451", "-0.0274012083175985843163673164969451067965072227321516076011300741554417159349076625633936516", "-0E-91" ], "B": [ "0.0768346004643678895823862174362637098739643035176555881937789781214287448805287484127870113", "1.00030786418077282002138442181409342166236715099680053297190147467516038933162470597982678", "0E-91" ] }, "root_record": { "r": "1.55627245501994612112848726095748611897229605086043663528603029512527032893882668412561543", "b": "0.0406948471454444494647750374441196470215143880662032202616414411399375370380350670749653966", "h": "0.000366998768370031034853885802332081908631662144039864989840982178772151047301971835785678371", "A": "0.416636285541303352738344505566021865107113612461793164560915844496383795221321629701468908", "denominator": "0.999428849925759475251073838297797419159081645733079891689233300760171515194224835400912388", "polynomial_residual": "4.9963143547297932432536E-67", "bracket_initial_signs": [ "1.45546446723171549565090931691816002947263848647575280951461018342274962643815327296081666", "-2.03776278367225573179677709142231107046004502147451581575960018623600670887308253155962163" ], "bracket_derivative_max": "-5.57303169159290939705695185186294803719309750779592392928148402744337143059235643781160964", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "1E-91", "0E-182", "-2E-90", "0E-182", "-2.81767296373913956014822726525800731432848219384080378817990735394084661853726716696564721E-68", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.3", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06099957312769494, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.005812244689404632, "alfven_n": 0.01533093881417523, "fast": 0.869064054812249 }, "right": { "slow": 0.007153766983533758, "alfven_n": 0.01912544574484093, "fast": 0.6951045379454491 } }, "front_relative_normal_velocity": { "left": -0.6414955256669584, "right": -0.9983418166140283 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.556272455019946, "pressure_ratio": 2.4991526725362943, "entropy_over_cv": 0.17879589334647805, "tangential_field_ratio": 1.5565903516406072 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.275, "theta_Bn_degrees": 88.275, "compression": 1.5563183421447533, "u2x_km_s": -386.4642081284445, "u2y_km_s": -16.409280761157078, "speed2_km_s": 386.8124205082408, "signed_deflection_degrees": 2.431319949341131, "p2_over_p1": 2.499366850408068, "B2_over_B1": 1.5562314049676242, "entropy_over_cv": 0.1788324484653137, "upstream_fast_Mach": 1.4362852640580204, "downstream_fast_Mach": 0.7381312190429148, "downstream_alfven_margin": 0.6259365924138778, "state_global_normalized": { "rho": "1.55631834214475328972362269050122764027360675119034162214410147227371185730337176241107036", "p": "0.101374319452551251808095352621247693189719863759119059569564430389347958052000016621665398", "u": [ "-0.644107013547407478512792678925804541350513472962041703828330556171874148229699084020508923", "-0.0273488012685951301327252369200138765063216745626653692174835443955993445438662032640325821", "-0E-91" ], "B": [ "0.0766801287942523690568126556032477091910714004509332949260204613341212978861005280355659441", "1.00034776283059976661081301557901105483971828609234096065673422193080116208047253008480904", "0E-91" ] }, "root_record": { "r": "1.55631834214475328972362269050122764027360675119034162214410147227371185730337176241107036", "b": "0.0406928073059038562782490840316180535250125362309609152862464681266509807501046630579578236", "h": "0.000377849991750677538399103816825101542236074073070578589169060652733446723946778239115662277", "A": "0.416604531922470722923417670795877021785320754841358998520717395266329389361710003341980944", "denominator": "0.999411945127259176826734111144214700242266091562838726459173845453754356365694919695627163", "polynomial_residual": "1.398325249852503278315566E-65", "bracket_initial_signs": [ "1.45565481157507678813717411507616645543901254323390377388877450535502103327013855324349830", "-2.03738062953804144056544937074962402974707060938443985524896669071206550600855939204589567" ], "bracket_derivative_max": "-5.57275967440146409610831542499079090429155090407070009322522488183561340668665958516669547", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "0E-91", "0E-182", "7E-90", "0E-182", "-7.88682959679664894849519446593046538409641645297546565333141924149681514714915449012214373E-67", "4E-91" ], "diagnosis": { "case_id": "R95_phi_-3.275", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06061468012752918, 0.0 ], "rh_scaled_inf": 2.1910746171618417e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1910746171618417e-16 }, "characteristics": { "left": { "slow": 0.005897685820921648, "alfven_n": 0.01555609683074148, "fast": 0.8690767612788414 }, "right": { "slow": 0.0072589492691769175, "alfven_n": 0.01940661793133269, "fast": 0.6951034474881551 } }, "front_relative_normal_velocity": { "left": -0.6414926892446193, "right": -0.9983668386231653 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5563183421447533, "pressure_ratio": 2.4993668504080686, "entropy_over_cv": 0.17883244846531376, "tangential_field_ratio": 1.556645680349473 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.25, "theta_Bn_degrees": 88.25, "compression": 1.5563639595360148, "u2x_km_s": -386.44393873616343, "u2y_km_s": -16.377821382552884, "speed2_km_s": 386.79083600721265, "signed_deflection_degrees": 2.4267914025122543, "p2_over_p1": 2.4995798501268736, "B2_over_B1": 1.5562744734671958, "entropy_over_cv": 0.17886881519956907, "upstream_fast_Mach": 1.4363232742752587, "downstream_fast_Mach": 0.7381172442638017, "downstream_alfven_margin": 0.625708595420571, "state_global_normalized": { "rho": "1.55636395953601470333702489975510651778868958116410898055941997591237860933090846966517750", "p": "0.101382958721145982890318145803095739283326621812693174339440340486903567437457711140936466", "u": [ "-0.644073231226939092263321518652464064194965086346731526048158044097823580209802195413016320", "-0.0272963689709214758832908799413808029443419685672025553566426496024085176922215865924447310", "-0E-91" ], "B": [ "0.0765256175278407731110400172793719948889046039921277887167748452886498576174497465463932583", "1.00038744148139288158032587825387104439998278444878203414286678181418992147286814670140078", "0E-91" ] }, "root_record": { "r": "1.55636395953601470333702489975510651778868958116410898055941997591237860933090846966517750", "b": "0.0406907831132422989111768239725352185280550575920809867256663002177705617908656482371956127", "h": "0.000388858754337900571702631493461059061555635926641521188681324670194657252425086041866257092", "A": "0.416572781099225841105420319236071846998605634417704832699209333708200781246957534739028676", "denominator": "0.999394794249398422632630094258834520750388608528504994234319143533028783281452964923201034", "polynomial_residual": "8.18687084972261460421966E-66", "bracket_initial_signs": [ "1.45584352871970268278865850229561049356155086296276306902536562426972293023370570765097083", "-2.03699987456873432222014683706509442505929809566329189412729640784482188404030951539137923" ], "bracket_derivative_max": "-5.57248769046647389158241266549101501017230173006477579690138178025625886800229953763305494", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.03047252676915655127231697559575842965858665396986205208583293726328230941961069464543818E-90", "1E-91", "0E-182", "-2E-90", "0E-182", "-4.61812422259627176579392922797828413491374733398754894788247238863096973281701521403603287E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_-3.25", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.06022978092680628, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.005983125980805487, "alfven_n": 0.01578124661804229, "fast": 0.8690893581255312 }, "right": { "slow": 0.007364130671369535, "alfven_n": 0.019687786423078328, "fast": 0.6951023411224178 } }, "front_relative_normal_velocity": { "left": -0.6414898420386133, "right": -0.9983916705573488 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5563639595360148, "pressure_ratio": 2.4995798501268736, "entropy_over_cv": 0.178868815199569, "tangential_field_ratio": 1.5567008781088112 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.225, "theta_Bn_degrees": 88.22500000000001, "compression": 1.5564093072054621, "u2x_km_s": -386.4237638604311, "u2y_km_s": -16.34634692329245, "speed2_km_s": 386.76934771747216, "signed_deflection_degrees": 2.42225952645486, "p2_over_p1": 2.499791671364672, "B2_over_B1": 1.5563172351735395, "entropy_over_cv": 0.1789049935017146, "upstream_fast_Mach": 1.4363610440297232, "downstream_fast_Mach": 0.7381033505701097, "downstream_alfven_margin": 0.6254805958484486, "state_global_normalized": { "rho": "1.55640930720546217879461438819018814718708415784649329822044429965153812527733148485397607", "p": "0.101391550190551102445607713761131166758697972912512134443414428074121803480023898932641473", "u": [ "-0.644039606434051908674901785387883548249403273504806987128066966454156609505467212934096715", "-0.0272439115388207518081277884172277217038969154907613768082700194191528299076498639709496054", "-0E-91" ], "B": [ "0.0763710668950345702059894748352093761980095362868189588562601508105093502991514274411650828", "1.00042690010958748144303538243944360063400836077470810044209138222604221077796993697810350", "0E-91" ] }, "root_record": { "r": "1.55640930720546217879461438819018814718708415784649329822044429965153812527733148485397607", "b": "0.0406887745643617278894976109336505592728024489089744896166314099024715874294584014300818356", "h": "0.000400025036773983184736031998912275191076242451078088777880012076075031094159689691267276063", "A": "0.416541033059180468757023452693647583457887553388743831686535440955738468152128744596034792", "denominator": "0.999377397309649765300187361129914963363255721135659107521232188456635950714592778804727628", "polynomial_residual": "-6.66789094674838601886817E-66", "bracket_initial_signs": [ "1.45603061891341717485326140797853553665270725125198594768141863981103944087571236810502494", "-2.03662051854261992303820640981862889392285156720020814344747383804870294118149598633722955" ], "bracket_derivative_max": "-5.57221573977387169152068731767131058952131715895159094973258561546063652699834562316320448", "iterations": 216 }, "flux_residuals": [ "3E-90", "-8.03037602713760125441487399682523031372649225395707718842509537537956839394690212009537621E-90", "0E-91", "0E-182", "-3E-90", "0E-182", "3.76174679322082391772416488774872145786661892537160903593165751161644506603392700739488204E-67", "-4E-91" ], "diagnosis": { "case_id": "R95_phi_-3.225", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05984487556249686, 0.0 ], "rh_scaled_inf": 2.1909009034307596e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": -1.7837671483926592e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1909009034307596e-16 }, "characteristics": { "left": { "slow": 0.006068565168280916, "alfven_n": 0.016006388192086923, "fast": 0.8691018453514027 }, "right": { "slow": 0.007469311177301243, "alfven_n": 0.01996895116654734, "fast": 0.6951012188486995 } }, "front_relative_normal_velocity": { "left": -0.6414869840405355, "right": -0.9984163124118512 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5564093072054621, "pressure_ratio": 2.499791671364672, "entropy_over_cv": 0.17890499350171463, "tangential_field_ratio": 1.5567559449546595 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.2, "theta_Bn_degrees": 88.2, "compression": 1.5564543851646766, "u2x_km_s": -386.40368350548573, "u2y_km_s": -16.31485745193164, "speed2_km_s": 386.7479556510731, "signed_deflection_degrees": 2.417724334088794, "p2_over_p1": 2.5000023137948157, "B2_over_B1": 1.5563596900907193, "entropy_over_cv": 0.17894098332442904, "upstream_fast_Mach": 1.4363985733151234, "downstream_fast_Mach": 0.7380895379442627, "downstream_alfven_margin": 0.6252525936731819, "state_global_normalized": { "rho": "1.55645438516467652408351999133965085064367835016489811031037202286240571397572128711627468", "p": "0.101400093847517726802815338299078018497607056236941420617383273713750706615341642821922204", "u": [ "-0.644006139175809460772695863193246076269412409681870898393374866503182967404604265116423659", "-0.0271914290865527359321937446283179251520698052636973322027280191536129524644629927529669480", "-0E-91" ], "B": [ "0.0762164771257396722576814792348944705420571098237226820515323587396437696626791665641844374", "1.00046613869173630132784950697882529638025189283788522966894836891802470896515878081590345", "0E-91" ] }, "root_record": { "r": "1.55645438516467652408351999133965085064367835016489811031037202286240571397572128711627468", "b": "0.0406867816561882648447339199576745643995553995255543585789741353139335232912816496009742704", "h": "0.000411348819944614252739198207689441058836494838490739932073807693801914392473228307030872971", "A": "0.416509287789950644736664628065842669543304138717663071708911431142190224148544028162701520", "denominator": "0.999359754325364890195336239890716330326892856312246498812216355259139827457428945958182980", "polynomial_residual": "2.96452882802090933852581E-66", "bracket_initial_signs": [ "1.45621608240329382771580190781904220556654722342793135926772549163612513138649557998439408", "-2.03624256123716689975061182436766880463208592576001827485294047021418488487675884284841392" ], "bracket_derivative_max": "-5.57194382230754390125802350787471576416065094604237109953970466817610346700392989235006315", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "1E-91", "0E-182", "2E-90", "0E-182", "-1.67266948677350677430141708687037852733142173271128018134971961284816841419535522729105095E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_-3.2", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05945996407158613, 0.0 ], "rh_scaled_inf": 2.1908157360410835e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1908157360410835e-16 }, "characteristics": { "left": { "slow": 0.006154003382562614, "alfven_n": 0.016231521568874287, "fast": 0.86911422295556 }, "right": { "slow": 0.007574490774161379, "alfven_n": 0.020250112108209924, "fast": 0.6951000806674699 } }, "front_relative_normal_velocity": { "left": -0.6414841152420562, "right": -0.998440764181981 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5564543851646766, "pressure_ratio": 2.500002313794816, "entropy_over_cv": 0.1789409833244292, "tangential_field_ratio": 1.5568108809227772 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.175, "theta_Bn_degrees": 88.175, "compression": 1.5564991934250876, "u2x_km_s": -386.3836976755751, "u2y_km_s": -16.283353037036264, "speed2_km_s": 386.72665982005805, "signed_deflection_degrees": 2.4131858383435736, "p2_over_p1": 2.5002117770920433, "B2_over_B1": 1.5564018382228062, "entropy_over_cv": 0.17897678462059896, "upstream_fast_Mach": 1.4364358621251734, "downstream_fast_Mach": 0.7380758063688155, "downstream_alfven_margin": 0.6250245888705278, "state_global_normalized": { "rho": "1.55649919342508750258116269573466967832490219261375680093867325291723415030032699806193489", "p": "0.101408589678853284149790649713204663758718863924790155095412972813528017753648944055325466", "u": [ "-0.643972829459291741197387079901866720836543354633818305885893137675068908600434019623204235", "-0.0271389217283937719088714992834381752770106417381384202226773362003424944010752611233318162", "-0E-91" ], "B": [ "0.0760618484498664569573144904954490278085942457451826777578808473864777160715560283601382846", "1.00050515720450950764764173205864262651327038969028335997309296612468223335158372229024725", "0E-91" ] }, "root_record": { "r": "1.55649919342508750258116269573466967832490219261375680093867325291723415030032699806193489", "b": "0.0406848043856721925006308545158717360424316896262832196500603998684251631327397262294800618", "h": "0.000422830084978805410598408846728804923583936903074100235218358576103257105833644863981559617", "A": "0.416477545279156665746481079756577728690646280640975004915109507804904129527486580327678669", "denominator": "0.999341865313774628171459721796023190491935104108572227129228114977845071282857675395645731", "polynomial_residual": "-6.86647682532120658964752E-66", "bracket_initial_signs": [ "1.45639991943565568819916803300947119751924217911517109219974289418398048133089338468899349", "-2.03586600242902796722729991865327519385099271968912372382293723322719439478279301693667867" ], "bracket_derivative_max": "-5.57167193804933163416299007738497357452175157923981834138635119956530523089232380002286213", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.03018762124292431205265970803856498104433744121816081757038794013297060038749155729248143E-90", "-3E-91", "0E-182", "0E-90", "0E-182", "3.87473304502349804493939138038614674653772686548190198137343931993522231419299847406092445E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.175", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.059075046491073785, 0.0 ], "rh_scaled_inf": 1.7836603973618384e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7836603973618384e-16, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.006239440622855239, "alfven_n": 0.016456646764393117, "fast": 0.8691264909371295 }, "right": { "slow": 0.007679669449138984, "alfven_n": 0.020531269194537006, "fast": 0.695098926579205 } }, "front_relative_normal_velocity": { "left": -0.641481235634921, "right": -0.9984650258630829 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5564991934250876, "pressure_ratio": 2.500211777092044, "entropy_over_cv": 0.17897678462059896, "tangential_field_ratio": 1.5568656860486447 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.15, "theta_Bn_degrees": 88.15, "compression": 1.5565437319979738, "u2x_km_s": -386.3638063749571, "u2y_km_s": -16.251833747182012, "speed2_km_s": 386.70546023645875, "signed_deflection_degrees": 2.4086440521583525, "p2_over_p1": 2.5004200609324836, "B2_over_B1": 1.5564436795738774, "entropy_over_cv": 0.17901239734331872, "upstream_fast_Mach": 1.4364729104535927, "downstream_fast_Mach": 0.7380621558264543, "downstream_alfven_margin": 0.6247965814163288, "state_global_normalized": { "rho": "1.55654373199797379743658785826549430236822503404662530501122277798015622961030105779544866", "p": "0.101417037671421532550966887174570797808736800796828045771612776433135724350812717703416095", "u": [ "-0.643939677291595141360024330280978557704320022345443140176597262360523211531040834658757217", "-0.0270863895786366868577562155588004689975371129786138943480643782351288535805208273148404609", "-0E-91" ], "B": [ "0.0759071810973297900328285877434974631680533005554373721719597304097706000876341156473752192", "1.00054395562469471058185371405350320948592621336476057591108705207262682165106874733669626", "0E-91" ] }, "root_record": { "r": "1.55654373199797379743658785826549430236822503404662530501122277798015622961030105779544866", "b": "0.0406828427497879447394888858965820145596576425652516855168054586824290185578255054731942560", "h": "0.000434468813248808789900536644525947914268583832725475297860060771799053007633094082871451582", "A": "0.416445805514423066804189480255175506856295534964032315581671335069931465543733851181575996", "denominator": "0.999323730291988968443436942149983898054629020417655421536532568273836912692856004785856442", "polynomial_residual": "4.68247617138303702623407E-66", "bracket_initial_signs": [ "1.45658213025607520655022082447994168754661952925329298345241450567909380517602208829736951", "-2.03549084189404083247450787139923297863935449267015544842934090752290144394355555815402940" ], "bracket_derivative_max": "-5.57140008697903190796948966316693538609331052220026732806886996925930595931483517365686274", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "2E-91", "0E-182", "-3E-90", "0E-182", "-2.64263243582983729565996238129437583508225153137486646498576248823132834105969275600996845E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-3.15", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05869012285797388, 0.0 ], "rh_scaled_inf": 2.1906487794133813e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1906487794133813e-16 }, "characteristics": { "left": { "slow": 0.00632487688835349, "alfven_n": 0.01668176379462202, "fast": 0.8691386492952582 }, "right": { "slow": 0.007784847189422804, "alfven_n": 0.020812422372000247, "fast": 0.6950977565843874 } }, "front_relative_normal_velocity": { "left": -0.6414783452109508, "right": -0.9984890974505379 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5565437319979738, "pressure_ratio": 2.5004200609324836, "entropy_over_cv": 0.17901239734331875, "tangential_field_ratio": 1.556920360367465 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.125, "theta_Bn_degrees": 88.125, "compression": 1.556588000894463, "u2x_km_s": -386.34400960789947, "u2y_km_s": -16.220299650954427, "speed2_km_s": 386.6843569122954, "signed_deflection_degrees": 2.4040989884818846, "p2_over_p1": 2.500627164993653, "B2_over_B1": 1.5564852141480165, "entropy_over_cv": 0.1790478214458902, "upstream_fast_Mach": 1.4365097182941056, "downstream_fast_Mach": 0.7380485862999956, "downstream_alfven_margin": 0.6245685712865124, "state_global_normalized": { "rho": "1.55658800089446297610379755027501469562818752486273543062816458722527910208312088341994558", "p": "0.101425437812142577920016998735159080027849738193145206412809285564284631780378182842153502", "u": [ "-0.643906682679832391094175319404040038509009222390308378828144065534971616525572726208886883", "-0.0270338327515907091965172377142564936810099098591814503760524211982823393177892662991654358", "-0E-91" ], "B": [ "0.0757524752980490474527315658924547119841190557080158254549536668811473013275026542726438359", "1.00058253392919697637350302461986539155071542063784732474587684557778870252430292541176652", "0E-91" ] }, "root_record": { "r": "1.55658800089446297610379755027501469562818752486273543062816458722527910208312088341994558", "b": "0.0406808967455340967481341999891783851397140986459976980231010462919464471279840153581034653", "h": "0.000446264986370035558159597610202508222028665497437027999126843488243266470676054329851210618", "A": "0.416414068483378601728846156632667711195955222342009407585681812892595355493629100737317580", "denominator": "0.999305349276997071582756005620194120856558698839423275707092637069378598571899493916358803", "polynomial_residual": "5.93941197047134496851907E-66", "bracket_initial_signs": [ "1.45676271510937416110398935078666600020661177190997726696790732280966038190262250606696696", "-2.03511707940722911495879913545686151711772165631395521916720609437502706301803858391482765" ], "bracket_derivative_max": "-5.57112826907439882671323045330642205041772157650519922160282444117189448689508000814937933", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-3E-91", "0E-182", "0E-90", "0E-182", "-3.35241656963739073939401881527108081191529466139222914769140441899871525521701170685089104E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.125", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05830519320931472, 0.0 ], "rh_scaled_inf": 3.5671134655731914e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 3.5671134655731914e-16, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1905669898616746e-16 }, "characteristics": { "left": { "slow": 0.006410312178242178, "alfven_n": 0.016906872675529597, "fast": 0.8691506980291139 }, "right": { "slow": 0.007890023982201276, "alfven_n": 0.02109357158707205, "fast": 0.6950965706835068 } }, "front_relative_normal_velocity": { "left": -0.641475443962042, "right": -0.9985129789397631 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.556588000894463, "pressure_ratio": 2.5006271649936536, "entropy_over_cv": 0.17904782144589027, "tangential_field_ratio": 1.5569749039141612 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.1, "theta_Bn_degrees": 88.10000000000001, "compression": 1.5566320001255314, "u2x_km_s": -386.32430737867946, "u2y_km_s": -16.188750816948833, "speed2_km_s": 386.66334985957707, "signed_deflection_degrees": 2.39955066027249, "p2_over_p1": 2.50083308895446, "B2_over_B1": 1.5565264419493139, "entropy_over_cv": 0.1790830568818228, "upstream_fast_Mach": 1.4365462856404418, "downstream_fast_Mach": 0.7380350977723873, "downstream_alfven_margin": 0.6243405584570916, "state_global_normalized": { "rho": "1.55663200012553145502683694311262788903242454844157612644377531066172550544518158285714687", "p": "0.101433790087992891947622318599365593362780881538573445145202958873155547112864528104019627", "u": [ "-0.643873845631132498805132604902291211948983093919067175438788147143081866279368129020765817", "-0.0269812513615813864666519735493948344257247652350770458340459257388006296596286261137940885", "-0E-91" ], "B": [ "0.0755977312819481375729648708689531589585286561591171711141859117499124222261523097275967420", "1.00062089209503883944056784810407614235002544776729388625676637469681886030847949570453779", "0E-91" ] }, "root_record": { "r": "1.55663200012553145502683694311262788903242454844157612644377531066172550544518158285714687", "b": "0.0406789663699333552434714793169889362813125785642578579517869470146807812368456239429603454", "h": "0.000458218586200975259716392127137504529901643710579837572611871945053514313490984664901252028", "A": "0.416382334173656223640421658967261700475154075818396341164843260135091774377964001043652461", "denominator": "0.999286722285667282633671004557447466105871371703135215943267765259513007508817995323766857", "polynomial_residual": "6.91752962138767597031048E-66", "bracket_initial_signs": [ "1.45694167423962358761976388159004411188133867826168813306679054585436736906949516784958542", "-2.03474471474280325327227018451058157208028248520539330917251194820471152500296466388441874" ], "bracket_derivative_max": "-5.57085648431114474828631728556624468785984826612954970006743158083221569223035831677761311", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.02991649448666550914351642688807702570127855345332712705107269046740018942660710210668579E-90", "0E-91", "0E-182", "-5E-90", "0E-182", "-3.90498064361652155687754963386287143465159099937760619134183596578469295444191337684848490E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_-3.1", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.057920257582138715, 0.0 ], "rh_scaled_inf": 0.0, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.006495746491696277, "alfven_n": 0.017131973423074563, "fast": 0.8691626371378867 }, "right": { "slow": 0.007995199814662535, "alfven_n": 0.02137471678622557, "fast": 0.6950953688770589 } }, "front_relative_normal_velocity": { "left": -0.6414725318801662, "right": -0.9985366703262117 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5566320001255314, "pressure_ratio": 2.50083308895446, "entropy_over_cv": 0.1790830568818228, "tangential_field_ratio": 1.5570293167233802 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.075, "theta_Bn_degrees": 88.075, "compression": 1.5566757297020044, "u2x_km_s": -386.3046996915844, "u2y_km_s": -16.1571873137703, "speed2_km_s": 386.6424390903014, "signed_deflection_degrees": 2.3949990804980166, "p2_over_p1": 2.5010378324952005, "B2_over_B1": 1.5565673629818664, "entropy_over_cv": 0.17911810360483302, "upstream_fast_Mach": 1.4365826124863361, "downstream_fast_Mach": 0.7380216902267077, "downstream_alfven_margin": 0.6241125429041642, "state_global_normalized": { "rho": "1.55667572970200446447639084757220868743791405359305028885704334224843751194321028341179010", "p": "0.101442094486005329984395378308609857010575273567787438801679848208981270109528158877235126", "u": [ "-0.643841166152640692115919643687723553292665494275147161152528356876759628893431787490593270", "-0.0269286455229505031529498561608279174257883347910951360535413060547884943711859656400185242", "-0E-91" ], "B": [ "0.0754429492789555232275864756252296841465745773172290036679342683252097815642848060110432882", "1.00065903009936031430172014114673654235645910887787485901394175982662395444380120059227225", "0E-91" ] }, "root_record": { "r": "1.55667572970200446447639084757220868743791405359305028885704334224843751194321028341179010", "b": "0.0406770516200325487775644004939305084280661951502014197965597397025824313665235470090361569", "h": "0.000470329594843115957816545648678389574930799869106773906588143829377883084045012692880776867", "A": "0.416350602572893065473123654578594142324176016355189744003827345963702394293921985721070590", "denominator": "0.999267849334747144350379156057699333760074766062471082827900927409610366491310284948562600", "polynomial_residual": "-1.009015627800163934968775E-65", "bracket_initial_signs": [ "1.45711900789014371328276577422739800184016816437380714217287540106573956561354430260831028", "-2.03437374767416139815330475485236346014284565948227256611073427187715427131118314886186975" ], "bracket_derivative_max": "-5.57058473266294143762313765722188947323035228685736795428434362867374496565875741820681337", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-1E-91", "0E-182", "5E-90", "0E-182", "5.69664381923411016001952099300925596566014799315071456305183009164411764308091715278387762E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.075", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.057535316013502286, 0.0 ], "rh_scaled_inf": 6.571220362542659e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 3.566912307817246e-16, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -6.571220362542659e-16 }, "characteristics": { "left": { "slow": 0.006581179827881013, "alfven_n": 0.017357066053205823, "fast": 0.8691744666207863 }, "right": { "slow": 0.008100374673994402, "alfven_n": 0.02165585791593473, "fast": 0.6950941511655467 } }, "front_relative_normal_velocity": { "left": -0.6414696089573699, "right": -0.9985601716053734 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5566757297020044, "pressure_ratio": 2.5010378324952005, "entropy_over_cv": 0.17911810360483316, "tangential_field_ratio": 1.5570835988294889 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.05, "theta_Bn_degrees": 88.05000000000001, "compression": 1.556719189634556, "u2x_km_s": -386.285186550911, "u2y_km_s": -16.1256092100336, "speed2_km_s": 386.62162461645477, "signed_deflection_degrees": 2.390444262135806, "p2_over_p1": 2.501241395297563, "B2_over_B1": 1.556607977249777, "entropy_over_cv": 0.17915296156884458, "upstream_fast_Mach": 1.4366186988255285, "downstream_fast_Mach": 0.7380083636461663, "downstream_alfven_margin": 0.6238845246039131, "state_global_normalized": { "rho": "1.55671918963455601353764871462222318834519129919756228858722704362300224793316886571004329", "p": "0.101450350993269148878998227759339082737736453468391164846624425499019176403671856124045189", "u": [ "-0.643808644251518359009847073073450482395476058505793511241258843967913526461260525571665814", "-0.0268760153500559984964845231399120863798643397458129627474491818682408630807927389669589625", "-0E-91" ], "B": [ "0.0752881295190042437640475548800821934100680898530004880886538162100442129139763571695886126", "1.00069694791941890731637836843448492988720027718836397153953585479358933663421644444827159", "0E-91" ] }, "root_record": { "r": "1.55671918963455601353764871462222318834519129919756228858722704362300224793316886571004329", "b": "0.0406751524929026181221895791319937447570416729205847158429081182732949279806084537259800633", "h": "0.000482597994640865177376809469725921556048821888265350342676296917400176376355354869586514066", "A": "0.416318873668730420502402199430958724714278243323075705134795211081131349275566425326784672", "denominator": "0.999248730440863410555195061049556053609841676781010052771035888437717581686507803869638143", "polynomial_residual": "-6.34816090444662608599789E-66", "bracket_initial_signs": [ "1.45729471630350389536514388969690959102808607819448516503140246646917295193019107320692599", "-2.03400417797389029187710701480980367292902750364409487702164875979387659620487328396726297" ], "bracket_derivative_max": "-5.57031301410142120553059727101296524332860965819352330374782864834378650816268342210700207", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.02974339703516427560646427282909939346694022981224912829194964823859475139445012433919031E-90", "1E-91", "0E-182", "-1E-90", "0E-182", "3.58444896415341549418014960652025438987042026245145158132736667517269135624659651243845683E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-3.05", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05715036854047574, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.006666612185951908, "alfven_n": 0.017582150581862598, "fast": 0.8691861864770452 }, "right": { "slow": 0.00820554854738438, "alfven_n": 0.021936994922674237, "fast": 0.6950929175494795 } }, "front_relative_normal_velocity": { "left": -0.6414666751857756, "right": -0.9985834827727736 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.556719189634556, "pressure_ratio": 2.501241395297563, "entropy_over_cv": 0.17915296156884464, "tangential_field_ratio": 1.5571377502665773 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.025, "theta_Bn_degrees": 88.025, "compression": 1.556762379933709, "u2x_km_s": -386.26576796096583, "u2y_km_s": -16.09401657436313, "speed2_km_s": 386.6009064500115, "signed_deflection_degrees": 2.385886218172658, "p2_over_p1": 2.501443777044626, "B2_over_B1": 1.5566482847571557, "entropy_over_cv": 0.17918763072798818, "upstream_fast_Mach": 1.436654544651764, "downstream_fast_Mach": 0.7379951180141029, "downstream_alfven_margin": 0.623656503532606, "state_global_normalized": { "rho": "1.55676237993370885524919859912128922260802379159700167891348625869944991454850136718253921", "p": "0.101458559596930024771497461511303508954269848240207134154618095051327417892650848666994396", "u": [ "-0.643776279934942989469372477995765040968313911723857529001631697804039386526825745870151808", "-0.0268233609572718843009525205113947995307449966847792392290817964442032767517089885862742998", "-0E-91" ], "B": [ "0.0751332722320319370238395776305714636052627219055906898451331122656008562081673110911344078", "1.00073464553258962823905053886343948525618114227955969454779884997461219609020028856674851", "0E-91" ] }, "root_record": { "r": "1.55676237993370885524919859912128922260802379159700167891348625869944991454850136718253921", "b": "0.0406732689856386067328101456142256374475986877499056560926193510986986571506397866900603663", "h": "0.000495023768181471647954030357363700665199342970803781538579795325894500556279319407274399415", "A": "0.416287147448813722885571515159429924210629909550510505747727213762187408077648707420630053", "denominator": "0.999229365620522059617700166664043579846147495699954321276696224784387467176528945264850360", "polynomial_residual": "-3.72739355806182831937358E-66", "bracket_initial_signs": [ "1.45746879972152256454011850743656776772923905890075252663411576238169414449441078658061611", "-2.03363600541376613403011003115823499968219916401905402633102823071563149125666172826968851" ], "bracket_derivative_max": "-5.57004132859617803317563895437830762309951511540772888512271322064250090860229982294651457", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.02965914417567850779586277977132184339918686705532096175980503180970988381799708778971332E-90", "0E-91", "0E-182", "0E-90", "0E-182", "2.10490748872725714759103499366240204188035624523145763645655365396582977748498998778984791E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_-3.025", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.056765415200143124, 0.0 ], "rh_scaled_inf": 0.0, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.006752043565054859, "alfven_n": 0.017807227024974514, "fast": 0.8691977967059157 }, "right": { "slow": 0.008310721422019652, "alfven_n": 0.02221812775291956, "fast": 0.6950916680293733 } }, "front_relative_normal_velocity": { "left": -0.6414637305575805, "right": -0.9986066038239745 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.556762379933709, "pressure_ratio": 2.501443777044626, "entropy_over_cv": 0.17918763072798816, "tangential_field_ratio": 1.5571917710684564 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -3.0, "theta_Bn_degrees": 88.00000000000001, "compression": 1.5568053006098344, "u2x_km_s": -386.24644392606484, "u2y_km_s": -16.062409475392897, "speed2_km_s": 386.5802846029347, "signed_deflection_degrees": 2.3813249616047933, "p2_over_p1": 2.5016449774208596, "B2_over_B1": 1.5566882855081186, "entropy_over_cv": 0.17922211103660118, "upstream_fast_Mach": 1.4366901499587925, "downstream_fast_Mach": 0.7379819533139883, "downstream_alfven_margin": 0.6234284796665955, "state_global_normalized": { "rho": "1.55680530060983445189271278181157191698844100720850177362392402717786459642710120641329646", "p": "0.101466720284190070841996965641531976620721346113524440501788032394749136297591377525077532", "u": [ "-0.643744073210108117611019915298999658103759836684726709744124718228232187085815778151209168", "-0.0267706824589881627321770043615974876928862706756980559223743331215779877551846689224660099", "-0E-91" ], "B": [ "0.0749783776479808612692882029657124464259931499259525136076439768463235896329847840309579217", "1.00077212291636500158793787692862261983274004822106635127432931220896199737095152337032731", "0E-91" ] }, "root_record": { "r": "1.55680530060983445189271278181157191698844100720850177362392402717786459642710120641329646", "b": "0.0406714010953596512919155860744096970503401360309949381859732959224510964549519959902968743", "h": "0.000507606898294947846435741795825637520582058950761841913936142518759213946828197137776126434", "A": "0.416255423900792528215982476880380329901213109089529629419588010765998412156569442021508819", "denominator": "0.999209754890108308054846591540578730173476510364434354776776676116175738567718655800395962", "polynomial_residual": "6.29871558729941363974416E-66", "bracket_initial_signs": [ "1.45764125838526717284316475661053434661905458100367315594141049368591766771243650488019229", "-2.03326922976475543368222102295008813418419877067277151923230224106309080797606169638454994" ], "bracket_derivative_max": "-5.56976967611476868224285815586915052449993620328378096349921943383239988791027136562493398", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-3E-91", "0E-182", "2E-90", "0E-182", "-3.55740274315959882365624249422409579322808014155675805102051091295398615816114860797132693E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-3", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.056380456029602136, 0.0 ], "rh_scaled_inf": 1.7833110696709725e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7833110696709725e-16, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.006837473964326193, "alfven_n": 0.01803229539846172, "fast": 0.8692092973066724 }, "right": { "slow": 0.00841589328508708, "alfven_n": 0.022499256353146983, "fast": 0.6950904026057511 } }, "front_relative_normal_velocity": { "left": -0.6414607750650573, "right": -0.9986295347545738 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5568053006098344, "pressure_ratio": 2.50164497742086, "entropy_over_cv": 0.17922211103660135, "tangential_field_ratio": 1.5572456612686603 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.975, "theta_Bn_degrees": 87.975, "compression": 1.556847951673153, "u2x_km_s": -386.22721445053395, "u2y_km_s": -16.030787981766448, "speed2_km_s": 386.55975908717545, "signed_deflection_degrees": 2.376760505437816, "p2_over_p1": 2.5018449961121267, "B2_over_B1": 1.5567279795067883, "entropy_over_cv": 0.17925640244922772, "upstream_fast_Mach": 1.4367255147403695, "downstream_fast_Mach": 0.7379688695294235, "downstream_alfven_margin": 0.6232004529823187, "state_global_normalized": { "rho": "1.55684795167315294043318993780810155023396204942433133218925899468621199558336165126948970", "p": "0.101474833042307855014589220457802631014458093129749644761035728190148249942250250446732378", "u": [ "-0.643712024084223264316118482813673006813872944632728773143278166605767902847819975887721162", "-0.0267179799696107441105950752432061060096041569734128320848004386879555253477125614955493421", "-0E-91" ], "B": [ "0.0748234459967979170572701365878725529224111611176506507816100128006737711928239482423789230", "1.00080938004835507782776907493341513217557606519996720741663697737271477003678969079105077", "0E-91" ] }, "root_record": { "r": "1.55684795167315294043318993780810155023396204942433133218925899468621199558336165126948970", "b": "0.0406695488192089723316749333941741972035901112788773418372247543297751172184165521291629816", "h": "0.000520347368053993338975869275556580226432062314715221273363969078768228833022739081512690505", "A": "0.416223703012320494090680093269967248840505371429735386548388012388803339133722640649795355", "denominator": "0.999189898265886624251995552541027941996121575135305547036133065398528528085790064310719731", "polynomial_residual": "7.04814158466594310558664E-66", "bracket_initial_signs": [ "1.45781209253505414627419852620928066710571112207640654771248455628164522858332077581333875", "-2.03290385079701584797073019714542450369801910969289127042115026666073343987784667103676881" ], "bracket_derivative_max": "-5.56949805662271379077490774249363521108495110136819647578959250700080757212242914305504358", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.02949522978794422095145610757767905532826779698345945303126848432548129484908649310012965E-90", "-1E-91", "0E-182", "4E-90", "0E-182", "-3.98115344675637270531176133666121686690573124862817529899804104911970470513528679315278236E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.975", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.055995491065963986, 0.0 ], "rh_scaled_inf": 2.1900998856737358e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1900998856737358e-16 }, "characteristics": { "left": { "slow": 0.006922903382892739, "alfven_n": 0.01825735571823498, "fast": 0.8692206882786105 }, "right": { "slow": 0.008521064123773198, "alfven_n": 0.022780380669833587, "fast": 0.6950891212791419 } }, "front_relative_normal_velocity": { "left": -0.6414578087005537, "right": -0.9986522755602062 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.556847951673153, "pressure_ratio": 2.5018449961121267, "entropy_over_cv": 0.1792564024492277, "tangential_field_ratio": 1.5572994209004447 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.95, "theta_Bn_degrees": 87.95, "compression": 1.5568903331337332, "u2x_km_s": -386.2080795387083, "u2y_km_s": -15.999152162136818, "speed2_km_s": 386.53932991467303, "signed_deflection_degrees": 2.3721928626866813, "p2_over_p1": 2.502043832805681, "B2_over_B1": 1.5567673667572945, "entropy_over_cv": 0.17929050492061838, "upstream_fast_Mach": 1.4367606389902554, "downstream_fast_Mach": 0.7379558666441407, "downstream_alfven_margin": 0.6229724234562971, "state_global_normalized": { "rho": "1.55689033313373309810952093206721743792299947649702589195846046907599443982827021380091723", "p": "0.101482897858598417616665814701447127112166186855936947510498151596923997579050264666719876", "u": [ "-0.643680132564513880357122235274294314276929338534014676273031064017637089518540020476572012", "-0.0266652536035613646965475390759741105597296118922857852542652657149573786060142234284395694", "-0E-91" ], "B": [ "0.0746684775084346690606288827034554899882868998144350731325116818872794521082520300621781587", "1.00084641690628744436683468261518283756948987886013323610213947807832539905342839328211106", "0E-91" ] }, "root_record": { "r": "1.55689033313373309810952093206721743792299947649702589195846046907599443982827021380091723", "b": "0.0406677121543538649358508430446885400201010072482569746013321717211126555297826400114680089", "h": "0.000533245160773918921703577472463222256248620882047243211355346666882219563079880119819844514", "A": "0.416191984771055360691480336331403945120854545198579327662552713178492590979223380279375895", "denominator": "0.999169795764000742304871710579576903903051085297648041706634830126952103346141401352304668", "polynomial_residual": "5.13864238558981543468025E-66", "bracket_initial_signs": [ "1.45798130241044884203479865813126777831571815365291978341217320261258979127276664145759461", "-2.03253986827989700710957544571947897257962634438315502869281358305795567284331687833168353" ], "bracket_derivative_max": "-5.56922647008349895470826449347683137196507404242526045610148311182850167670073566486118358", "iterations": 216 }, "flux_residuals": [ "-2E-90", "-8.02941556810355824450582566439131427963483477259976550207518806590256264554462206188872451E-90", "0E-91", "0E-182", "7E-90", "0E-182", "-2.90292582420237237242678234003677381055164016547954646789313094645052239495971372913742047E-67", "3E-91" ], "diagnosis": { "case_id": "R95_phi_-2.95", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.055610520346353304, 0.0 ], "rh_scaled_inf": 2.1900259724643199e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 1.7832182018671583e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1900259724643199e-16 }, "characteristics": { "left": { "slow": 0.007008331819871898, "alfven_n": 0.018482408000195783, "fast": 0.8692319696210467 }, "right": { "slow": 0.008626233925264203, "alfven_n": 0.023061500649457275, "fast": 0.695087824050082 } }, "front_relative_normal_velocity": { "left": -0.641454831456493, "right": -0.9986748262365419 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5568903331337332, "pressure_ratio": 2.502043832805681, "entropy_over_cv": 0.17929050492061827, "tangential_field_ratio": 1.5573530499967876 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.925, "theta_Bn_degrees": 87.925, "compression": 1.5569324450014923, "u2x_km_s": -386.1890391949328, "u2y_km_s": -15.967502085166503, "speed2_km_s": 386.518997097355, "signed_deflection_degrees": 2.3676220463756574, "p2_over_p1": 2.5022414871901697, "B2_over_B1": 1.5568064472637728, "entropy_over_cv": 0.17932441840573002, "upstream_fast_Mach": 1.4367955227022156, "downstream_fast_Mach": 0.7379429446420019, "downstream_alfven_margin": 0.6227443910651368, "state_global_normalized": { "rho": "1.55693244500149230817514751393468507864530122489734048160355684345302489588270648336114740", "p": "0.101490914720433288993627647440913525072519730377136060343546580367391515864866930129267469", "u": [ "-0.643648398658221290019276761019531499957143358880313565894305398063124898537976403085098458", "-0.0266125034752775044681900433920001445559457155421790936422463545961480717851251120056898331", "-0E-91" ], "B": [ "0.0745134724128473678380651085777598348236944912060714913012736797342916791105112210938450140", "1.00088323346800723636819080200041427440548161482939515743306125196607629153578348774555031", "0E-91" ] }, "root_record": { "r": "1.55693244500149230817514751393468507864530122489734048160355684345302489588270648336114740", "b": "0.0406658910979856895209225381673541164924104923866126659840685157731227297558767251695378506", "h": "0.000546300260012571559737818361161644386907781857667186004494783966875749001065315338219588834", "A": "0.416160269164658931379400753824887086423694643349705610157086416255812661810336631390662274", "denominator": "0.999149447400473675982415832926948464781311824017358678278507959301071163823517146519155462", "polynomial_residual": "-1.372085564152033891989283E-65", "bracket_initial_signs": [ "1.45814888825026551039456996754316912781415906444984681986006390958621806653858724995394397", "-2.03217728198194132583752084905209146183556074164770278715322196344109589774160266642313035" ], "bracket_derivative_max": "-5.56895491645857579511680950826516416637615011541531506780780598254820205475273886554963362", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.02933743665716738418309251410624459377560663754290858338431975919893464969979564283647162E-90", "-1E-91", "0E-182", "2E-90", "0E-182", "7.75214651429560808177904265066520970914246066584207962675786882591910941188988005048017375E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-2.925", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05522554390790797, 0.0 ], "rh_scaled_inf": 2.1899531838742768e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7831729242148554e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1899531838742768e-16 }, "characteristics": { "left": { "slow": 0.007093759274371692, "alfven_n": 0.01870745226023644, "fast": 0.8692431413333189 }, "right": { "slow": 0.008731402676745957, "alfven_n": 0.023342616238496764, "fast": 0.6950865109191139 } }, "front_relative_normal_velocity": { "left": -0.6414518433253733, "right": -0.9986971867792875 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5569324450014923, "pressure_ratio": 2.5022414871901697, "entropy_over_cv": 0.17932441840573, "tangential_field_ratio": 1.5574065485903887 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.9, "theta_Bn_degrees": 87.9, "compression": 1.5569742872861965, "u2x_km_s": -386.1700934235616, "u2y_km_s": -15.935837819527382, "speed2_km_s": 386.4987606471365, "signed_deflection_degrees": 2.363048069538288, "p2_over_p1": 2.5024379589556336, "B2_over_B1": 1.5568452210303652, "entropy_over_cv": 0.1793581428597258, "upstream_fast_Mach": 1.4368301658700207, "downstream_fast_Mach": 0.7379301035070002, "downstream_alfven_margin": 0.6225163557855281, "state_global_normalized": { "rho": "1.55697428728619652578858537385642023453701188764087545522614456283820138707138028841472182", "p": "0.101498883615240507079035114682509862056933380094863621534954438894131647442167552436797992", "u": [ "-0.643616822372602635217400742928133809475347344264375371887706446064184006717119186081632181", "-0.0265597296992123048918446894040162521917093123206306954418062718853068502903130046752084073", "-0E-91" ], "B": [ "0.0743584309399969715532771270558027916859245161052802417521718820316659722320978116702167166", "1.00091982971147714737500086672774483786251749734179130630169856379849796389684101537552797", "0E-91" ] }, "root_record": { "r": "1.55697428728619652578858537385642023453701188764087545522614456283820138707138028841472182", "b": "0.0406640856473198626963660574098711066867301741868604331143940084860869468188966814934708086", "h": "0.000559512649570260124044666324539304969752881119758966468446948083202807856089151378447483394", "A": "0.416128556180797053302379372503576520668555243242109827901644428526362880666184995680642226", "denominator": "0.999128853191207732810519249410411092770177603462931774810580371899694146478756955823736930", "polynomial_residual": "4.32368195845886923804889E-66", "bracket_initial_signs": [ "1.45831485029256726118082227421119068568206253022764237814646028938981313536162269270234375", "-2.03181609167088480131867277386852988127418592805229419365629969351115299232871630899507540" ], "bracket_derivative_max": "-5.56868339570736301117555471830649879092057019204206662693727236261733368120111377434484017", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "2E-91", "0E-182", "-1E-90", "0E-182", "-2.44313652920504417260587080323787209039500609765071591127726416019884512648799389376292389E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-2.9", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.054840561787779046, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.007179185745490843, "alfven_n": 0.018932488514240196, "fast": 0.8692542034147864 }, "right": { "slow": 0.008836570365403982, "alfven_n": 0.02362372738343162, "fast": 0.6950851818867875 } }, "front_relative_normal_velocity": { "left": -0.6414488442997683, "right": -0.9987193571841863 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5569742872861965, "pressure_ratio": 2.502437958955634, "entropy_over_cv": 0.17935814285972584, "tangential_field_ratio": 1.5574599167136711 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.875, "theta_Bn_degrees": 87.875, "compression": 1.5570158599974602, "u2x_km_s": -386.1512422289585, "u2y_km_s": -15.904159433900693, "speed2_km_s": 386.47862057592096, "signed_deflection_degrees": 2.3584709452173582, "p2_over_p1": 2.502633247793507, "B2_over_B1": 1.5568836880612207, "entropy_over_cv": 0.17939167823797478, "upstream_fast_Mach": 1.4368645684874466, "downstream_fast_Mach": 0.7379173432232586, "downstream_alfven_margin": 0.6222883175942454, "state_global_normalized": { "rho": "1.55701585999746024405358521569500570556650656749364528752566660279361946718094036597554102", "p": "0.101506804530504634920238398801024965673349256108534000475156370320242993017563343909782789", "u": [ "-0.643585403714930820107553834202892654079563025228869315248456416254415990350109372316165591", "-0.0265069323898344866846113685085386415376636040539685479170352892165555243868278636783958635", "-0E-91" ], "B": [ "0.0742033533198491676441267957276116373221008693574964399022278851573780706328391734507555270", "1.00095620561477743974998389670286751531645022234081821055052715548901275470774260693247228", "0E-91" ] }, "root_record": { "r": "1.55701585999746024405358521569500570556650656749364528752566660279361946718094036597554102", "b": "0.0406622957995958482040406877146730681641172339705337376913196483158046237731241387740471743", "h": "0.000572882313489681925679049200645861438811687722526668571668417389586239548367567319833042122", "A": "0.416096845807139598016216475085664656156667424192301985996912339513960348622874231155592664", "denominator": "0.999108013151984528276624660403146707932926823330735718408229273477486050736706655058624131", "polynomial_residual": "-5.80768621238850151109817E-66", "bracket_initial_signs": [ "1.45847918877466603488581116815467123931445289515939601522225798706961219060363151379186079", "-2.03145629711365779750862337430241302753389937443157681302621613343912213371916870005608520" ], "bracket_derivative_max": "-5.56841190778724741885672781194298989830043290176426741079533507220312435425757187407939477", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.02918576418215005484499156837852530738519237084469176269559751513002431910956495360635386E-90", "-1E-91", "0E-182", "-5E-90", "0E-182", "3.28208894356803077226139368158781575512558372849994750794999947163041819290129307719630265E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.875", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.054455574023130615, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": -0.0, "energy": -2.189810980007384e-16 }, "characteristics": { "left": { "slow": 0.007264611232318837, "alfven_n": 0.019157516778081324, "fast": 0.8692651558648293 }, "right": { "slow": 0.008941736978423452, "alfven_n": 0.023904834030742245, "fast": 0.6950838369536583 } }, "front_relative_normal_velocity": { "left": -0.6414458343723267, "right": -0.9987413374470168 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5570158599974602, "pressure_ratio": 2.502633247793507, "entropy_over_cv": 0.17939167823797486, "tangential_field_ratio": 1.5575131543987795 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.85, "theta_Bn_degrees": 87.85000000000001, "compression": 1.5570571631447465, "u2x_km_s": -386.13248561549665, "u2y_km_s": -15.87246699697696, "speed2_km_s": 386.4585768955993, "signed_deflection_degrees": 2.3538906864648554, "p2_over_p1": 2.5028273533966168, "B2_over_B1": 1.5569218483604945, "entropy_over_cv": 0.17942502449605205, "upstream_fast_Mach": 1.436898730548274, "downstream_fast_Mach": 0.737904663775031, "downstream_alfven_margin": 0.6220602764681473, "state_global_normalized": { "rho": "1.55705716314474646020870768784613371156613732929562468363086874756509233715885941020303321", "p": "0.101514677453766778159527800218344310609557472477434792676456556101169922224267282035959335", "u": [ "-0.643554142692494456193365184455850026099497408409200719801059848762460321226786659189121656", "-0.0264541116616282675690582164759542365495810882968704173845299745722764455811001727367832062", "-0E-91" ], "B": [ "0.0740482397823743944426059301593073695333453246368568895165222207354530833176051043916107492", "1.00099236115610595492893723076829789251088632038141599135379587470578967819940145379681756", "0E-91" ] }, "root_record": { "r": "1.55705716314474646020870768784613371156613732929562468363086874756509233715885941020303321", "b": "0.0406605215520771479366309124998681246170506696929865118412068559019358826499394628827800478", "h": "0.000586409236055850046957002986140230463440793531757302977026878769347763679703873486882532116", "A": "0.416065138031360442118673908296975297759177358933502516171650726573178252178211359967807872", "denominator": "0.999086927298465000155178935375041270390455638337850388901677733586541491564966944391080313", "polynomial_residual": "1.464295593864969290205975E-65", "bracket_initial_signs": [ "1.45864190393312257838585667388981978095795035698793470085867807314296995988879487058937393", "-2.03109789807638581599937750029275093453948811769318857579611602812559356986443812668064455" ], "bracket_derivative_max": "-5.56814045265358497537030814841103946279121156437998933764050088626497348795388633900028799", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.02911222300906084897561232791249747663313357806420298270012678872468481324836034876328229E-90", "-2E-91", "0E-182", "-2E-90", "0E-182", "-8.27616519365945683948156512375572107143712347360564722839550811575155707908866936823845993E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-2.85", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05407058065113969, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.007350035733935981, "alfven_n": 0.01938253706762525, "fast": 0.8692759986828499 }, "right": { "slow": 0.0090469025029892, "alfven_n": 0.024185936126909904, "fast": 0.6950824761202892 } }, "front_relative_normal_velocity": { "left": -0.6414428135357726, "right": -0.9987631275635946 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5570571631447465, "pressure_ratio": 2.5028273533966168, "entropy_over_cv": 0.1794250244960519, "tangential_field_ratio": 1.5575662616775814 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.825, "theta_Bn_degrees": 87.825, "compression": 1.5570981967373667, "u2x_km_s": -386.11382358755867, "u2y_km_s": -15.840760577455969, "speed2_km_s": 386.4386296180503, "signed_deflection_degrees": 2.349307306341936, "p2_over_p1": 2.5030202754591864, "B2_over_B1": 1.5569597019323484, "entropy_over_cv": 0.17945818158973836, "upstream_fast_Mach": 1.4369326520462893, "downstream_fast_Mach": 0.737892065146701, "downstream_alfven_margin": 0.6218322323841763, "state_global_normalized": { "rho": "1.55709819673736664196609020550358518677976256576272025134925810085643535397823718283261407", "p": "0.101522502372624602470843872330616558616503166086381077055992910298806496064627672726614345", "u": [ "-0.643523039312597807926799954104709982620699375210104702796026385861616676594731316024244134", "-0.0264012676290932800198107197297405799008890879047084815558131104653367851031632796499775858", "-0E-91" ], "B": [ "0.0738930905575478627463781327166150533938446679040131050719352311044771081685338738654354071", "1.00102829631377812348830135207603306187889711507946682487678772313854289267137314535745621", "0E-91" ] }, "root_record": { "r": "1.55709819673736664196609020550358518677976256576272025134925810085643535397823718283261407", "b": "0.0406587629020512930350936534824049998410695562354428956520653215961475813279750769560051958", "h": "0.000600093401796021469109092632531080597859918256059508422621757000832735618728136199305348737", "A": "0.416033432841137447896666653341337184869090974003988641686385251654943490724909225752718947", "denominator": "0.999065595646189422953924622058985642693029672549249051964382806935486042396856033334928052", "polynomial_residual": "1.632450265701380594999587E-65", "bracket_initial_signs": [ "1.45880299600374642526672632069939130808025249484673844871088548916110951045571288215162791", "-2.03074089432439025335608538701455232548598737504908476816667792477008860931218825121418302" ], "bracket_derivative_max": "-5.56786903025970178936098664920121285208929747146196826775362708026634514482822650651685280", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.02904021178504094970082835130386844351796283337393568610726593786122529782514350301075426E-90", "1E-91", "0E-182", "1E-90", "0E-182", "-9.22770140843951537199120661598820480490228334171334959303983322376211506123552273625275024E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_-2.825", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.053685581708996066, 0.0 ], "rh_scaled_inf": 2.1896732730043096e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7829995200215517e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1896732730043096e-16 }, "characteristics": { "left": { "slow": 0.007435459249413475, "alfven_n": 0.019607549398728618, "fast": 0.8692867318682709 }, "right": { "slow": 0.009152066926285694, "alfven_n": 0.024467033618416723, "fast": 0.6950810993872498 } }, "front_relative_normal_velocity": { "left": -0.6414397817829048, "right": -0.9987847275297711 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5570981967373667, "pressure_ratio": 2.5030202754591864, "entropy_over_cv": 0.17945818158973825, "tangential_field_ratio": 1.557619238581666 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.8, "theta_Bn_degrees": 87.80000000000001, "compression": 1.5571389607844808, "u2x_km_s": -386.09525614953645, "u2y_km_s": -15.809040244046694, "speed2_km_s": 386.4187787551403, "signed_deflection_degrees": 2.344720817918886, "p2_over_p1": 2.503212013676833, "B2_over_B1": 1.5569972487809507, "entropy_over_cv": 0.1794911494750201, "upstream_fast_Mach": 1.436966332975283, "downstream_fast_Mach": 0.7378795473227832, "downstream_alfven_margin": 0.6216041853193586, "state_global_normalized": { "rho": "1.55713896078448069399918588499220985845671550918104031350219616050173203910472596161847627", "p": "0.101530279274732350952086942501851852604671555789843551561722474829387542340874141538795596", "u": [ "-0.643492093582560738803144155396727655278630903608037091553994639550369824595124669726318040", "-0.0263484004067444890018591457800779888612698781449701088702713938893868185409118591393775453", "-0E-91" ], "B": [ "0.0737379058753495773426707479716901252734311618378275276290657969038195538421705949187250301", "1.00106401106622697502673403303508933198186840505758971000544458166743909258419054377642895", "0E-91" ] }, "root_record": { "r": "1.55713896078448069399918588499220985845671550918104031350219616050173203910472596161847627", "b": "0.0406570198468298350650610317730846858451018781839729294330052222099289697686086485207129499", "h": "0.000613934795479625995970152066484249463683741329537102783487897004275498849224558710067400372", "A": "0.416001730224152443986481463797823636804037581154157975060719564075388039413580411401278109", "denominator": "0.999044018210577422481017967969504563372010686040119498798983756306620020079114727856565553", "polynomial_residual": "-3.75791360245952951747463E-66", "bracket_initial_signs": [ "1.45896246522159588074973937277480637939766218110862353432620819178087093403288194470619282", "-2.03038528562218914495847004088450751051176614162759127350574339301118810382997427461741285" ], "bracket_derivative_max": "-5.56759764055689511687340321164262038277640029450570609042701852604921609193031806589859319", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "3E-91", "0E-182", "3E-90", "0E-182", "2.12448432438808398175132135865181560544382328887930231067679981990611270910905570035292618E-67", "3E-91" ], "diagnosis": { "case_id": "R95_phi_-2.8", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05330057723390226, 0.0 ], "rh_scaled_inf": 4.379212211003904e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7829580951810149e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -4.379212211003904e-16 }, "characteristics": { "left": { "slow": 0.0075208817778134795, "alfven_n": 0.01983255378723944, "fast": 0.8692973554205364 }, "right": { "slow": 0.009257230235497052, "alfven_n": 0.02474812645174571, "fast": 0.695079706755116 } }, "front_relative_normal_velocity": { "left": -0.6414367391065979, "right": -0.9988061373414341 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5571389607844808, "pressure_ratio": 2.503212013676833, "entropy_over_cv": 0.17949114947501998, "tangential_field_ratio": 1.557672085142346 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.775, "theta_Bn_degrees": 87.77499999999999, "compression": 1.5571794552950968, "u2x_km_s": -386.0767833058312, "u2y_km_s": -15.777306065467265, "speed2_km_s": 386.3990243187231, "signed_deflection_degrees": 2.340131234275088, "p2_over_p1": 2.5034025677465697, "B2_over_B1": 1.557034488910476, "entropy_over_cv": 0.17952392810808906, "upstream_fast_Mach": 1.4369997733290518, "downstream_fast_Mach": 0.7378671102879216, "downstream_alfven_margin": 0.6213761352508042, "state_global_normalized": { "rho": "1.55717945529509692457925699908844746169360238480772828899687815121433800742620922259143047", "p": "0.101538008147800861473065424001917970044906576655983803363768160460629736278689745045471332", "u": [ "-0.643461305509718657949991156465959542252983413248254687716358032741257566192248407858079536", "-0.0262955101091121097004041040560810540594559355994155034810882873621461723573692936719122325", "-0E-91" ], "B": [ "0.0735826859657643584852914705038849724980921618245306406805125034422568255334464616729812190", "1.00109950539200314786066063906149792485183329309142388303972694647019365852495354576822034", "0E-91" ] }, "root_record": { "r": "1.55717945529509692457925699908844746169360238480772828899687815121433800742620922259143047", "b": "0.0406552923837483372721493208271496084931206860253366763478593578922911390698910258171606241", "h": "0.000627933402118195973265003277713066187779240799172042696270633484742396727144461398130801889", "A": "0.415970030168091206046957449205471165855166130240324953403722551639367258775537166059460431", "denominator": "0.999022195006927990532962338091159479684934597974090895079669095147284423098911074762254635", "polynomial_residual": "-3.43831581767700414287378E-66", "bracket_initial_signs": [ "1.45912031182097801121311912372045472945198482111106059040703625727364338351947346406731148", "-2.03003107173349789535970495039090736558574998333711846201885137996085633433597678479591417" ], "bracket_derivative_max": "-5.56732628349443434309739588929493898080275185166879152618291751508231407065300518277394807", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-3E-91", "0E-182", "2E-90", "0E-182", "1.94404206285834688025234802130786258789003623554162646389921890758605294326352252376954904E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-2.775", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.052915567263073296, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.0076063033181891695, "alfven_n": 0.020057550248997164, "fast": 0.869307869339113 }, "right": { "slow": 0.009362392417807031, "alfven_n": 0.025029214573380757, "fast": 0.6950782982244705 } }, "front_relative_normal_velocity": { "left": -0.6414336854998014, "right": -0.9988273569945072 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5571794552950968, "pressure_ratio": 2.5034025677465697, "entropy_over_cv": 0.17952392810808926, "tangential_field_ratio": 1.5577248013906568 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.75, "theta_Bn_degrees": 87.75, "compression": 1.557219680278072, "u2x_km_s": -386.0584050608535, "u2y_km_s": -15.745558110444916, "speed2_km_s": 386.37936632064014, "signed_deflection_degrees": 2.3355385684989804, "p2_over_p1": 2.5035919373668043, "B2_over_B1": 1.5570714223251054, "entropy_over_cv": 0.17955651744534237, "upstream_fast_Mach": 1.4370329731013969, "downstream_fast_Mach": 0.7378547540268913, "downstream_alfven_margin": 0.6211480821557069, "state_global_normalized": { "rho": "1.55721968027807201236040754969008739965483194663629588992602373836069645580774755101364748", "p": "0.101545688979597583979122146067618090578729127089949690115142476778539022956643345693511633", "u": [ "-0.643430675101422467210016180736341629788580872498050278970996781974778030222678450904057637", "-0.0262425968507415252420601740786574288970129237482992092190187370999352063363195408746454308", "-0E-91" ], "B": [ "0.0734274310587818633255439510769095630182698773459484160188964892410141270403738947675647140", "1.00113477926977489853376704287836358600596293149384283034231990861674026931421113092866749", "0E-91" ] }, "root_record": { "r": "1.55721968027807201236040754969008739965483194663629588992602373836069645580774755101364748", "b": "0.0406535805101663659161252103663820073269658375777977249329305747722269477951224486522656723", "h": "0.000642089206965296803054317086546331110162538088241235762200094676657238819625057837497024268", "A": "0.415938332660643437445563555477917777698926454531932435992253372728087730944778221252393742", "denominator": "0.999000126050419499703346995029902494245889274252795086682656678058350211234944250778794019", "polynomial_residual": "4.13117843560131366049684E-66", "bracket_initial_signs": [ "1.45927653603544863830319021577375863388301199834854938335828161901774151868410168512138977", "-2.02967825242122999517536463208361728655462155613034840383038388093863514310096633709949186" ], "bracket_derivative_max": "-5.56705495901956194990487692531274623006639647124881990221128727107043403577260506533371642", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "2E-91", "0E-182", "-2E-90", "0E-182", "-2.33607609296558300595572840419930182231457379560308329842623555938736582314094879057633936E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-2.75", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05253055183373666, 0.0 ], "rh_scaled_inf": 2.1894751418645454e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1894751418645454e-16 }, "characteristics": { "left": { "slow": 0.007691723869584804, "alfven_n": 0.02028253879983278, "fast": 0.8693182736234869 }, "right": { "slow": 0.009467553460399016, "alfven_n": 0.025310297929806654, "fast": 0.6950768737959029 } }, "front_relative_normal_velocity": { "left": -0.6414306209555397, "right": -0.9988483864849507 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.557219680278072, "pressure_ratio": 2.5035919373668043, "entropy_over_cv": 0.1795565174453423, "tangential_field_ratio": 1.557777387357356 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.725, "theta_Bn_degrees": 87.725, "compression": 1.557259635742111, "u2x_km_s": -386.0401214190231, "u2y_km_s": -15.713796447715923, "speed2_km_s": 386.35980477272005, "signed_deflection_degrees": 2.3309428336880242, "p2_over_p1": 2.5037801222373424, "B2_over_B1": 1.5571080490290268, "entropy_over_cv": 0.17958891744338232, "upstream_fast_Mach": 1.4370659322861246, "downstream_fast_Mach": 0.7378424785245967, "downstream_alfven_margin": 0.6209200260113438, "state_global_normalized": { "rho": "1.55725963574211097331294174109406500463131704662110604627223672378821786767774442546678924", "p": "0.101553321757946597750477751804758186386830335249960730007105773247572985129771991010443681", "u": [ "-0.643400202365038508717328127740267572112484718677635904311954572904075292238121307595462655", "-0.0261896607461932044072376651354372847317365095739973067874916303626716134470393548859148304", "-0E-91" ], "B": [ "0.0732721413843966072978165726954563710373932979991839885520008062038564760696020405950717448", "1.00116983267832811114040121379083720241551222521807009114131175080921622811167113038625840", "0E-91" ] }, "root_record": { "r": "1.55725963574211097331294174109406500463131704662110604627223672378821786767774442546678924", "b": "0.0406518842234674816838809465028070012627966483326951314451068498900751276422151371534310047", "h": "0.000656402195516458252909277067264747670073246073984965179726845857594740226801413432359065175", "A": "0.415906637689502749957307965793163644356866146740741007595410018906340419321710852757189799", "denominator": "0.998977811356109718312382290788614157594439698249947441859699019339959376318279677301685849", "polynomial_residual": "1.90996577254842754250408E-66", "bracket_initial_signs": [ "1.45943113809781233763008790616539145217702850189827085943931732534463648417775305067895880", "-2.02932682744749772451493757204142839816096611626366349426931756243246382576672913537988894" ], "bracket_derivative_max": "-5.56678366707749446918983170714893460789277259559950491937750955481505340171319704581756050", "iterations": 216 }, "flux_residuals": [ "2E-90", "8.02876746502984355465215480102435359197143864119870823085598227343327727067292558147710573E-90", "0E-91", "0E-182", "-3E-90", "0E-182", "-1.08016908086014415068668956718076466811395577577301358390962131098061403283618302858749263E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-2.725", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05214553098313217, 0.0 ], "rh_scaled_inf": 2.1894113454833996e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1894113454833996e-16 }, "characteristics": { "left": { "slow": 0.007777143431035798, "alfven_n": 0.02050751945556895, "fast": 0.8693285682731671 }, "right": { "slow": 0.009572713350456025, "alfven_n": 0.025591376467509093, "fast": 0.695075433470009 } }, "front_relative_normal_velocity": { "left": -0.6414275454669127, "right": -0.9988692258087608 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.557259635742111, "pressure_ratio": 2.5037801222373424, "entropy_over_cv": 0.17958891744338246, "tangential_field_ratio": 1.5578298430729234 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.7, "theta_Bn_degrees": 87.7, "compression": 1.5572993216957671, "u2x_km_s": -386.0219323847691, "u2y_km_s": -15.682021146025571, "speed2_km_s": 386.3403396867788, "signed_deflection_degrees": 2.326344042948662, "p2_over_p1": 2.503967122059384, "B2_over_B1": 1.5571443690264346, "entropy_over_cv": 0.17962112805901617, "upstream_fast_Mach": 1.4370986508770467, "downstream_fast_Mach": 0.7378302837660728, "downstream_alfven_margin": 0.6206919667950752, "state_global_normalized": { "rho": "1.55729932169576712780483732350600758147801195785420325819186478353708821340515283719026268", "p": "0.101560906470728628617330036424717844827875543416521620601628014044897404745513080068098064", "u": [ "-0.643369887307948512967191033063783928409160796765168989496050912028262466248379889684519116", "-0.0261367019100426193335226953630848580839055985320192346805235019874853145399823742665026303", "-0E-91" ], "B": [ "0.0731168171726079854606183989105343677358989757006322792362356554690189421946025025598513890", "1.00120466559656630646284915918811549930890389439950360443799584294103437556196321008031046", "0E-91" ] }, "root_record": { "r": "1.55729932169576712780483732350600758147801195785420325819186478353708821340515283719026268", "b": "0.0406502035210592311811703589940935150126216155831259211805428584132196741709956798909440253", "h": "0.000670872353509106559388203101742284494742964285699007587628645886252056180659533254514262468", "A": "0.415874945242366644476414517727977205383903552638164017957800941110074823892835818514384630", "denominator": "0.998955250938935825457223402585671816013096888890084767034811995831846440208700602785724023", "polynomial_residual": "3.3915326979498085801484E-67", "bracket_initial_signs": [ "1.45958411824012244204271607230656540605061101662407843037662109071947398149875126094423317", "-2.02897679657361284296825833952870427986074866703343421772885509899149116473369279230794330" ], "bracket_derivative_max": "-5.56651240761142342202281783254636671420046228290141965124929842826031995624385656782355494", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "2E-91", "0E-182", "-1E-90", "0E-182", "-1.91829448526097532527123702050027188384708863620871866091897972310648623236207172224376978E-68", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.7", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05176050474851182, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.007862562001568782, "alfven_n": 0.02073249223202009, "fast": 0.8693387532876833 }, "right": { "slow": 0.009677872075160705, "alfven_n": 0.025872450132974695, "fast": 0.695073977247392 } }, "front_relative_normal_velocity": { "left": -0.6414244590270953, "right": -0.99888987496197 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5572993216957671, "pressure_ratio": 2.503967122059384, "entropy_over_cv": 0.1796211280590161, "tangential_field_ratio": 1.5578821685675626 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.675, "theta_Bn_degrees": 87.67500000000001, "compression": 1.5573387381474422, "u2x_km_s": -386.0038379625297, "u2y_km_s": -15.650232274128099, "speed2_km_s": 386.3209710746196, "signed_deflection_degrees": 2.3217422093962883, "p2_over_p1": 2.504152936535529, "B2_over_B1": 1.557180382321529, "entropy_over_cv": 0.17965314924925616, "upstream_fast_Mach": 1.43713112886798, "downstream_fast_Mach": 0.7378181697364847, "downstream_alfven_margin": 0.6204639044843453, "state_global_normalized": { "rho": "1.55733873814744206783112496225084981484976135074798386138071940490475359814398479211966382", "p": "0.101568443105881066130747921318901556858092932491335393048063174158121566231533681770111605", "u": [ "-0.643339729937549547378910474688786875488273783876965575081549259668010647826880304389120909", "-0.0260837204568801632098758984133184783751958102392123604293958279371696041307141194932443823", "-0E-91" ], "B": [ "0.0729614586534202937938361329513387906811200844577603504409902390393698311906602696813762146", "1.00123927800351065092245050849466026802006818201866281400376357074769153909497295297828530", "0E-91" ] }, "root_record": { "r": "1.55733873814744206783112496225084981484976135074798386138071940490475359814398479211966382", "b": "0.0406485384003731385030582318504429096788272228411880111666818081609339564665341731706374917", "h": "0.000685499666922497325392782209808499231462597064117090620992882390820047647408657533421218174", "A": "0.415843255306936491740701304152969433356032229775458089775388046104932683775664854065509802", "denominator": "0.998932444813714426183075828779816166478265817114517632058013355208819755998964279660987570", "polynomial_residual": "-5.0479086507700487353201E-67", "bracket_initial_signs": [ "1.45973547669368104947776052492758154315375735771260293571576021423667100600626813029998433", "-2.02862815956008726615908303088156737998456872365089945501120132326674819147449101790250644" ], "bracket_derivative_max": "-5.56624118056251624363122273649123962535467301369384850782530681051788251118029664745438081", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-1E-91", "0E-182", "-2E-90", "0E-182", "2.85551112442254436798485355903993370840575133253439447492383584122043604504275970145278070E-68", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.675", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05137547316713971, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7827625244572338e-16, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.00794797958020166, "alfven_n": 0.020957457144992475, "fast": 0.8693488286665865 }, "right": { "slow": 0.00978302962169532, "alfven_n": 0.026153518872690996, "fast": 0.6950725051286607 } }, "front_relative_normal_velocity": { "left": -0.6414213616293377, "right": -0.998910333940647 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5573387381474422, "pressure_ratio": 2.504152936535529, "entropy_over_cv": 0.1796531492492559, "tangential_field_ratio": 1.5579343638711995 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.65, "theta_Bn_degrees": 87.65, "compression": 1.5573778851053857, "u2x_km_s": -385.9858381567524, "u2y_km_s": -15.61842990078664, "speed2_km_s": 386.3016989480326, "signed_deflection_degrees": 2.317137346155204, "p2_over_p1": 2.504337565369773, "B2_over_B1": 1.5572160889185178, "entropy_over_cv": 0.1796849809713191, "upstream_fast_Mach": 1.437163366252746, "downstream_fast_Mach": 0.7378061364211272, "downstream_alfven_margin": 0.6202358390566807, "state_global_normalized": { "rho": "1.55737788510538562439096697349302001960154879377707653628659119142459341822851428621654289", "p": "0.101575931651397980689398582716444937413311470632713157340097257034844004736498864772951695", "u": [ "-0.643309730261253965351683220513246373337305394675686163902252705491827022645789176608207453", "-0.0260307165013110679614701826797779345307673480006009959244756361422454727543073787921916090", "-0E-91" ], "B": [ "0.0728060660568427504529857678094003886086139587369696765244517115095999961908453976149088830", "1.00127366987829996534451864289853403099665157599235843168001418941145028744442102448633607", "0E-91" ] }, "root_record": { "r": "1.55737788510538562439096697349302001960154879377707653628659119142459341822851428621654289", "b": "0.0406468888588646968830359183960108310091634446038644196566077540353949019388169511644799448", "h": "0.000700284121977649210986041686997852438805009044200274094142178841185469281602059135654109758", "A": "0.415811567870917513068596696773655508268934414556158685184879688154287771110445596108838861", "denominator": "0.998909392995141566775076944993073762533618356657344186799868193679242460292486821623522556", "polynomial_residual": "-6.84500537249294729154027E-66", "bracket_initial_signs": [ "1.45988521368903903537763388488529830607487564849215682174783033452157848670765297385043986", "-2.02828091616663372887789974644893391171952665958981419445687427495727576804888901390458654" ], "bracket_derivative_max": "-5.56596998586991719421641972543136726586629014809879974584914009646189924325046580769911002", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "2E-91", "0E-182", "3E-90", "0E-182", "3.87256975287150301301840160403195337053908822340183809190598775289645585186942387443836060E-67", "3E-91" ], "diagnosis": { "case_id": "R95_phi_-2.65", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.050990436276291885, 0.0 ], "rh_scaled_inf": 2.1892266966578675e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1892266966578675e-16 }, "characteristics": { "left": { "slow": 0.00803339616594369, "alfven_n": 0.021182414210284346, "fast": 0.8693587944094497 }, "right": { "slow": 0.009888185977241754, "alfven_n": 0.02643458263314648, "fast": 0.6950710171144316 } }, "front_relative_normal_velocity": { "left": -0.641418253266965, "right": -0.9989306027408966 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5573778851053857, "pressure_ratio": 2.504337565369773, "entropy_over_cv": 0.17968498097131913, "tangential_field_ratio": 1.5579864290134837 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.625, "theta_Bn_degrees": 87.62500000000001, "compression": 1.5574167625776958, "u2x_km_s": -385.9679329718937, "u2y_km_s": -15.586614094773195, "speed2_km_s": 386.2825233187952, "signed_deflection_degrees": 2.312529466358586, "p2_over_p1": 2.5045210082675085, "B2_over_B1": 1.5572514888216142, "entropy_over_cv": 0.1797166231826266, "upstream_fast_Mach": 1.437195363025172, "downstream_fast_Mach": 0.7377941838054252, "downstream_alfven_margin": 0.6200077704896916, "state_global_normalized": { "rho": "1.55741676257769583501223095212034719081978305658298051707018179435738467186309418627065337", "p": "0.101583372095330140622146077142559658455840091155343073656280227000708907635357916113543544", "u": [ "-0.643279888286489355813211397326019434511999467845283323458403923186947370888848171855504740", "-0.0259776901579553219249880813960749962237334430025434996274043982628220228163274373807066045", "-0E-91" ], "B": [ "0.0726506396128895169812324542850156414464616038594604369791387731929216639058458636393907076", "1.00130784120019073353702988741889214784480866622632772382418783548700010882823333582772140", "0E-91" ] }, "root_record": { "r": "1.55741676257769583501223095212034719081978305658298051707018179435738467186309418627065337", "b": "0.0406452548940133604207565463685775625849262250525659985082467968645127475352035077483344632", "h": "0.000715225705137278417258683215861875765378008439128095498185292021482009193344473972743060773", "A": "0.415779882922018761108728102195530621346146302869178574325263831371556695907555108696060952", "denominator": "0.998886095497792750170949004933328141384703401963312836809038909543269623308147724376429788", "polynomial_residual": "-1.073787472414706186437003E-65", "bracket_initial_signs": [ "1.46003332945599606967229787608662655939053470222288989159115452836893284195470677940320930", "-2.02793506615216643480593351018087122156823714890366523080112037289647346196865268162078991" ], "bracket_derivative_max": "-5.56569882347074825561884379736317045025430910798169888574374349930730864749172845536598724", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "0E-91", "0E-182", "-9E-90", "0E-182", "6.07570755929996477210313936610885668818197365555696422635400231417469385305866877477547868E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-2.625", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.050605394113256236, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": -1.782689686463541e-16, "t1_momentum": 1.0408340855860843e-17, "t2_momentum": -0.0, "t1_induction": 2.220446049250313e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.00811881175779553, "alfven_n": 0.021407363443686014, "fast": 0.8693686505158664 }, "right": { "slow": 0.009993341128981502, "alfven_n": 0.026715641360830572, "fast": 0.6950695132053273 } }, "front_relative_normal_velocity": { "left": -0.6414151339333776, "right": -0.9989506813588601 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5574167625776958, "pressure_ratio": 2.5045210082675085, "entropy_over_cv": 0.1797166231826267, "tangential_field_ratio": 1.5580383640237865 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.6, "theta_Bn_degrees": 87.60000000000001, "compression": 1.5574553705723189, "u2x_km_s": -385.95012241241915, "u2y_km_s": -15.554784924868551, "speed2_km_s": 386.2634441986715, "signed_deflection_degrees": 2.3079185831484486, "p2_over_p1": 2.5047032649355283, "B2_over_B1": 1.5572865820350386, "entropy_over_cv": 0.17974807584080454, "upstream_fast_Mach": 1.4372271191790897, "downstream_fast_Mach": 0.7377823118749335, "downstream_alfven_margin": 0.6197796987610709, "state_global_normalized": { "rho": "1.55745537057231891142335600181085193075534805220772099676381255771159235911377398576510500", "p": "0.101590764425785029226559629594800610107480778946212540010838489827302857710821647712121997", "u": [ "-0.643250204020698493260885445026732963115856923859258625872566195999848350310865246971680301", "-0.0259246415414475875141993417834677872195819702344876389185574086095266081003179156515678283", "-0E-91" ], "B": [ "0.0724951795515797194799519662236419424595400146406699086811660734201476744492878266822959082", "1.00134179194855711068304589523007242207005246847671147247395691442152979144566292783667867", "0E-91" ] }, "root_record": { "r": "1.55745537057231891142335600181085193075534805220772099676381255771159235911377398576510500", "b": "0.0406436365033225358883436027231162648778970980701357413250424790912896849754788966971568530", "h": "0.000730324403105733962834876542632432143057104802057603233746055336208595466754314322874414015", "A": "0.415748200447953100602018831007915839639481665070064707270429605962098526493472618950976298", "denominator": "0.998862552336122951494420055206600973143924577822372297350420988274363880929245087871137114", "polynomial_residual": "1.12747900941187669757102E-66", "bracket_initial_signs": [ "1.46017982422360063831997839481879684826379496203910629749043691291066021036076210259458602", "-2.02759060927480169284217290873371399565641174962446737796264046891319732215413393974322645" ], "bracket_derivative_max": "-5.56542769330011001384189029312986416711530224974788108873649023549133390002710518880281121", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.02846094764179516301161849320515862958712433969892779578522116573907639364556967173539615E-90", "2E-91", "0E-182", "5E-90", "0E-182", "-6.38028464766309713158696350079073645485716182838315791920732956456958264530393798679220636E-68", "3E-91" ], "diagnosis": { "case_id": "R95_phi_-2.6", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.05022034671533236, 0.0 ], "rh_scaled_inf": 2.1891092132209577e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1891092132209577e-16 }, "characteristics": { "left": { "slow": 0.008204226354749319, "alfven_n": 0.021632304860979952, "fast": 0.8693783969854524 }, "right": { "slow": 0.010098495064095669, "alfven_n": 0.026996695002233655, "fast": 0.6950679934019776 } }, "front_relative_normal_velocity": { "left": -0.6414120036220508, "right": -0.9989705697907147 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5574553705723189, "pressure_ratio": 2.5047032649355283, "entropy_over_cv": 0.17974807584080454, "tangential_field_ratio": 1.5580901689312023 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.575, "theta_Bn_degrees": 87.575, "compression": 1.5574937090970493, "u2x_km_s": -385.9324064828036, "u2y_km_s": -15.522942459862271, "speed2_km_s": 386.2444615994126, "signed_deflection_degrees": 2.303304709675605, "p2_over_p1": 2.504884335082023, "B2_over_B1": 1.5573213685630176, "entropy_over_cv": 0.17977933890368325, "upstream_fast_Mach": 1.4372586347083365, "downstream_fast_Mach": 0.7377705206153369, "downstream_alfven_margin": 0.6195516238485943, "state_global_normalized": { "rho": "1.55749370909704920737231146119886716915460748128088428780463948470172185758901773109064296", "p": "0.101598108630926861763369574280208341377953221118241709976641077248423488746790044016075994", "u": [ "-0.643220677471339288295343101446977220283116245796909016245219264608782592590137968679661888", "-0.0258715707664371188756395078320724786421039613350328242241634508874756257771241649483309833", "-0E-91" ], "B": [ "0.0723396861029374697386069997182107662227364234069647976035364249997453482882266397805675286", "1.00137552210289093154683296762920717760312184725001023827044523858070138391828008781198239", "0E-91" ] }, "root_record": { "r": "1.55749370909704920737231146119886716915460748128088428780463948470172185758901773109064296", "b": "0.0406420336843195746152271314919522720649036967322964861248971996800094571454337306849766914", "h": "0.000745580202828933752613087565535696601866712031921332386423336759532640788428261698639716725", "A": "0.415716520436437189156228530622688312258069472118270300363586093573081598893736075413583352", "denominator": "0.998838763524466633709410318573509204918781219145195646691171224809805664283284841257516647", "polynomial_residual": "1.241597420091508191649833E-65", "bracket_initial_signs": [ "1.46032469822015006940185813571157878230379682671934261017455747995641430894391872845654668", "-2.02724754529185854004511375327814825879364892288501532799671590166385779918003197740652221" ], "bracket_derivative_max": "-5.56515659529108252744542122421928772028792482002347470264741399172312432760970630938150840", "iterations": 216 }, "flux_residuals": [ "2E-90", "8.02840423237693127323614914795933461878680455203998011656461440364323130916131599697770302E-90", "-2E-91", "0E-182", "-8E-90", "0E-182", "-7.02692694147856415327052603233224687077183443246598985239539956932222103648638758713349991E-67", "-4E-91" ], "diagnosis": { "case_id": "R95_phi_-2.575", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.049835294119831494, 0.0 ], "rh_scaled_inf": 3.469446951953614e-18, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.008289639955788726, "alfven_n": 0.021857238477940934, "fast": 0.8693880338178444 }, "right": { "slow": 0.010203647769764968, "alfven_n": 0.02727774350384709, "fast": 0.695066457705018 } }, "front_relative_normal_velocity": { "left": -0.6414088623265352, "right": -0.9989902680326739 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5574937090970493, "pressure_ratio": 2.504884335082023, "entropy_over_cv": 0.17977933890368314, "tangential_field_ratio": 1.55814184376455 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.55, "theta_Bn_degrees": 87.55, "compression": 1.5575317781595293, "u2x_km_s": -385.9147851875308, "u2y_km_s": -15.491086768552607, "speed2_km_s": 386.2255755327564, "signed_deflection_degrees": 2.2986878590996307, "p2_over_p1": 2.505064218416583, "B2_over_B1": 1.5573558484097842, "entropy_over_cv": 0.17981041232929715, "upstream_fast_Mach": 1.4372899096067546, "downstream_fast_Mach": 0.7377588100124498, "downstream_alfven_margin": 0.6193235457301204, "state_global_normalized": { "rho": "1.55753177815952918659245020349939926277984624718617605571340733043451122377562250633817175", "p": "0.101605404698976602406908761905599371115254642694241225711243776279074514097512353832470190", "u": [ "-0.643191308645884738646214642780082144995029621620547076193263973936687157174692805456420099", "-0.0258184779475876795342103542447629910611657157130082191120419693537267658287990086283610821", "-0E-91" ], "B": [ "0.0721841594969918863247114059294072228785890483973548912467082765132521336135255839623283010", "1.00140903164280171849364166661067985311142044760560574138285288698389521635921550325601145", "0E-91" ] }, "root_record": { "r": "1.55753177815952918659245020349939926277984624718617605571340733043451122377562250633817175", "b": "0.0406404464345557644514622213502006927996707470224797255349252644862752348461190052866785596", "h": "0.000760993091494301438341988303217633726087290735340162857634240466914720457759434543457153261", "A": "0.415684842875191458032872702470601634006535247862128045569493461611026169072854506246706442", "denominator": "0.998814729077037763394982685642019473388658953612898978846368380030598776956299325004137879", "polynomial_residual": "-1.329472438304307147398315E-65", "bracket_initial_signs": [ "1.46046795167319056376590088755689966704967353881652285951811458765226427646914084064925170", "-2.02690587395985935120078325108536612834876953921289931633896362935712268018220270338851328" ], "bracket_derivative_max": "-5.56488552937472618181954605427401549118249226787938133930537865321918995856219292062655988", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "0E-91", "0E-182", "0E-90", "0E-182", "7.52518202511621631455482993335390087678642910489390521605543853117463884629989991788765428E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-2.55", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.049450236364076326, 0.0 ], "rh_scaled_inf": 2.1889962213727294e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1889962213727294e-16 }, "characteristics": { "left": { "slow": 0.00837505255988903, "alfven_n": 0.02208216431033608, "fast": 0.8693975610127008 }, "right": { "slow": 0.010308799233169708, "alfven_n": 0.0275587868121632, "fast": 0.6950649061150918 } }, "front_relative_normal_velocity": { "left": -0.6414057100404564, "right": -0.9990097760809875 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5575317781595293, "pressure_ratio": 2.505064218416583, "entropy_over_cv": 0.17981041232929706, "tangential_field_ratio": 1.55819338855237 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.525, "theta_Bn_degrees": 87.525, "compression": 1.5575695777672494, "u2x_km_s": -385.8972585310937, "u2y_km_s": -15.459217919746477, "speed2_km_s": 386.2067860104273, "signed_deflection_degrees": 2.294068044588827, "p2_over_p1": 2.505242914650197, "B2_over_B1": 1.5573900215795782, "entropy_over_cv": 0.1798412960758847, "upstream_fast_Mach": 1.4373209438681913, "downstream_fast_Mach": 0.7377471800522167, "downstream_alfven_margin": 0.6190954643835902, "state_global_normalized": { "rho": "1.55756957776724939091506076995020573467508247914797144610523020125103640622322373737619358", "p": "0.101612652618211981151577071884127501783690057451466351061185082930733354961775631172735951", "u": [ "-0.643162097551822880689867582396450044042391062466033604862706251784174331791215008669195614", "-0.0257653631995774600285231285602442938226933153711221553538694934587915460596266115601170409", "-0E-91" ], "B": [ "0.0720285999637771156346553253772037535677747365375713029296651983193660252537964417052488181", "1.00144232054801668932310969068689398543249097261709790064270449933006021839240270070362879", "0E-91" ] }, "root_record": { "r": "1.55756957776724939091506076995020573467508247914797144610523020125103640622322373737619358", "b": "0.0406388747516063218094849024439497608255964361914250302641591681613102431449605948415954381", "h": "0.000776563056530704070635965240258127469417860239313744958644430288593184505775578254140070979", "A": "0.415653167751940092946456893650327600299718921360533535389532975235467703688867493935869592", "denominator": "0.998790449007929826641057040896854612575357629307153093490089031416985468223800886270866385", "polynomial_residual": "-5.1102661345793889395765E-67", "bracket_initial_signs": [ "1.46060958480951723021503085925088992860068184498685186519378557556302816271605104924445143", "-2.02656559503453043502847651396200084321741074946190023131821784639721054365688564073364450" ], "bracket_derivative_max": "-5.56461449548008252934922577420162259444805808169195267839146538515654225580950613934278695", "iterations": 216 }, "flux_residuals": [ "2E-90", "8.02829538961915785863860402020902970755267489943105535385935448685333237823290994649920341E-90", "0E-91", "0E-182", "2E-90", "0E-182", "2.89290525818568013896650001374382066941856715841680908752870475632405734642455633848129429E-68", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.525", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04906517348540092, 0.0 ], "rh_scaled_inf": 2.1889414095275528e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": -1.7825532480398349e-16, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1889414095275528e-16 }, "characteristics": { "left": { "slow": 0.008460464166017175, "alfven_n": 0.02230708237392502, "fast": 0.8694069785697014 }, "right": { "slow": 0.0104139494414898, "alfven_n": 0.027839824873675315, "fast": 0.695063338632848 } }, "front_relative_normal_velocity": { "left": -0.6414025467575152, "right": -0.9990290939319414 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5575695777672494, "pressure_ratio": 2.505242914650197, "entropy_over_cv": 0.17984129607588484, "tangential_field_ratio": 1.5582448033229268 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.5, "theta_Bn_degrees": 87.5, "compression": 1.5576071079275484, "u2x_km_s": -385.87982651799405, "u2y_km_s": -15.427335982259399, "speed2_km_s": 386.1880930441366, "signed_deflection_degrees": 2.2894452793201836, "p2_over_p1": 2.5054204234952544, "B2_over_B1": 1.5574238880766456, "entropy_over_cv": 0.17987199010188837, "upstream_fast_Mach": 1.4373517374864995, "downstream_fast_Mach": 0.7377356307207116, "downstream_alfven_margin": 0.6188673797870273, "state_global_normalized": { "rho": "1.55760710792754840852842478000265885999553545894440692679586485670556072637489541688564742", "p": "0.101619852376967510674366492411502589220847041968115788424544312659761598492513350471280773", "u": [ "-0.643133044196656741458967006743160381427388640122118441135372084603601137600364717233615444", "-0.0257122266370989955358056545034874279576036678961807495655009468328131562883212316173140062", "-0E-91" ], "B": [ "0.0718730077333323529061640650807144648961974518129793380548683913547996289894603218741826439", "1.00147538879838076491625059836355769432019858018667357053215234069684265568656848937199553", "0E-91" ] }, "root_record": { "r": "1.55760710792754840852842478000265885999553545894440692679586485670556072637489541688564742", "b": "0.0406373186330703837842610145640548515515129909529069202724336944610542349275950097944161131", "h": "0.000792290085608390542039208020283219883965327086038889842310767516392781689932180119716867034", "A": "0.415621495054411014875961222244207244174508230153633241579195112633053778477519992844588349", "denominator": "0.998765923331115845064889235242058830556352726113566376474106258202216930188954336606643222", "polynomial_residual": "-8.98764369023084149841765E-66", "bracket_initial_signs": [ "1.46074959785517412523495955817421570544830427255736761858691749672631584357495640741926529", "-2.02622670827080261703550572524372356098852877505039496748148827628368425887810823437971474" ], "bracket_derivative_max": "-5.56434349353417511548013130297388236367269229094542695971965385531287008897632332755606377", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-4E-91", "0E-182", "-5E-90", "0E-182", "5.08849729833574866715255398557169655837561794325830185636633156242301102550620355505218810E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_-2.5", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.048680105521150575, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7825210625607677e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.008545874773131837, "alfven_n": 0.022531992684459944, "fast": 0.8694162864885473 }, "right": { "slow": 0.010519098381904738, "alfven_n": 0.02812085763487775, "fast": 0.6950617552589431 } }, "front_relative_normal_velocity": { "left": -0.6413993724714873, "right": -0.9990482215818578 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5576071079275484, "pressure_ratio": 2.5054204234952544, "entropy_over_cv": 0.17987199010188837, "tangential_field_ratio": 1.558296088104207 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.475, "theta_Bn_degrees": 87.47500000000001, "compression": 1.557644368647613, "u2x_km_s": -385.86248915274257, "u2y_km_s": -15.395441024915451, "speed2_km_s": 386.16949664558183, "signed_deflection_degrees": 2.2848195764793413, "p2_over_p1": 2.505596744665545, "B2_over_B1": 1.5574574479052388, "entropy_over_cv": 0.1799024943659543, "upstream_fast_Mach": 1.4373822904555362, "downstream_fast_Mach": 0.7377241620041383, "downstream_alfven_margin": 0.6186392919185378, "state_global_normalized": { "rho": "1.55764436864761284238318824334801790657450304487447939243030677679731333770979634935264584", "p": "0.101627003963634503153484056172811849927269808741836820611706573462074373257209139404902954", "u": [ "-0.643104148587904291143670701133688207532836760192797729569624608495495294720017690161422587", "-0.0256590683748590834861944421899913124438715805533611789505304758620200581808255118327393993", "-0E-91" ], "B": [ "0.0717173830357018631931634387672278429555846404085521231360800650204214724452702557930318654", "1.00150823637385657669599057753185704950038664825092242850899453511323592056221396749730839", "0E-91" ] }, "root_record": { "r": "1.55764436864761284238318824334801790657450304487447939243030677679731333770979634935264584", "b": "0.0406357780765710003517840508942493169925391729255713574610603070735359258042878349303477697", "h": "0.000808174166638930820751822414349514997441480554229295409422453306241028140685100996497951559", "A": "0.415589824770335860888510964260580963131619954734825441610865682935824392596979631072288536", "denominator": "0.998741152060448391948316603874650215092043839364466039592747537290628491941213549420792534", "polynomial_residual": "-1.030138025609647566467148E-65", "bracket_initial_signs": [ "1.46088799103545429725702182135905846737583091470099932528089180108356666196491141712657688", "-2.02588921342281180903213093487921723118456390810462103812501341619682213874035248583206076" ], "bracket_derivative_max": "-5.56407252346201029069606956670666206942351082810091900049451815152584585072833066841050816", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.02819266354761618361052264551735727177586453658298094602717416934469508690764288282995380E-90", "1E-91", "0E-182", "-1E-90", "0E-182", "5.83300187647868528924910003009572912903690862500490102209837214235483679176613469441117638E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-2.475", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04829503250868174, 0.0 ], "rh_scaled_inf": 1.7824896466127373e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7824896466127373e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.008631284380183485, "alfven_n": 0.02275689525768575, "fast": 0.8694254847689613 }, "right": { "slow": 0.010624246041593618, "alfven_n": 0.028401885042265835, "fast": 0.6950601559940396 } }, "front_relative_normal_velocity": { "left": -0.6413961871762236, "right": -0.999067159027095 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.557644368647613, "pressure_ratio": 2.505596744665545, "entropy_over_cv": 0.17990249436595418, "tangential_field_ratio": 1.5583472429239222 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.45, "theta_Bn_degrees": 87.45, "compression": 1.5576813599344772, "u2x_km_s": -385.845246439859, "u2y_km_s": -15.36353311654722, "speed2_km_s": 386.15099682644717, "signed_deflection_degrees": 2.2801909492605548, "p2_over_p1": 2.5057718778762594, "B2_over_B1": 1.5574907010696168, "entropy_over_cv": 0.17993280882693227, "upstream_fast_Mach": 1.4374126027691645, "downstream_fast_Mach": 0.7377127738888302, "downstream_alfven_margin": 0.61841120075631, "state_global_normalized": { "rho": "1.55768135993447727874385758061818762300762865689643790977411323920486367177912280808365969", "p": "0.101634107366661087043109744463625984308540681574010322561570237270083494793709773160513232", "u": [ "-0.643075410733098396084281190559402234522019368703910964987508689539538137297409395243456552", "-0.0256058885275787011662330399373313402018354705857160580090410815796869918065587916590910097", "-0E-91" ], "B": [ "0.0715617261009350023038241745326300701483619566206546206037076728220065437826361779568697375", "1.00154086325452447390121507297234738488988985624291092093227337692411130059910767610248525", "0E-91" ] }, "root_record": { "r": "1.55768135993447727874385758061818762300762865689643790977411323920486367177912280808365969", "b": "0.0406342530797551266458784233323851866570693476529385811990016800576588427517928316683934235", "h": "0.000824215287775155974635869971644244166025981294452633933340380982218186144093622440207905011", "A": "0.415558156887449964975168998536065414128488571378779096146913348498278762959612440320851378", "denominator": "0.998716135209659608495773015311345786673661325450957514601634916891090610997521510828216151", "polynomial_residual": "-1.451966401842541361618261E-65", "bracket_initial_signs": [ "1.46102476457489983545145159477417284236259981705912528571864874972432341939853754196556558", "-2.02555311024389956531771025168206036788110748770494812501650345697576601059009817876379193" ], "bracket_derivative_max": "-5.56380158518657800841817305619556435924386888830659031885026292308401672416105199138803701", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.02814359414600518939840410727373173927698414289524615188264093446127776643992213709027548E-90", "-1E-91", "0E-182", "1E-90", "0E-182", "8.22254478834704795420211193601082477856689890866754316366016599477274358210974478913496809E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.45", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04790995448536183, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.008716692986114456, "alfven_n": 0.022981790109340122, "fast": 0.8694345734106875 }, "right": { "slow": 0.010729392407735109, "alfven_n": 0.02868290704233592, "fast": 0.6950585408388071 } }, "front_relative_normal_velocity": { "left": -0.64139299086565, "right": -0.9990859062640476 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5576813599344772, "pressure_ratio": 2.50577187787626, "entropy_over_cv": 0.17993280882693252, "tangential_field_ratio": 1.558398267809505 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.425, "theta_Bn_degrees": 87.42500000000001, "compression": 1.5577180817950242, "u2x_km_s": -385.82809838387203, "u2y_km_s": -15.331612325995755, "speed2_km_s": 386.132593598403, "signed_deflection_degrees": 2.275559410866655, "p2_over_p1": 2.50594582284399, "B2_over_B1": 1.5575236475740453, "entropy_over_cv": 0.17996293344387562, "upstream_fast_Mach": 1.4374426744212523, "downstream_fast_Mach": 0.7377014663612504, "downstream_alfven_margin": 0.618183106278614, "state_global_normalized": { "rho": "1.55771808179502425588623334096234423466671540459177048185922860290937287843092555271980631", "p": "0.101641162574552223804326297744872129285683164243606751415462555135074512977573936415479682", "u": [ "-0.643046830639786772255179791232319705916452768437146154981157624054299418185653229017570232", "-0.0255526872099929233113979481152482699142235925159703666570696068247368829971821036941395353", "-0E-91" ], "B": [ "0.0714060371590862377025578838119771913308983854727055501088430760873730301730583560597147345", "1.00157326942058253067428669816898772696517430205319462709661397457424701511934659167969040", "0E-91" ] }, "root_record": { "r": "1.55771808179502425588623334096234423466671540459177048185922860290937287843092555271980631", "b": "0.0406327436402936153132650367818066732551448240966162714904721981215069417562904553575541087", "h": "0.000840413437411098985123691799647949461860739704989165905252758909542610384975014783190335179", "A": "0.415526491393492338898785973932846052862881569640301839690956049981238397357113117203189343", "denominator": "0.998690872792361220213077524754411254299934798296692733767882310933376377303603365184679581", "polynomial_residual": "7.97020461214870559565753E-66", "bracket_initial_signs": [ "1.46115991869730192304659696896050894700953449040513176348676468726040762455030760349768143", "-2.02521839848661362554897615164138395261252072478640317308453631297517617958929766874391559" ], "bracket_derivative_max": "-5.56353067862885260883593123652590896994219959974901080025533308339960187222266206571663080", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.02809605377105305580545200405826514678853618515538240924902947007790870922505229522986130E-90", "0E-91", "0E-182", "-1E-90", "0E-182", "-4.51410983740058624570533808609577382262703218667303371661604049455138360485222313473486715E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-2.425", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.047524871488569195, 0.0 ], "rh_scaled_inf": 6.938893903907228e-18, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.008802100589858999, "alfven_n": 0.02320667725515363, "fast": 0.8694435524134918 }, "right": { "slow": 0.010834537467507458, "alfven_n": 0.02896392358158538, "fast": 0.695056909793922 } }, "front_relative_normal_velocity": { "left": -0.6413897835337676, "right": -0.9991044632891464 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5577180817950242, "pressure_ratio": 2.5059458228439895, "entropy_over_cv": 0.1799629334438756, "tangential_field_ratio": 1.5584491627881132 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.4, "theta_Bn_degrees": 87.4, "compression": 1.5577545342359842, "u2x_km_s": -385.81104498931916, "u2y_km_s": -15.299678722110505, "speed2_km_s": 386.1142869731063, "signed_deflection_degrees": 2.270924974509011, "p2_over_p1": 2.506118579286729, "B2_over_B1": 1.5575562874227962, "entropy_over_cv": 0.17999286817604104, "upstream_fast_Mach": 1.4374725054056725, "downstream_fast_Mach": 0.7376902394079918, "downstream_alfven_margin": 0.6179550084638025, "state_global_normalized": { "rho": "1.55775453423598423294059678568591765722073163926410955540168966651156440949948454063948609", "p": "0.101648169575869724592257696097702583301894398690182674474050211564216305917966987454420056", "u": [ "-0.643018408315531939239870737431654556670764877189768550444583974264971006354187093356994358", "-0.0254994645368508396874734976961404949891360685717028046194703224913835177546326860875103828", "-0E-91" ], "B": [ "0.0712503164402151693767369803084177326430853389802023024089789664488423847218824315662205467", "1.00160545485234655296199547169933948361221116360982791988381895945660911118343487848147254", "0E-91" ] }, "root_record": { "r": "1.55775453423598423294059678568591765722073163926410955540168966651156440949948454063948609", "b": "0.0406312497558812089468465008399451380029892488505831159958482921869695045816430798661240576", "h": "0.000856768604181936350655325560230513470054659334405458829325410205360184848746019388102520054", "A": "0.415494828276205653053844130796542779097102576505953912482617734997398862148956615826405841", "denominator": "0.998665364822044553407001792704152408257571531742891092541532128010755881900335606752362578", "polynomial_residual": "1.423687034236263013491192E-65", "bracket_initial_signs": [ "1.46129345362570089516964281103485898620075783311553392887511245557648022987107064903558394", "-2.02488507790270844430121371980872645747277183143843473950544294047816675024284651369072102" ], "bracket_derivative_max": "-5.56325980370779358868002488046119156078439277868372731189288791700226334098042458544931182", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.02805004237749468656165030462234069790771482041512890373914152980668483766860830637320654E-90", "-2E-91", "0E-182", "3E-90", "0E-182", "-8.06436431349933866242709425849319384420915565002680264568348157995656771546757103720895730E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-2.4", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04713978355569291, 0.0 ], "rh_scaled_inf": 0.0, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.008887507190343365, "alfven_n": 0.023431556710849857, "fast": 0.8694524217771612 }, "right": { "slow": 0.010939681208088503, "alfven_n": 0.02924493460651264, "fast": 0.6950552628600667 } }, "front_relative_normal_velocity": { "left": -0.6413865651746524, "right": -0.9991228300988584 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5577545342359842, "pressure_ratio": 2.506118579286729, "entropy_over_cv": 0.1799928681760411, "tangential_field_ratio": 1.5584999278866272 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.375, "theta_Bn_degrees": 87.375, "compression": 1.5577907172639356, "u2x_km_s": -385.7940862607467, "u2y_km_s": -15.267732373749283, "speed2_km_s": 386.0960769621998, "signed_deflection_degrees": 2.266287653407494, "p2_over_p1": 2.5062901469238725, "B2_over_B1": 1.557588620620148, "entropy_over_cv": 0.18002261298288844, "upstream_fast_Mach": 1.4375020957163032, "downstream_fast_Mach": 0.7376790930157765, "downstream_alfven_margin": 0.6177269072903099, "state_global_normalized": { "rho": "1.55779071726393555888046668775929199235437188327852483859656055678354702344879470290524955", "p": "0.101655128359232266899452898700167692058567603535527069991296453533168003432490146999034042", "u": [ "-0.642990143767911174696966415408238514123927190848662413272232486623887222708257881697342380", "-0.0254462206229154726605971749532029852107244837772455935919483363487241274470472260744302120", "-0E-91" ], "B": [ "0.0710945641743865506689108376287912868624513265823955091176320683918153395383868305951916785", "1.00163741953025008522990203259141015071123825970439295167185978187564824768978875375465407", "0E-91" ] }, "root_record": { "r": "1.55779071726393555888046668775929199235437188327852483859656055678354702344879470290524955", "b": "0.0406297714242365325971697479770140774080533237776944576536096429643981181848434889261427091", "h": "0.000873280776963930479276273045139223291618990620370546753148074613836025583246843319785430891", "A": "0.415463167523336217338230775900062877872320286934989014653898657604785073176148436148077523", "denominator": "0.998639611312080551805622517801826512532784153498432665236366915016511956176884563428941916", "polynomial_residual": "-5.93086313923336853111822E-66", "bracket_initial_signs": [ "1.46142536958238630120447808471235267285046627077866752578988583443040805732318061456067660", "-2.02455314824314570733298588926619478398225601847033110178458462648836353672361342166499927" ], "bracket_derivative_max": "-5.56298896034034635694680721882516363603976381214292928761181992560836763742335860122506668", "iterations": 216 }, "flux_residuals": [ "-1E-90", "1.60560111198430428048941474486131299773411227702016250411982694665381225629751516452163764E-89", "-1E-91", "0E-182", "-9E-90", "0E-182", "3.35990081366457041040443332147543756185680033406407148594897739065855307834686710749314425E-67", "-4E-91" ], "diagnosis": { "case_id": "R95_phi_-2.375", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.046754690724132734, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.008972912786485848, "alfven_n": 0.02365642849214547, "fast": 0.8694611815015048 }, "right": { "slow": 0.011044823616655638, "alfven_n": 0.029525940063617157, "fast": 0.6950536000379309 } }, "front_relative_normal_velocity": { "left": -0.6413833357824553, "right": -0.9991410066896868 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5577907172639356, "pressure_ratio": 2.5062901469238725, "entropy_over_cv": 0.18002261298288835, "tangential_field_ratio": 1.558550563131651 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.35, "theta_Bn_degrees": 87.35, "compression": 1.5578266308853044, "u2x_km_s": -385.7772222027099, "u2y_km_s": -15.235773349778217, "speed2_km_s": 386.0779635773127, "signed_deflection_degrees": 2.2616474607904395, "p2_over_p1": 2.5064605254762182, "B2_over_B1": 1.557620647170385, "entropy_over_cv": 0.18005216782408087, "upstream_fast_Mach": 1.4375314453470274, "downstream_fast_Mach": 0.7376680271714562, "downstream_alfven_margin": 0.6174988027366524, "state_global_normalized": { "rho": "1.55782663088530444165674587727319500898946199826858386722174134799392139870397521419536586", "p": "0.101662038913315411155551257309799207765650212089754235461246560121897398043944354750143764", "u": [ "-0.642962037004516469316947701634131970385273189213922270827251391691854850847908119858744380", "-0.0253929555829636947557969490954987114293357560448370376895564036267777135646354089258893680", "-0E-91" ], "B": [ "0.0709387805916703090752903797828936263342839706943012204826002669772100744076986730361944771", "1.00166916343484441699003410321181392583085664285535248641875620758143449351914256329736476", "0E-91" ] }, "root_record": { "r": "1.55782663088530444165674587727319500898946199826858386722174134799392139870397521419536586", "b": "0.0406283086431020863620242676029807432258663187386752231484191002585465270959077779313866200", "h": "0.000889949944874372870031320647391636321833140469623932582431903695934695207995979449021757590", "A": "0.415431509122633962036877476988657772971727935591657673516537261999979467965202612401026373", "denominator": "0.998613612275719793299466221315220073371798420455836316619059614350899047338602182931919019", "polynomial_residual": "2.82541663596324162752501E-66", "bracket_initial_signs": [ "1.46155566678889697166241362244340923856264064104648273346014465012090045590878808322486947", "-2.02422260925809483456492013257988569834039392071986377048477248097364259416372498281928011" ], "bracket_derivative_max": "-5.56271814844144297658415874481434480385690338492970994254105933403616425697402979983669325", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "0E-91", "0E-182", "5E-90", "0E-182", "-1.60082546913893950010910463187754372640153662643495560619749996368970843127881572173542803E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.35", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04636959303129893, 0.0 ], "rh_scaled_inf": 2.188589153379239e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7823441078787474e-16, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.188589153379239e-16 }, "characteristics": { "left": { "slow": 0.009058317377196867, "alfven_n": 0.023881292614750353, "fast": 0.8694698315863522 }, "right": { "slow": 0.011149964680385833, "alfven_n": 0.029806939899399466, "fast": 0.6950519213282106 } }, "front_relative_normal_velocity": { "left": -0.6413800953514027, "right": -0.999158993058171 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5578266308853044, "pressure_ratio": 2.5064605254762182, "entropy_over_cv": 0.18005216782408096, "tangential_field_ratio": 1.558601068549511 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.325, "theta_Bn_degrees": 87.325, "compression": 1.5578622751063649, "u2x_km_s": -385.7604528197727, "u2y_km_s": -15.203801719071688, "speed2_km_s": 386.0599468300602, "signed_deflection_degrees": 2.257004409894608, "p2_over_p1": 2.506629714665967, "B2_over_B1": 1.5576523670777993, "entropy_over_cv": 0.18008153265948437, "upstream_fast_Mach": 1.4375605542917336, "downstream_fast_Mach": 0.7376570418620122, "downstream_alfven_margin": 0.6172706947814279, "state_global_normalized": { "rho": "1.55786227510636491747707924284906789342250482345276215452655186381646327693163056903622087", "p": "0.101668901226851617283265844803113421921228978812968417814085657257564626760286404895038170", "u": [ "-0.642934088032954482269536366602858058854539108062184299111632060251159596817411146362289592", "-0.0253396695317861462038422315297819941518203283905306095433792860526131487594499052133608452", "-0E-91" ], "B": [ "0.0707829659221415670112732094185429726308251743068002873160714143149988333774985784146749612", "1.00170068654679858914189608246671563655291786709462983811225397063256125804708945762018457", "0E-91" ] }, "root_record": { "r": "1.55786227510636491747707924284906789342250482345276215452655186381646327693163056903622087", "b": "0.0406268614102442380541346053695967828503069592215331760647789345144148776326361786574392707", "h": "0.000906776097271528082794556712566676421247182759216016801233979354998662965208681645265206195", "A": "0.415399853061852418717201109561722198096855848919732105272075676691473755909371258588218971", "denominator": "0.998587367726092506803454809457234810871785501103680227882573215535254979825654129217557062", "polynomial_residual": "-1.485508897767044108709658E-65", "bracket_initial_signs": [ "1.46168434546602108956152470797855247508124742201853235176765375757599359339616927810747296", "-2.02389346069693346978294059750471131271821946818093479560636345423663078994408907633358370" ], "bracket_derivative_max": "-5.56244736792400289214832557389701260491595283283446404897120701047336641249453027143014150", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.02792118165437685064854071825526939322595143773503063707076999608935183278338157209844776E-90", "1E-91", "0E-182", "4E-90", "0E-182", "8.41762675983625222350611042388549475481695950249938166865502489742156791740666830329320352E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.325", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.045984490514612175, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.009143720961379016, "alfven_n": 0.024106149094367688, "fast": 0.8694783720315559 }, "right": { "slow": 0.011255104386455616, "alfven_n": 0.03008793406036116, "fast": 0.695050226731609 } }, "front_relative_normal_velocity": { "left": -0.6413768438757956, "right": -0.9991767892008868 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5578622751063649, "pressure_ratio": 2.506629714665967, "entropy_over_cv": 0.18008153265948446, "tangential_field_ratio": 1.5586514441662591 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.3, "theta_Bn_degrees": 87.3, "compression": 1.5578976499332389, "u2x_km_s": -385.74377811650794, "u2y_km_s": -15.171817550512293, "speed2_km_s": 386.0420267320434, "signed_deflection_degrees": 2.252358513965149, "p2_over_p1": 2.5067977142167224, "B2_over_B1": 1.5576837803466883, "entropy_over_cv": 0.18011070744916777, "upstream_fast_Mach": 1.437589422544315, "downstream_fast_Mach": 0.7376461370745552, "downstream_alfven_margin": 0.6170425834033162, "state_global_normalized": { "rho": "1.55789764993323882023024707861872303917505150379002199081606435366271817471162714761919170", "p": "0.101675715288630261210720766092438603261572466240069149405206011101362364749395344186420117", "u": [ "-0.642906296860846497141519467721850516137299326458339374463185536784675079491783751728530456", "-0.0252863625841871524762301638996839856340474812233075487307455183106816012553414658954453026", "-0E-91" ], "B": [ "0.0706271203958806625447812946842202659438354406452116890359296557804687818547606108715054248", "1.00173198884689940012675126634929797521327724775726537666037667289559531853584616510522756", "0E-91" ] }, "root_record": { "r": "1.55789764993323882023024707861872303917505150379002199081606435366271817471162714761919170", "b": "0.0406254297234532159469062166499790500017852167061706864701054108794780278097642385188911196", "h": "0.000923759223754578496180168174214091282470337725844425832572653443385297332418576583089736804", "A": "0.415368199328748701136282954678287122380020687123021438397197982096657504843891409352014784", "denominator": "0.998560877676208589239661428852978099111808415846605882413043655686602710365041354707054698", "polynomial_residual": "1.87077342851402415639317E-66", "bracket_initial_signs": [ "1.46181140583379626631046134462549197745811751837883936830948251505763040981460540294342298", "-2.02356570230824795707619935808659885887398677414753207755579315374557144764749145832317318" ], "bracket_derivative_max": "-5.56217661869893364344123444546011908466408170187638756727697405700086506726204307718822903", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "1E-91", "0E-182", "-4E-90", "0E-182", "-1.06020172925466653192967971195025807386101568321452192407794536888050277576846982915524276E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.3", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04559938321150346, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.009229123537927137, "alfven_n": 0.024330997946694074, "fast": 0.8694868028369888 }, "right": { "slow": 0.01136024272204108, "alfven_n": 0.030368922493004925, "fast": 0.6950485162488352 } }, "front_relative_normal_velocity": { "left": -0.6413735813500103, "right": -0.999194395114446 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5578976499332389, "pressure_ratio": 2.5067977142167224, "entropy_over_cv": 0.18011070744916768, "tangential_field_ratio": 1.5587016900076687 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.275, "theta_Bn_degrees": 87.275, "compression": 1.5579327553718958, "u2x_km_s": -385.727198097497, "u2y_km_s": -15.139820912990785, "speed2_km_s": 386.0242032948493, "signed_deflection_degrees": 2.2477097862555637, "p2_over_p1": 2.5069645238534926, "B2_over_B1": 1.5577148869813564, "entropy_over_cv": 0.18013969215340273, "upstream_fast_Mach": 1.4376180500986704, "downstream_fast_Mach": 0.7376353127963252, "downstream_alfven_margin": 0.6168144685810781, "state_global_normalized": { "rho": "1.55793275537189575105541984568130134300253536176767139154510326209049204977094988283923328", "p": "0.101682481087497651340178345210246505976588003826199989260827816778339931811289537719875451", "u": [ "-0.642878663495828378364868615626041011322071947996944683734596380192770581024219663016357657", "-0.0252330348549846418081289970756216842856434913826960052809061943684105472724453767217581220", "-0E-91" ], "B": [ "0.0704712442429731700981831569332809438680570822359247483982406295588549421922766997552769832", "1.00176307031605141189513580714812401774022451219278578069673849212378425186779824741345250", "0E-91" ] }, "root_record": { "r": "1.55793275537189575105541984568130134300253536176767139154510326209049204977094988283923328", "b": "0.0406240135805431015981842023848344712397530322955677058936690487664388001736054434356267404", "h": "0.000940899314163569853183034088854074006201391072564383656677112693575272466778691877454240065", "A": "0.415336547911083486159722112356228741754883077215184836759102869624699799599549101046680900", "denominator": "0.998534142138957622640887219940509606175331912050911238357672435689869938668667977227705140", "polynomial_residual": "1.383681569391542167027544E-65", "bracket_initial_signs": [ "1.46193684811150962209263752510585243987611719927671298444635539066082905374911002020178920", "-2.02323933383983380401983027326189440690384480593015789677251880129145108140285596652476496" ], "bracket_derivative_max": "-5.56190590067513156513766075544744262978759243981424904552759604544685491783608728048359304", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-1E-91", "0E-182", "2E-90", "0E-182", "-7.84253322117195603591519521612651498840632303645644583534035654314391512910444175047152171E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.275", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04521427115941392, 0.0 ], "rh_scaled_inf": 6.938893903907228e-18, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.009314525105728383, "alfven_n": 0.024555839187419617, "fast": 0.8694951240025461 }, "right": { "slow": 0.011465379674317863, "alfven_n": 0.03064990514383452, "fast": 0.6950467898806056 } }, "front_relative_normal_velocity": { "left": -0.6413703077684978, "right": -0.9992118107954966 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5579327553718958, "pressure_ratio": 2.5069645238534926, "entropy_over_cv": 0.18013969215340264, "tangential_field_ratio": 1.5587518060992378 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.25, "theta_Bn_degrees": 87.25, "compression": 1.557967591428153, "u2x_km_s": -385.71071276733034, "u2y_km_s": -15.107811875406037, "speed2_km_s": 386.0064765300508, "signed_deflection_degrees": 2.243058240027664, "p2_over_p1": 2.5071301433026885, "B2_over_B1": 1.5577456869861142, "entropy_over_cv": 0.1801684867326634, "upstream_fast_Mach": 1.4376464369487034, "downstream_fast_Mach": 0.7376245690146918, "downstream_alfven_margin": 0.6165863502935564, "state_global_normalized": { "rho": "1.55796759142815304805610259593993004109746344030227656635229413378981933359282251530524938", "p": "0.101689198612357044973191909019211259645790361650337486335861216821273211322864551801049714", "u": [ "-0.642851187945550528134999957513138916512666271819958797965268453288881546489981614610988640", "-0.0251796864590100627091003848551440825320636744621323424333192849602665976955142645942016561", "-0E-91" ], "B": [ "0.0703153376935099211195724281067162911825196897323967556261124597646622553415219845340133701", "1.00179393093527695568756313693264022300912864498739652721462985030760077183519006192685096", "0E-91" ] }, "root_record": { "r": "1.55796759142815304805610259593993004109746344030227656635229413378981933359282251530524938", "b": "0.0406226129793518227519848943857063198149714045290817573028625064245740349115534945320207048", "h": "0.000958196358579357594202565726554361451702543520762883362755706162951649211623332781269805646", "A": "0.415304898796620994692099560550509397183886612910760889956677667228153188106774269212619327", "denominator": "0.998507161127108891375070662902004671096136484737361746266388572022383260572592903686248589", "polynomial_residual": "-6.67741715802135717588177E-66", "bracket_initial_signs": [ "1.46206067251769787074677918421129429162125207200416009490316058033736261481498792336159905", "-2.02291435503869613161251890614016885139878342887669779532965563232808522470746217425103565" ], "bracket_derivative_max": "-5.56163521375948247241150942968255153735295516513359302995108107656131971241233236832138189", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.02780608027406413901269122801754054060040458732960506103149301700910706541939909053404171E-90", "1E-91", "0E-182", "0E-90", "0E-182", "3.78513699647175273496264496747918021075254051641821316413344027038269300091661250686575425E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.25", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.044829154395794754, 0.0 ], "rh_scaled_inf": 2.1884125484229284e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1884125484229284e-16 }, "characteristics": { "left": { "slow": 0.009399925663662278, "alfven_n": 0.024780672832228044, "fast": 0.8695033355281444 }, "right": { "slow": 0.01157051523046117, "alfven_n": 0.03093088195935482, "fast": 0.6950450476276432 } }, "front_relative_normal_velocity": { "left": -0.6413670231257844, "right": -0.9992290362407229 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.557967591428153, "pressure_ratio": 2.5071301433026885, "entropy_over_cv": 0.1801684867326635, "tangential_field_ratio": 1.5588017924661877 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.225, "theta_Bn_degrees": 87.22500000000001, "compression": 1.5580021581076757, "u2x_km_s": -385.6943221306067, "u2y_km_s": -15.07579050666498, "speed2_km_s": 385.98884644920645, "signed_deflection_degrees": 2.238403888551539, "p2_over_p1": 2.507294572292127, "B2_over_B1": 1.5577761803652788, "entropy_over_cv": 0.18019709114762644, "upstream_fast_Mach": 1.4376745830883224, "downstream_fast_Mach": 0.7376139057171535, "downstream_alfven_margin": 0.6163582285196746, "state_global_normalized": { "rho": "1.55800215810767575615859948492856361295490898361997206013578472202756978507477242715978959", "p": "0.101695867852168664692219714870419654191088766689123270989562332399513319923058557776279366", "u": [ "-0.642823870217677843819023678890167599658883263813226016337686746425716597259722175032304340", "-0.0251263175111083014614224742849602169803541570398225780319698148413136524938794041181266923", "-0E-91" ], "B": [ "0.0701594009775870247241745785534253624428195291637823275657946023939226365834299451865617356", "1.00182457068571613762837719524806572796649800578311631565655851062059821829693563096415804", "0E-91" ] }, "root_record": { "r": "1.55800215810767575615859948492856361295490898361997206013578472202756978507477242715978959", "b": "0.0406212279177411463181606957453660196178913961310062328658885980754207271331211654008466143", "h": "0.000975650347323553977107671781050743310759748288344906317960926104974488054659173412667435911", "A": "0.415273251973128972618989254743843471661729123069584519760696407770141547189465207756187750", "denominator": "0.998479934653311399490542300873119473308600846634766549332138030302953267514798276461517999", "polynomial_residual": "-1.357229608965291951856200E-65", "bracket_initial_signs": [ "1.46218287927014740913987880635654650015441527522222841864666589877924030861631050429684647", "-2.02259076565105011097875205693604270759022439520568339219833058876522000845381715455760766" ], "bracket_derivative_max": "-5.56136455785686233257035198418243883033251219696352369597441130835397068295340637552709162", "iterations": 216 }, "flux_residuals": [ "1E-90", "1.60555415412103321168495624355963795078567058243565946851615474707621454420594467112043173E-89", "-3E-91", "0E-182", "-9E-90", "0E-182", "7.69448026617004381970255312825659244239602925082785058368357294714606641916024486871725684E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_-2.225", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.044444032958107116, 0.0 ], "rh_scaled_inf": 3.469446951953614e-18, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.009485325210600781, "alfven_n": 0.025005498896796794, "fast": 0.8695114374137217 }, "right": { "slow": 0.011675649377645736, "alfven_n": 0.031211852886071804, "fast": 0.6950432894906772 } }, "front_relative_normal_velocity": { "left": -0.6413637274164714, "right": -0.9992460714468455 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5580021581076757, "pressure_ratio": 2.507294572292127, "entropy_over_cv": 0.1801970911476265, "tangential_field_ratio": 1.5588516491334634 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.2, "theta_Bn_degrees": 87.2, "compression": 1.5580364554159767, "u2x_km_s": -385.67802619193384, "u2y_km_s": -15.04375687568256, "speed2_km_s": 385.9713130638605, "signed_deflection_degrees": 2.2337467451055146, "p2_over_p1": 2.5074578105510286, "B2_over_B1": 1.5578063671231737, "entropy_over_cv": 0.18022550535917095, "upstream_fast_Mach": 1.4377024885114418, "downstream_fast_Mach": 0.7376033228913385, "downstream_alfven_margin": 0.6161301032384378, "state_global_normalized": { "rho": "1.55803645541597659711483097867427717136824989728321104437176946760259085294562490049129975", "p": "0.101702488795949714698735396590404042393899696778913189890485772373567047871761758314417404", "u": [ "-0.642796710319889675853834781460285803061568684026206998847609912447078420943925760329680497", "-0.0250729281261375996058357292341193822036072488849847965992651714155542256506672662018153274", "-0E-91" ], "B": [ "0.0700034343253058883066535532662673278841387909260899058320392499878975740270071355880849899", "1.00185498954862684413271241527493111647082763314170752909187439276597878149923639805830355", "0E-91" ] }, "root_record": { "r": "1.55803645541597659711483097867427717136824989728321104437176946760259085294562490049129975", "b": "0.0406198583935966714299590202274631174009983608945226917875647941638058205815759228875598646", "h": "0.000993261270958475984005153076978798818940648243377881474752075426445882339882808675124690245", "A": "0.415241607428378671760452727864599960008764460056468910436632536335637883806379290229673236", "denominator": "0.998452462730093888182138715666255501975709467690793527266332283875356221014736568063308672", "polynomial_residual": "-8.28075305758565563729042E-66", "bracket_initial_signs": [ "1.46230346858589441102867287758474748572431935197112814040809677352227013987327051689970178", "-2.02226856542232138684548069955070025015099849900092278798204298130449160787458194435459556" ], "bracket_derivative_max": "-5.56109393287013792270724677033723135991290091028953131521769452070728366281489845233603071", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "1E-91", "0E-182", "5E-90", "0E-182", "4.69514119017340337150182636655773771095111703119857227953246842175149664065612801932074411E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.2", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.044058906883821934, 0.0 ], "rh_scaled_inf": 2.1883309757904123e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1883309757904123e-16 }, "characteristics": { "left": { "slow": 0.009570723745408365, "alfven_n": 0.025230317396797146, "fast": 0.8695194296592375 }, "right": { "slow": 0.011780782103045848, "alfven_n": 0.03149281787049258, "fast": 0.695041515470444 } }, "front_relative_normal_velocity": { "left": -0.6413604206352349, "right": -0.9992629164106211 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5580364554159767, "pressure_ratio": 2.5074578105510286, "entropy_over_cv": 0.1802255053591708, "tangential_field_ratio": 1.558901376125733 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.175, "theta_Bn_degrees": 87.17500000000001, "compression": 1.558070483358416, "u2x_km_s": -385.66182495592784, "u2y_km_s": -15.011711051381683, "speed2_km_s": 385.95387638554286, "signed_deflection_degrees": 2.2290868229761176, "p2_over_p1": 2.5076198578100195, "B2_over_B1": 1.5578362472641292, "entropy_over_cv": 0.18025372932837813, "upstream_fast_Mach": 1.4377301532119802, "downstream_fast_Mach": 0.737592820525004, "downstream_alfven_margin": 0.6159019744289319, "state_global_normalized": { "rho": "1.55807048335841593964933853781479496280587013909036116350272896303724795123961828613907498", "p": "0.101709061432774397107870130427852638337862326197767403943917011768660469033129711715117662", "u": [ "-0.642769708259879786133899849801888574900086625638583803867573493536998195671615774473465130", "-0.0250195184189694714145334751341863992754299357668818403437104988182992476399901097497398984", "-0E-91" ], "B": [ "0.0698474379667732381250899970271993363555552074507116190430220580290303396507493045112453059", "1.00188518750538474712651803703145630715622725976202921632221575729169879405909838685695556", "0E-91" ] }, "root_record": { "r": "1.55807048335841593964933853781479496280587013909036116350272896303724795123961828613907498", "b": "0.0406185044048278225794366123955506702669826462111121366582442580421231653483785280050242077", "h": "0.00101102912028709401437825390913131500494749510873513158930712280339452574745732126542188201", "A": "0.415209965150144830835953714562068058128713342898632826173970033451465683388464348274473975", "denominator": "0.998424745369864853378190722065703072462056781232194088085851374942716856357381674683800594", "polynomial_residual": "1.62606646121594203756995E-66", "bracket_initial_signs": [ "1.46242244068122492540582651655180795356383316570233247549916244954518566998675245678295651", "-2.02194775409714648780280048465906766494291510266191547853199418194246525688774906318926490" ], "bracket_derivative_max": "-5.56082333870016747337875316815505012423590810367186703654663678287846366393582042906778378", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-4E-91", "0E-182", "-6E-90", "0E-182", "-9.22082886075496671652097084084217646072803536506245220160600890547841089638213156293225844E-68", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-2.175", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04367377621041987, 0.0 ], "rh_scaled_inf": 1.7821726591756666e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7821726591756666e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.009656121266942048, "alfven_n": 0.02545512834789427, "fast": 0.8695273122646731 }, "right": { "slow": 0.011885913393835325, "alfven_n": 0.031773776859125365, "fast": 0.6950397255676867 } }, "front_relative_normal_velocity": { "left": -0.6413571027768261, "right": -0.9992795711288428 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.558070483358416, "pressure_ratio": 2.50761985781002, "entropy_over_cv": 0.18025372932837813, "tangential_field_ratio": 1.5589509734673892 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.15, "theta_Bn_degrees": 87.15, "compression": 1.5581042419402018, "u2x_km_s": -385.64571842721375, "u2y_km_s": -14.979653102693174, "speed2_km_s": 385.93653642576896, "signed_deflection_degrees": 2.224424135458032, "p2_over_p1": 2.5077807138011323, "B2_over_B1": 1.5578658207924816, "entropy_over_cv": 0.18028176301653137, "upstream_fast_Mach": 1.4377575771838615, "downstream_fast_Mach": 0.7375823986060366, "downstream_alfven_margin": 0.6156738420703239, "state_global_normalized": { "rho": "1.55810424194020176975031374011830451341381719644613852086875732689737866925756254357667566", "p": "0.101715585751773928199621550030862196770758643265723154632891293732926360146113033988598069", "u": [ "-0.642742864045356306888597473031476629731415560819585178257518501748578777272119699569122639", "-0.0249660885044886213512192006581649075604920380448937684842719896759713544230206760053958132", "-0E-91" ], "B": [ "0.0696914121321011398574026967640440289804265042345502024958744085391758342070697595229521001", "1.00191516453748330907960393051268799611857895231930037496594316132961346138680018760505949", "0E-91" ] }, "root_record": { "r": "1.55810424194020176975031374011830451341381719644613852086875732689737866925756254357667566", "b": "0.0406171659493678428306909677993943033292139535700487472545950170824594846987395612602462597", "h": "0.00102895388635298136426651688783053331353090588367121473806661927177065877698383367535604981", "A": "0.415178325126205656440629387818974097437651758280531171464373652725157578058096997159237322", "denominator": "0.998396782584912563448401837906786941893065712602682975120404775445200985909278391931634766", "polynomial_residual": "-6.62310218104882299533061E-66", "bracket_initial_signs": [ "1.46253979577167497932707769245329444706752768217191841894474404015188048675437729870771768", "-2.02162833141937322335812447940080896516468579338700646689434516643527951418917914264094615" ], "bracket_derivative_max": "-5.56055277524580129831793436864738299804274276748598394835075054035674483338751365674179286", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "0E-91", "0E-182", "-9E-90", "0E-182", "3.75617621839836761917079133869462349499597743806331938619893537687121519751094714967943564E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-2.15", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04328864097539117, 0.0 ], "rh_scaled_inf": 1.7821512424206992e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": -1.7821512424206992e-16, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.009741517774051493, "alfven_n": 0.0256799317657474, "fast": 0.8695350852300319 }, "right": { "slow": 0.011991043237187526, "alfven_n": 0.03205472979847955, "fast": 0.6950379197831547 } }, "front_relative_normal_velocity": { "left": -0.6413537738360713, "right": -0.9992960355983396 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5581042419402018, "pressure_ratio": 2.5077807138011323, "entropy_over_cv": 0.18028176301653143, "tangential_field_ratio": 1.5590004411825473 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.125, "theta_Bn_degrees": 87.125, "compression": 1.5581377311663898, "u2x_km_s": -385.629706610425, "u2y_km_s": -14.947583098555716, "speed2_km_s": 385.9192931960395, "signed_deflection_degrees": 2.2197586958540683, "p2_over_p1": 2.5079403782578047, "B2_over_B1": 1.5578950877125737, "entropy_over_cv": 0.18030960638511598, "upstream_fast_Mach": 1.4377847604210154, "downstream_fast_Mach": 0.737572057122452, "downstream_alfven_margin": 0.6154457061418617, "state_global_normalized": { "rho": "1.55813773116638966110449098024566546352565672983654398482759962908740658889004759831804443", "p": "0.101722061742136554626664267153325663079254463704423741076570734425103733807591098652461345", "u": [ "-0.642716177684041700048972939830812596222814668250840700565467185391032403190159840258411216", "-0.0249126384975928615180526965366970239294152544428678797389123389121663371600451063732164367", "-0E-91" ], "B": [ "0.0695353570514070191309848225234279444527407340955722508538809107530411795460843246775678002", "1.00194492062653378785166472596175012068963991005383989881396601011937424974142073026035787", "0E-91" ] }, "root_record": { "r": "1.55813773116638966110449098024566546352565672983654398482759962908740658889004759831804443", "b": "0.0406158430251737871108710097678169078172472040870784348301316731229305278135527477839679188", "h": "0.00104703556044026449116250492355269788626326621186964333961303726984701590949377701050612280", "A": "0.415146687344342804032854859465895534510789568290907205463511327034256430023772896939156780", "denominator": "0.998368574387405077032634178634641931222004319171553362040920175564792272805993025809546937", "polynomial_residual": "5.87976839633063672863984E-66", "bracket_initial_signs": [ "1.46265553407203068521566144071030368305696742347664362917369390465363370469686815922587446", "-2.02131029713206106779319345397096495300834491636428460215229990407733291256043649131639811" ], "bracket_derivative_max": "-5.56028224240388241019102737565930151190763609656730412434784487093859378163914098285825016", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-3E-91", "0E-182", "-1.1E-89", "0E-182", "-3.33501310466463122341211268621627334821944411153583741856442792010877785711940586719586605E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_-2.125", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.042903501216235485, 0.0 ], "rh_scaled_inf": 2.1882170274092918e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1882170274092918e-16 }, "characteristics": { "left": { "slow": 0.00982691326557905, "alfven_n": 0.025904727666009875, "fast": 0.869542748555338 }, "right": { "slow": 0.012096171620275339, "alfven_n": 0.032335676635065654, "fast": 0.6950360981176043 } }, "front_relative_normal_velocity": { "left": -0.6413504338078716, "right": -0.9993123098159769 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5581377311663898, "pressure_ratio": 2.5079403782578047, "entropy_over_cv": 0.18030960638511584, "tangential_field_ratio": 1.559049779295047 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.1, "theta_Bn_degrees": 87.10000000000001, "compression": 1.5581709510418826, "u2x_km_s": -385.6137895102036, "u2y_km_s": -14.91550110791582, "speed2_km_s": 385.90214670784076, "signed_deflection_degrees": 2.2150905174751214, "p2_over_p1": 2.5080988509148807, "B2_over_B1": 1.5579240480287548, "entropy_over_cv": 0.18033725939581915, "upstream_fast_Mach": 1.4378117029173758, "downstream_fast_Mach": 0.737561796062395, "downstream_alfven_margin": 0.6152175666228739, "state_global_normalized": { "rho": "1.55817095104188274567574506306701465812180623615894760383945464259323397909150253451613235", "p": "0.101728489393107569578796682602383554479394728034020328989773811881277465125691620155065759", "u": [ "-0.642689649183672717103770776090434170670834195255101887691212317998603186060747786693251124", "-0.0248591685131930290893071527089738200887012409588844253992351766747610781264422228288130956", "-0E-91" ], "B": [ "0.0693792729548136820263265068578183239587677290320439315688147843629525277572088362522675488", "1.00197445575426524135123866274859653697869670110905152619414510540956242504090630958870744", "0E-91" ] }, "root_record": { "r": "1.55817095104188274567574506306701465812180623615894760383945464259323397909150253451613235", "b": "0.0406145356302265155789296162659897297936191273227543338501491111486594501511785323720904265", "h": "0.00106527413407357406430536780087265748464829152315331161367000962119085786297535870996700841", "A": "0.415115051792341358933037659382515344375939262471522193652083403466693466260441210413629121", "denominator": "0.998340120789390260990620016848622350600893002844596156323014386884041814775587488761286549", "polynomial_residual": "2.42926649823773297606846E-66", "bracket_initial_signs": [ "1.46276965579632835264040242044938458629513930009470860209055234700327207986599652015413244", "-2.02099365097748153083313979712981702185262521330238879216102455917355578334117891235990594" ], "bracket_derivative_max": "-5.56001174006924712240634295683216722127881506736949072276786905488425233401018206528883066", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "0E-91", "0E-182", "-1E-90", "0E-182", "-1.37805101682758237405724924241824146381727089306075489161129427039760402884288271256228690E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.1", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04251835697046188, 0.0 ], "rh_scaled_inf": 1.7821107154397717e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7821107154397717e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.009912307740359831, "alfven_n": 0.02612951606432929, "fast": 0.8695503022406376 }, "right": { "slow": 0.012201298530271179, "alfven_n": 0.03261661731539537, "fast": 0.6950342605717982 } }, "front_relative_normal_velocity": { "left": -0.6413470826872031, "right": -0.9993283937786562 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5581709510418826, "pressure_ratio": 2.5080988509148807, "entropy_over_cv": 0.18033725939581924, "tangential_field_ratio": 1.5590989878284518 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.075, "theta_Bn_degrees": 87.075, "compression": 1.5582039015714317, "u2x_km_s": -385.5979671312002, "u2y_km_s": -14.883407199727744, "speed2_km_s": 385.8850969726443, "signed_deflection_degrees": 2.210419613640133, "p2_over_p1": 2.5082561315086127, "B2_over_B1": 1.557952701745381, "entropy_over_cv": 0.18036472201052983, "upstream_fast_Mach": 1.4378384046668824, "downstream_fast_Mach": 0.7375516154141396, "downstream_alfven_margin": 0.6149894234927694, "state_global_normalized": { "rho": "1.55820390157143168442723718410854657921531367009777330049920285057485096377040491421986995", "p": "0.101734868693989328904058599935704137087050537840200086004545596962370414206577365710683881", "u": [ "-0.642663278552000359444611644008635221216049508413716051198639726849268565819297349616893067", "-0.0248056786662129037315593725780309602804035216525773099312098992520697242685677438048456167", "-0E-91" ], "B": [ "0.0692231600724493355553952661080691210484166896621197548443439814913349120240982482119832978", "1.00200376990252453200755718258319636218306076643697455074741108297035044838403763843725908", "0E-91" ] }, "root_record": { "r": "1.55820390157143168442723718410854657921531367009777330049920285057485096377040491421986995", "b": "0.0406132437625306870720810268648128958864732989077044208295467279158660503887615629619760721", "h": "0.00108366959901799680005564170458002880964246150342871742299081776212460961454411670198683013", "A": "0.415083418457989817333578971027039683476547148323136883218376884465020911623151029731815836", "denominator": "0.998311421802795808472618339473114216163024116098857874852892315167275985152233451541539659", "polynomial_residual": "4.97101591674682925871943E-66", "bracket_initial_signs": [ "1.46288216115785460456393202234392239999681533278799191874413771245663069740170677619919681", "-2.02067839269711851513669204447394901160821406025371820693729348118679339347592780166018538" ], "bracket_derivative_max": "-5.55974126813472563698384248172735502381642950560420791319776241101625315298927131659467499", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.02759101362271117802922785697568836767199519961152638090445983372877544457990085670667554E-90", "1E-91", "0E-182", "-4E-90", "0E-182", "-2.82025310756090577787785703370542658250990579960770743941333211652177133070374829627264044E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-2.075", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.042133208275588585, 0.0 ], "rh_scaled_inf": 3.564183210279609e-16, "rh_components": { "mass": 0.0, "normal_momentum": 3.564183210279609e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.009997701197221757, "alfven_n": 0.026354296976347547, "fast": 0.8695577462859987 }, "right": { "slow": 0.012306423954346973, "alfven_n": 0.03289755178598155, "fast": 0.6950324071465063 } }, "front_relative_normal_velocity": { "left": -0.6413437204691169, "right": -0.9993442874833157 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5582039015714317, "pressure_ratio": 2.5082561315086127, "entropy_over_cv": 0.18036472201052978, "tangential_field_ratio": 1.5591480668060491 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.05, "theta_Bn_degrees": 87.05000000000001, "compression": 1.5582365827596347, "u2x_km_s": -385.58223947807386, "u2y_km_s": -14.851301442953474, "speed2_km_s": 385.8681440019067, "signed_deflection_degrees": 2.205745997676053, "p2_over_p1": 2.5084122197766585, "B2_over_B1": 1.5579810488668142, "entropy_over_cv": 0.1803919941913386, "upstream_fast_Mach": 1.4378648656634796, "downstream_fast_Mach": 0.7375415151660889, "downstream_alfven_margin": 0.6147612767310382, "state_global_normalized": { "rho": "1.55823658275963463818695496777396928044123166240401986509469754820363347310079979020909691", "p": "0.101741199634141267186553982595585844406783323920893248001434976941007545365457991608784674", "u": [ "-0.642637065796789839200183069820505100190926483563890562769863372621629037155372012727442670", "-0.0247521690715891250102352972868182322070721927489125190831802750218772016117656884697492019", "-0E-91" ], "B": [ "0.0690670186344476081155457360352519549246892849782907060461566095336647690713421697960249592", "1.00203286305327633105524090700603427974589167815042580246189199842615320919163036633187873", "0E-91" ] }, "root_record": { "r": "1.55823658275963463818695496777396928044123166240401986509469754820363347310079979020909691", "b": "0.0406119674201147526299265961445888275384075124752440283387815779472982000163248293656113135", "h": "0.00110222194727902808204007810739085700804722513301173237865142664324200676638708456290323911", "A": "0.415051787329080067319938463428101493325460665717820085079706475163926375288129496979545168", "denominator": "0.998282477439429257111036827652200580640838207985196444008782046243561560374295588757620112", "polynomial_residual": "1.377486778118578918008768E-65", "bracket_initial_signs": [ "1.46299305036914649805755403217742341202275944053271176972515706635932506474597456559653732", "-2.02036452203166866061647803380599633765711758481283630386905479193440742743515019460485415" ], "bracket_derivative_max": "-5.55947082649114261849372290124274789081308910069693436725645455004285976585886616234952908", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "0E-91", "0E-182", "-2E-90", "0E-182", "-7.81597492453273811979267644371753070163302515259055260078691303267971691342800933625895483E-67", "-4E-91" ], "diagnosis": { "case_id": "R95_phi_-2.05", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04174805516914296, 0.0 ], "rh_scaled_inf": 4.376226340010196e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7820732635865053e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 4.376226340010196e-16 }, "characteristics": { "left": { "slow": 0.010083093634985638, "alfven_n": 0.02657907041770101, "fast": 0.8695650806915108 }, "right": { "slow": 0.012411547879674174, "alfven_n": 0.033178479993338235, "fast": 0.6950305378425048 } }, "front_relative_normal_velocity": { "left": -0.6413403471487392, "right": -0.9993599909269292 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5582365827596347, "pressure_ratio": 2.5084122197766585, "entropy_over_cv": 0.18039199419133856, "tangential_field_ratio": 1.5591970162508495 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.025, "theta_Bn_degrees": 87.025, "compression": 1.5582689946109372, "u2x_km_s": -385.5666065554923, "u2y_km_s": -14.819183906562666, "speed2_km_s": 385.85128780707, "signed_deflection_degrees": 2.2010696829178027, "p2_over_p1": 2.5085671154580846, "B2_over_B1": 1.558009089397423, "entropy_over_cv": 0.1804190759005375, "upstream_fast_Mach": 1.437891085901117, "downstream_fast_Mach": 0.7375314953067749, "downstream_alfven_margin": 0.6145331263172503, "state_global_normalized": { "rho": "1.55826899461093723865649441087186678876780993209575202469613244738436623246486288669835679", "p": "0.101747482202979913781013023524388138770169136461171329728802443179383775554722082327719503", "u": [ "-0.642611010925820540559316414448464320630727516184300710693554841360929495003625233853473352", "-0.0246986398442711097823330636536990041316831003081313442633931603432449522581653848026757625", "-0E-91" ], "B": [ "0.0689108488709475699197301685156556144429699659507905268669983067151224986426548505530679782", "1.00206173518860312263179725327207765997588555825431516501315613068042882166147138296864265", "0E-91" ] }, "root_record": { "r": "1.55826899461093723865649441087186678876780993209575202469613244738436623246486288669835679", "b": "0.0406107066010309490962127958183312883241917488774882797851146005375647578142961911318092914", "h": "0.00112093117110252536575970364693913873028496711070393921384088356285371847290174856660931985", "A": "0.415020158393407369902739621903628006040579760121231629303793369292191528773637823128480632", "denominator": "0.998253287710978007333040777241762979893689532253927323269451112243677670912033059598229196", "polynomial_residual": "-2.44368404803327238464422E-66", "bracket_initial_signs": [ "1.46310232364199164947935058548848229860691567194278798579773137383583797617412729314251964", "-2.02005203872104167559825585968562407973855190124108324354767072395751601116335181298247782" ], "bracket_derivative_max": "-5.55920041502731775407222554512564591512325241707613383664683295688999872116441531201321690", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.02754332291693231742271614288415669003019159309854308871448038927437268574940970463007803E-90", "2E-91", "0E-182", "2E-90", "0E-182", "1.38673522077469673980536261164750332162634076408228670136505051231559743561570242447961545E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-2.025", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04136289768866136, 0.0 ], "rh_scaled_inf": 2.1880807930003295e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7820556907463825e-16, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1880807930003295e-16 }, "characteristics": { "left": { "slow": 0.010168485052465247, "alfven_n": 0.02680383640402058, "fast": 0.8695723054572849 }, "right": { "slow": 0.01251667029342375, "alfven_n": 0.03345940188398067, "fast": 0.6950286526605768 } }, "front_relative_normal_velocity": { "left": -0.6413369627212709, "right": -0.999375504106507 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5582689946109372, "pressure_ratio": 2.5085671154580846, "entropy_over_cv": 0.18041907590053763, "tangential_field_ratio": 1.559245836185587 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -2.0, "theta_Bn_degrees": 87.00000000000001, "compression": 1.5583011371296325, "u2x_km_s": -385.5510683681316, "u2y_km_s": -14.787054659532581, "speed2_km_s": 385.83452839956107, "signed_deflection_degrees": 2.1963906827082353, "p2_over_p1": 2.508720818293366, "B2_over_B1": 1.5580368233415824, "entropy_over_cv": 0.18044596710062, "upstream_fast_Mach": 1.4379170653737492, "downstream_fast_Mach": 0.7375215558248587, "downstream_alfven_margin": 0.6143049722310564, "state_global_normalized": { "rho": "1.55830113712963255956293375569801328869291069706751822617382570716010646645764866839625457", "p": "0.101753716389978908804127524840486779248976739708134177498867790985634008636312258231252666", "u": [ "-0.642585113946885981582825447296864164670361764270558171711345316035151527979181584609363687", "-0.0246450910992209695751458467048719926982977004012740222878958192102060585793059894153128474", "-0E-91" ], "B": [ "0.0687546510120937534037811155596264797170277164396732842376675435603895789107730453467955894", "1.00209038629070520768787455686785863231817551877953710454649941470055230049860497805454273", "0E-91" ] }, "root_record": { "r": "1.55830113712963255956293375569801328869291069706751822617382570716010646645764866839625457", "b": "0.0406094613033552927981858035155180014119351468064519928298560736420293693219251953792719458", "h": "0.00113979726297466236735871504754493065794226794657490654512620193043622950118017689404167874", "A": "0.414988531638770340060852541538992882147285035889818209329587823422954808660227585786181142", "denominator": "0.998223852629009340794171570865729374402290796400404243410900914414147741526330490683646132", "polynomial_residual": "-3.17958032644770091302143E-66", "bracket_initial_signs": [ "1.46320998118742836411218781280730131639454812115066191533503519828328591811453209555353694", "-2.01974094250436065482777308281718113467608216314336620758850109771025441311719864310344407" ], "bracket_derivative_max": "-5.55893003363006629952276894243412283118948489049746115497785263455558299821887570458425179", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.02752177025777493414796662370015115674574916825533361400317131989037916821197219745973901E-90", "-2E-91", "0E-182", "1E-90", "0E-182", "1.80455887256901311570771256142964359142030018532657669436262746551372242110710781456971847E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-2", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.040977735871688965, 0.0 ], "rh_scaled_inf": 2.1880495369570475e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1880495369570475e-16 }, "characteristics": { "left": { "slow": 0.010253875448467342, "alfven_n": 0.027028594950931798, "fast": 0.8695794205834542 }, "right": { "slow": 0.01262179118276617, "alfven_n": 0.03374031740442529, "fast": 0.6950267516015118 } }, "front_relative_normal_velocity": { "left": -0.6413335671819882, "right": -0.9993908270190958 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5583011371296325, "pressure_ratio": 2.5087208182933654, "entropy_over_cv": 0.18044596710062, "tangential_field_ratio": 1.559294526632721 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.975, "theta_Bn_degrees": 86.97500000000001, "compression": 1.5583330103198612, "u2x_km_s": -385.5356249206763, "u2y_km_s": -14.754913770848058, "speed2_km_s": 385.8178657907919, "signed_deflection_degrees": 2.1917090103980974, "p2_over_p1": 2.508873328024384, "B2_over_B1": 1.558064250703674, "entropy_over_cv": 0.18047266775428078, "upstream_fast_Mach": 1.4379428040753366, "downstream_fast_Mach": 0.7375116967091304, "downstream_alfven_margin": 0.6140768144521868, "state_global_normalized": { "rho": "1.55833301031986108795365149348366378505773131596345002575611256975420552133334356969751624", "p": "0.101759902184669019082693413863709168967941130233878246429963970948893739585761654850790792", "u": [ "-0.642559374867793776503984828191524417477529831880078415929882962439746460163894999356986695", "-0.0245915229514134279508067616175670362127256947680783707373723129367796124046121673838644244", "-0E-91" ], "B": [ "0.0685984252880361736115377117474064516230140088455565807264326721218504685912169448300200441", "1.00211881634190070771022718296795302360744278117885302677154766654468307864898510880048376", "0E-91" ] }, "root_record": { "r": "1.55833301031986108795365149348366378505773131596345002575611256975420552133334356969751624", "b": "0.0406082315251875733035074515186291559286840409720130372892427163630388594160452763805034441", "h": "0.00115882021562188403625621281744903807541775405487361555179751545694766107250646927272654328", "A": "0.414956907052970927795391208862832755656719210136178004777646942534064803671676227346256735", "denominator": "0.998194172204970438932998405910852329325699362168615913708626944016866151695719567719961078", "polynomial_residual": "4.8075624282640162955462E-67", "bracket_initial_signs": [ "1.46331602321574577025834817423767325868096795769989420289992287172406588436585086087157182", "-2.01943123311996238433382605791043949986093781822647257926408792886275385953172249026393412" ], "bracket_derivative_max": "-5.55865968218419961151039050203310596878474829472801222526250983169549634028864100003220100", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "2E-91", "0E-182", "1E-90", "0E-182", "-2.72884542917545019536374708767991311466981272149327202422018492030024363883860891565715994E-68", "2E-91" ], "diagnosis": { "case_id": "R95_phi_-1.975", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.04059256975577975, 0.0 ], "rh_scaled_inf": 2.1880194018163026e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.782022851078717e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1880194018163026e-16 }, "characteristics": { "left": { "slow": 0.01033926482179178, "alfven_n": 0.027253346074054958, "fast": 0.8695864260701726 }, "right": { "slow": 0.012726910534871417, "alfven_n": 0.034021226501189744, "fast": 0.6950248346661063 } }, "front_relative_normal_velocity": { "left": -0.6413301605262417, "right": -0.999405959661778 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5583330103198612, "pressure_ratio": 2.508873328024384, "entropy_over_cv": 0.1804726677542806, "tangential_field_ratio": 1.5593430876144327 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.95, "theta_Bn_degrees": 86.95, "compression": 1.5583646141856107, "u2x_km_s": -385.5202762178194, "u2y_km_s": -14.722761309501443, "speed2_km_s": 385.80129999215956, "signed_deflection_degrees": 2.1870246793459898, "p2_over_p1": 2.5090246443944317, "B2_over_B1": 1.5580913714880853, "entropy_over_cv": 0.18049917782441574, "upstream_fast_Mach": 1.4379683019998435, "downstream_fast_Mach": 0.7375019179485092, "downstream_alfven_margin": 0.6138486529604524, "state_global_normalized": { "rho": "1.55836461418561069563394287544007953351022693610540857810076219432542000101412212952979239", "p": "0.101766039576638154058594050661928341418123559025989973504547655463946320856201333430085394", "u": [ "-0.642533793696365598517529746123446382334010703674425765204448111892735657381229061113799242", "-0.0245379355158357378564781203426405410771921158832389562108003184008206217250051242783167351", "-0E-91" ], "B": [ "0.0684421719289303485585869562923958220192308688766002743700417284596238967699646093112300862", "1.00214702532462556825734572313982169993638763704263489968034815463991014662285434651754212", "0E-91" ] }, "root_record": { "r": "1.55836461418561069563394287544007953351022693610540857810076219432542000101412212952979239", "b": "0.0406070172646513472546977437961573054250418379445099693939520008953419599999475084698444732", "h": "0.00117800002201086231134717441257297154804846886503913005470901685855158700267616653448709815", "A": "0.414925284623814399194562358203708886874446431565070133049491121587424338277320546635576508", "denominator": "0.998164246450188401646828076554179545982642429157493158807694721893604670930528147803235866", "polynomial_residual": "1.338105230132341498576565E-65", "bracket_initial_signs": [ "1.46342044993648395778758401741835246933827096245042925809665725158900190897569758277279187", "-2.01912291030539763315596277462191946158910399279045788477212276457530307085336124351321977" ], "bracket_derivative_max": "-5.55838936057252566585736662544239777216092096584546905480283831891700975953550917224392238", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "1E-91", "0E-182", "-5E-90", "0E-182", "-7.59621083823058080123188697018162923361756348734188706475828298207916607567864436582669740E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.95", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.040207399378496295, 0.0 ], "rh_scaled_inf": 2.187990387521241e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.187990387521241e-16 }, "characteristics": { "left": { "slow": 0.010424653171231538, "alfven_n": 0.027478089789005195, "fast": 0.8695933219176167 }, "right": { "slow": 0.012832028336908967, "alfven_n": 0.0343021291207929, "fast": 0.6950229018551632 } }, "front_relative_normal_velocity": { "left": -0.6413267427494576, "right": -0.9994209020316729 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5583646141856107, "pressure_ratio": 2.5090246443944317, "entropy_over_cv": 0.1804991778244157, "tangential_field_ratio": 1.5593915191526295 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.925, "theta_Bn_degrees": 86.925, "compression": 1.5583959487307166, "u2x_km_s": -385.5050222642623, "u2y_km_s": -14.69059734449256, "speed2_km_s": 385.78483101504565, "signed_deflection_degrees": 2.182337702918332, "p2_over_p1": 2.5091747671482096, "B2_over_B1": 1.5581181856992108, "entropy_over_cv": 0.18052549727412182, "upstream_fast_Mach": 1.4379935591412405, "downstream_fast_Mach": 0.7374922195320427, "downstream_alfven_margin": 0.613620487735744, "state_global_normalized": { "rho": "1.55839594873071661074729148491913124007650402477456974921061862935170857937453054962320479", "p": "0.101772128555531381650657811344073705621443344879319233891726040050882057015396533514522768", "u": [ "-0.642508370440437143057060906027220719131448501201499594222042613680442183660348629339192883", "-0.0244843289074875989600073552092144364485336537123616339948415797551833286971854295135350750", "-0E-91" ], "B": [ "0.0682858911649373195753913913434936830222353796146117503903991392842568436951561616487810479", "1.00217501322143356230770598753762709505316082734495138686905608595040551477521811480446360", "0E-91" ] }, "root_record": { "r": "1.55839594873071661074729148491913124007650402477456974921061862935170857937453054962320479", "b": "0.0406058185198939322810695844306621319313971522661782436539568925697134744486155302120076097", "h": "0.00119733667534845266048346184116746578090941096012289036972967127349779414812272740723204139", "A": "0.414893664339109317509303049894859850425168668898109816986181544863453598022474728731422503", "denominator": "0.998134075375870266088498701946828764591001333009631340495341448850314350988202510173614548", "polynomial_residual": "6.54721958156241742929461E-66", "bracket_initial_signs": [ "1.46352326155843412113545436515455236134306698221285979526450641951688784120739174822472121", "-2.01881597379743143194514425872944825151675090198266277437103659156134650350063742686154332" ], "bracket_derivative_max": "-5.55811906867584956194776566139382728522789656962534232780165082490615812570409306128655701", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-2E-91", "0E-182", "-8E-90", "0E-182", "-3.71720382316256652631537176224091428927114497124432689700634858249805793725527938482630140E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.925", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.0398222247774097, 0.0 ], "rh_scaled_inf": 2.1879624940171045e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7819930858969557e-16, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1879624940171045e-16 }, "characteristics": { "left": { "slow": 0.01051004049557281, "alfven_n": 0.027702826111392614, "fast": 0.8696001081259842 }, "right": { "slow": 0.012937144576047799, "alfven_n": 0.03458302520975487, "fast": 0.6950209531694922 } }, "front_relative_normal_velocity": { "left": -0.6413233138471365, "right": -0.9994356541259355 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5583959487307166, "pressure_ratio": 2.5091747671482096, "entropy_over_cv": 0.1805254972741217, "tangential_field_ratio": 1.559439821268941 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.9, "theta_Bn_degrees": 86.9, "compression": 1.5584270139588614, "u2x_km_s": -385.4898630647149, "u2y_km_s": -14.658421944828646, "speed2_km_s": 385.768458870817, "signed_deflection_degrees": 2.177648094489321, "p2_over_p1": 2.509323696031828, "B2_over_B1": 1.5581446933414511, "entropy_over_cv": 0.1805516260666968, "upstream_fast_Mach": 1.4380185754935024, "downstream_fast_Mach": 0.7374826014489081, "downstream_alfven_margin": 0.6133923187580319, "state_global_normalized": { "rho": "1.55842701395886138949815460038286352459142478402130783644156034699871305222800351262454356", "p": "0.101778169111050944073423260547146644503310024465909866372700970193901648139812915546999044", "u": [ "-0.642483105107858091560741996341699061246877106254811479399779558782824507358656846769963083", "-0.0244307032413810749708719354280322220170101288942387305482683572826078014618499395896256912", "-0E-91" ], "B": [ "0.0681295832262236716305745738225921825254872975869126643080080252130854655631110478483797647", "1.00220278001499629342059011667916361969721444962373387087369865404944397112140133214514635", "0E-91" ] }, "root_record": { "r": "1.55842701395886138949815460038286352459142478402130783644156034699871305222800351262454356", "b": "0.0406046352890864009881217950026087034997326902250311555362438040168963944466714267507766117", "h": "0.00121683016908165140295005032768030770940997054393465377985655748319992064771851047673725292", "A": "0.414862046186667524239644177818139957083538556959844765843017906966981373024661692307930911", "denominator": "0.998103658993103025584284387014374340573344101053827499459598661908813090426399698394110792", "polynomial_residual": "-1.173992747636489290760697E-65", "bracket_initial_signs": [ "1.46362445828963870674887434918358902202546474355709222147917750942713269925910258236333478", "-2.01851042333204333844555135339756164646770671273448761839500575470779993234414499267669381" ], "bracket_derivative_max": "-5.55784880637297401324857304911751490151445109086393409309776901402010353038779514817112632", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.02745084378425922041267539644769912574111302277513966108555459775350961792330828977301941E-90", "4E-91", "0E-182", "3E-90", "0E-182", "6.66618861026714015037110202186065776072844028244873084436215052944692160629607560954409894E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.9", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03943704599009945, 0.0 ], "rh_scaled_inf": 2.187935721251231e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.187935721251231e-16 }, "characteristics": { "left": { "slow": 0.010595426793595044, "alfven_n": 0.027927555056822356, "fast": 0.8696067846954951 }, "right": { "slow": 0.013042259239456375, "alfven_n": 0.034863914714597, "fast": 0.6950189886099097 } }, "front_relative_normal_velocity": { "left": -0.6413198738148543, "right": -0.9994502159417572 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5584270139588614, "pressure_ratio": 2.5093236960318284, "entropy_over_cv": 0.18055162606669695, "tangential_field_ratio": 1.5594879939847213 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.875, "theta_Bn_degrees": 86.875, "compression": 1.5584578098735749, "u2x_km_s": -385.4747986238952, "u2y_km_s": -14.626235179524306, "speed2_km_s": 385.75218357082485, "signed_deflection_degrees": 2.172955867440892, "p2_over_p1": 2.5094714307928077, "B2_over_B1": 1.5581708944192132, "entropy_over_cv": 0.1805775641656394, "upstream_fast_Mach": 1.4380433510506099, "downstream_fast_Mach": 0.737473063688411, "downstream_alfven_margin": 0.6131641460073669, "state_global_normalized": { "rho": "1.55845780987357488801712325494451286061552930725348153709314473287040943347358873903097651", "p": "0.101784161232956273612845055953803412632352381230561035052608494520341018163119123669016862", "u": [ "-0.642457997706492075725179710596147464035850617105930435008349868338010043522688220732414772", "-0.0243770586325405109462356126049522978101074505123651706415932983462859683050949552079377454", "-0E-91" ], "B": [ "0.0679732483429615536351357440602438917986957098130967302974335852045569825308837688576416101", "1.00223032568810319870943275066836137687785588076032773472475729326435573074906029035588136", "0E-91" ] }, "root_record": { "r": "1.55845780987357488801712325494451286061552930725348153709314473287040943347358873903097651", "b": "0.0406034675704235750243569326638990505195648199830563868277089192452689492954573627983402794", "h": "0.00123648049689755381465605369649835923525383012082544986986550261852682008568875842975506218", "A": "0.414830430154304120231737173742386493698751970505128960053715371284972220221340497306661950", "denominator": "0.998072997312853648672938896975674386470523815995664262389567485979378158580932833787434424", "polynomial_residual": "1.399395630976322231943271E-65", "bracket_initial_signs": [ "1.46372404033739156497587405556695218400555949076734079495025402597931853687574731833409546", "-2.01820625864442768986559559184371235863541550365577645478456901120436095652120495181636467" ], "bracket_derivative_max": "-5.55757857354069982395491303447810342553860000910881536674457812752265510701286818527561960", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.02743693312225983005058588297958227842294257152913032589298398908467755958036117591605940E-90", "0E-91", "0E-182", "2E-90", "0E-182", "-7.94704001505492806620685425258590539571675340628659526828027031742176983135416116077937474E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.875", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.0390518630541533, 0.0 ], "rh_scaled_inf": 2.1879100691730554e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1879100691730554e-16 }, "characteristics": { "left": { "slow": 0.01068081206407103, "alfven_n": 0.028152276640894734, "fast": 0.8696133516263904 }, "right": { "slow": 0.01314737231430266, "alfven_n": 0.0351447975818419, "fast": 0.6950170081772389 } }, "front_relative_normal_velocity": { "left": -0.6413164226482616, "right": -0.9994645874763657 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5584578098735749, "pressure_ratio": 2.5094714307928077, "entropy_over_cv": 0.18057756416563941, "tangential_field_ratio": 1.5595360373210478 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.85, "theta_Bn_degrees": 86.85000000000001, "compression": 1.5584883364782343, "u2x_km_s": -385.45982894652997, "u2y_km_s": -14.59403711760147, "speed2_km_s": 385.73600512640513, "signed_deflection_degrees": 2.1682610351626828, "p2_over_p1": 2.509617971180079, "B2_over_B1": 1.5581967889369106, "entropy_over_cv": 0.18060331153464892, "upstream_fast_Mach": 1.438067885806548, "downstream_fast_Mach": 0.7374636062399859, "downstream_alfven_margin": 0.6129359694638787, "state_global_normalized": { "rho": "1.55848833647823423436832007422276840150609478018370991113783456827216119147553316168909413", "p": "0.101790104911064008358973557230580671953004862810247478745835250759532136828254622153740525", "u": [ "-0.642433048244216642247379335772166784886301711873022205768892647710722709020391839467233401", "-0.0243233951960024505819383381521054043116650095927259701120899524946338971481721364368910526", "-0E-91" ], "B": [ "0.0678168867453286987283651057413809235519355369479552533630232883203279745242480433267990923", "1.00225765022366155162764480740185526057813468918377969072421015859855188743432951033458335", "0E-91" ] }, "root_record": { "r": "1.55848833647823423436832007422276840150609478018370991113783456827216119147553316168909413", "b": "0.0406023153621240192254908545229094914962608233972943929540393913459473448986102123784914481", "h": "0.00125628765272331301576450861456068584733814978117077902235618509734018526635882388835822973", "A": "0.414798816229837446785481235516419770613897638844528341911189374404830754462361707572762087", "denominator": "0.998042090345969098265907521625903083497371822736622496810020343698215563521354981402726536", "polynomial_residual": "-1.443131225710130217438760E-65", "bracket_initial_signs": [ "1.46382200790823810639663083602170428032837889415553210345932025250738738648023039641045731", "-2.01790347946899384214606488150437315051997898105688018355524808314991340553609089528549885" ], "bracket_derivative_max": "-5.55730837005382635176677647843744291805865087493924468890843188676987250141434492878894796", "iterations": 216 }, "flux_residuals": [ "1E-90", "-1.60548491016282906076773326809474868046628050016865598942026034816299264129571920442334444E-89", "2E-91", "0E-182", "-1E-90", "0E-182", "8.19640484217027251004903217397296049937284417637504125337989519380217560852948178330777756E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.85", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03866667600716718, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.010766196305766931, "alfven_n": 0.028376990879205307, "fast": 0.8696198089189333 }, "right": { "slow": 0.013252483787754083, "alfven_n": 0.03542567375801343, "fast": 0.6950150118723094 } }, "front_relative_normal_velocity": { "left": -0.641312960343084, "right": -0.9994787687270248 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5584883364782343, "pressure_ratio": 2.509617971180079, "entropy_over_cv": 0.1806033115346488, "tangential_field_ratio": 1.5595839512987228 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.825, "theta_Bn_degrees": 86.825, "compression": 1.5585185937760637, "u2x_km_s": -385.4449540373539, "u2y_km_s": -14.561827828089331, "speed2_km_s": 385.7199235488786, "signed_deflection_degrees": 2.163563611051993, "p2_over_p1": 2.5097633169439844, "B2_over_B1": 1.558222376898963, "entropy_over_cv": 0.18062886813762535, "upstream_fast_Mach": 1.4380921797553075, "downstream_fast_Mach": 0.737454229093196, "downstream_alfven_margin": 0.612707789107777, "state_global_normalized": { "rho": "1.55851859377606380069890015015317887252102238992579000292185616169454503105153398261068612", "p": "0.101796000135248007895640941492784778947003190146671291167501006812185374599657132792450441", "u": [ "-0.642408256728923218054671858742954500933082931772180886849835327119596549728428756536136322", "-0.0242697130468155534882421988422907908472105728385291981935100424054053521949350537358968677", "-0E-91" ], "B": [ "0.0676604986635084445462311482032138201793381251829091640393199032409847553756882117230766331", "1.00228475360469646456686703487477398369146302701465622947794152678401919465634399482184532", "0E-91" ] }, "root_record": { "r": "1.55851859377606380069890015015317887252102238992579000292185616169454503105153398261068612", "b": "0.0406011786624300358360214075692020689332842475050291943674863737813704058747684720889482075", "h": "0.00127625163072609964048926378382864052767780107784517184190511859055500352526674521911301921", "A": "0.414767204401089066772688465423163135864638344462674113145914333878774546028474495774252889", "denominator": "0.998010938103176350928737400673497088666919749899494465195108082118388965878887205012734939", "polynomial_residual": "7.86505743615164756859210E-66", "bracket_initial_signs": [ "1.46391836120797546259290636905334147041602869256146412529265079868001251830780115647829674", "-2.01760208553936639613320684451717623735823415698711995771500051697012728925781412589603038" ], "bracket_derivative_max": "-5.55703819578515195680454950974873127735347097845191546421582733390380451266880458572115326", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.02741369684812837846421602096506607159826579675909639390668151966838019518138125886125263E-90", "-1E-91", "0E-182", "-9E-90", "0E-182", "-4.46757812252286244552399030697208250754174570207638673692198336289309191941429138578385802E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-1.825", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03828148488674503, 0.0 ], "rh_scaled_inf": 4.3757242537760206e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.781942778144037e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -4.3757242537760206e-16 }, "characteristics": { "left": { "slow": 0.010851579517442391, "alfven_n": 0.028601697787345025, "fast": 0.8696261565734087 }, "right": { "slow": 0.013357593646977573, "alfven_n": 0.03570654318963673, "fast": 0.6950129996959576 } }, "front_relative_normal_velocity": { "left": -0.641309486895122, "right": -0.9994927596910347 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5585185937760637, "pressure_ratio": 2.5097633169439844, "entropy_over_cv": 0.18062886813762546, "tangential_field_ratio": 1.5596317359382719 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.8, "theta_Bn_degrees": 86.80000000000001, "compression": 1.5585485817701352, "u2x_km_s": -385.4301739011102, "u2y_km_s": -14.529607380024308, "speed2_km_s": 385.7039388495504, "signed_deflection_degrees": 2.158863608513745, "p2_over_p1": 2.5099074678362765, "B2_over_B1": 1.5582476583097964, "entropy_over_cv": 0.18065423393866908, "upstream_fast_Mach": 1.438116232890884, "downstream_fast_Mach": 0.7374449322377337, "downstream_alfven_margin": 0.6124796049193509, "state_global_normalized": { "rho": "1.55854858177013517553052238423867501426675836206273150414378515804524288293891726472887393", "p": "0.101801846895439368947186457278339091787283463085948689711300401669503299522377245480470769", "u": [ "-0.642383623168517076022511479719785339843529298533185351948621188723065244301689009590802269", "-0.0242160123000405124501557166926937413920268296384432769378801598408101818816746313231031895", "-0E-91" ], "B": [ "0.0675040843276897534730114639386276226565773186128736703411703487424698098579822086668891206", "1.00231163581435089126760511617111439160637032464363060741196868372699751381632212461831978", "0E-91" ] }, "root_record": { "r": "1.55854858177013517553052238423867501426675836206273150414378515804524288293891726472887393", "b": "0.0406000574696076588081240566946062239101533061317363059701826437634104215281958230121886096", "h": "0.00129637242531306228879170163783190910071760268090117631584806752485373425986659089738307069", "A": "0.414735594655883745765724363889482142173027669416844048799199470530034962760520756474443983", "denominator": "0.997979540595082416283717676962278845016259233010815108621058076978157062346627997205347199", "polynomial_residual": "1.287473258268946074596564E-65", "bracket_initial_signs": [ "1.46401310044165265135308692596524739098928890285514392712093210108630038553138733153264723", "-2.01730207658838541066442489857313878509885980204884891738234809533128780539204726774375079" ], "bracket_derivative_max": "-5.55676805060547443667052310210803392809902499673969136296993277694602378965096674848756967", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "3E-91", "0E-182", "-2E-90", "0E-182", "-7.31410418611479800699098044227525077064328960663004591857589084698005437643847032683473060E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.8", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03789628973049874, 0.0 ], "rh_scaled_inf": 1.7819321224470181e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7819321224470181e-16, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.010936961697850552, "alfven_n": 0.02882639738090027, "fast": 0.8696323945901229 }, "right": { "slow": 0.013462701879139522, "alfven_n": 0.03598740582323823, "fast": 0.6950109716490269 } }, "front_relative_normal_velocity": { "left": -0.6413060023002513, "right": -0.9995065603657316 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5585485817701352, "pressure_ratio": 2.5099074678362765, "entropy_over_cv": 0.18065423393866897, "tangential_field_ratio": 1.5596793912599451 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.775, "theta_Bn_degrees": 86.775, "compression": 1.558578300463367, "u2x_km_s": -385.41548854255035, "u2y_km_s": -14.497375842449982, "speed2_km_s": 385.68805103971016, "signed_deflection_degrees": 2.154161040960446, "p2_over_p1": 2.5100504236101195, "B2_over_B1": 1.5582726331738437, "entropy_over_cv": 0.18067940890208095, "upstream_fast_Mach": 1.4381400452072783, "downstream_fast_Mach": 0.7374357156634196, "downstream_alfven_margin": 0.6122514168789688, "state_global_normalized": { "rho": "1.55857830046336713619266090950833976224187328609524600503894785561135210113034365696614220", "p": "0.101807645181626440982253279047378733750417650478384123653024134596787688383632175169094864", "u": [ "-0.642359147570917301180045358373682772161829209566354947546797789199923745049244202204790380", "-0.0241622930707499706721588558874323684845250506200940964722611998889474492926541362987760329", "-0E-91" ], "B": [ "0.0673476439680672328769385412501483138511322483746066358682114269822696824345788012653736201", "1.00233829683588562904219771908074457096590829198871772905966280024382976167114861961842602", "0E-91" ] }, "root_record": { "r": "1.55857830046336713619266090950833976224187328609524600503894785561135210113034365696614220", "b": "0.0405989517819466481778426964217815995360986334486813058793043341975043983749411127484091933", "h": "0.00131665003113128875971439910855294426724266680791037201874987532924874508955987489409064726", "A": "0.414703986982049433176561182276786381282014742005279335476079624658472666650974937421151149", "denominator": "0.997947897832174356533781940246790245416505954688404547177670785279030783789950392861041290", "polynomial_residual": "3.22268288736578518040555E-66", "bracket_initial_signs": [ "1.46410622581357074631009241063069006600855700304092464416795450266473767323971165189425322", "-2.01700345234810660257413451454646020876445552662925234182870231121131721916384715849156070" ], "bracket_derivative_max": "-5.55649793438359144766344907902335872915365310366915002818087512465131326732158211347158366", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-3E-91", "0E-182", "-3E-90", "0E-182", "-1.83102028097249797776354995373179471126049762575945455914165517561093087141925223282731257E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.775", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03751109057604797, 0.0 ], "rh_scaled_inf": 1.7819222352054697e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7819222352054697e-16, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.011022342845738158, "alfven_n": 0.029051089675453022, "fast": 0.8696385229694044 }, "right": { "slow": 0.0135678084714058, "alfven_n": 0.036268261605345645, "fast": 0.6950089277323668 } }, "front_relative_normal_velocity": { "left": -0.6413025065544218, "right": -0.9995201707484881 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.558578300463367, "pressure_ratio": 2.5100504236101195, "entropy_over_cv": 0.180679408902081, "tangential_field_ratio": 1.5597269172837156 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.75, "theta_Bn_degrees": 86.75, "compression": 1.5586077498585256, "u2x_km_s": -385.40089796643406, "u2y_km_s": -14.465133284417062, "speed2_km_s": 385.67226013063174, "signed_deflection_degrees": 2.14945592181215, "p2_over_p1": 2.51019218402009, "B2_over_B1": 1.5582973014955437, "entropy_over_cv": 0.180704392992362, "upstream_fast_Mach": 1.4381636166984963, "downstream_fast_Mach": 0.7374265793602033, "downstream_alfven_margin": 0.6120232249670782, "state_global_normalized": { "rho": "1.55860774985852562139762837620296922495187473063572722884924602724559688745010613156630181", "p": "0.101813394983854841774689254414994173967972459415022696798670193158487247325860136421705695", "u": [ "-0.642334829944056757403360354180906012016903691895197302947818900557853529610284461369578155", "-0.0241085554740284390071510725551791836378132444115663883706526294368777937567703234002222260", "-0E-91" ], "B": [ "0.0671911778148411553306320443715777498128168287596611385157301658548898991864738535947394291", "1.00236473665267932081006849552114407406361622214076766101846604019581113885927422732168611", "0E-91" ] }, "root_record": { "r": "1.55860774985852562139762837620296922495187473063572722884924602724559688745010613156630181", "b": "0.0405978615977604845185443247353864617725322852736537877924575201012345393727006003561898848", "h": "0.00133708444306776806609321062830114371233553417475460205986547423104994577851506423974275123", "A": "0.414672381367417243406181696650714434440376784227462174643921540183817184595432911263326810", "denominator": "0.997916009824819306107706520318470747938675192001903451044816960829447624836655801999157097", "polynomial_residual": "-2.92293112987485861989127E-66", "bracket_initial_signs": [ "1.46419773752728305100948679925493829121128623838932456008257904008950839718112572212211191", "-2.01670621254980153362719955137474425493605036152562038424857594749723992718297548389098781" ], "bracket_derivative_max": "-5.55622784698630091215309356623135415363106918147263270347340254234900423894095658072268026", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-1E-91", "0E-182", "1E-90", "0E-182", "1.66091271380024197141381832725971628515836055861422362132514961370817983218133997029436004E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-1.75", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.037125887461020086, 0.0 ], "rh_scaled_inf": 2.1877986174745155e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7819131164013395e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1877986174745155e-16 }, "characteristics": { "left": { "slow": 0.011107722959845582, "alfven_n": 0.029275774686580918, "fast": 0.869644541711603 }, "right": { "slow": 0.013672913410941743, "alfven_n": 0.036549110482488004, "fast": 0.6950068679468339 } }, "front_relative_normal_velocity": { "left": -0.6412989996536591, "right": -0.9995335908367129 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5586077498585256, "pressure_ratio": 2.51019218402009, "entropy_over_cv": 0.18070439299236196, "tangential_field_ratio": 1.5597743140292812 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.725, "theta_Bn_degrees": 86.725, "compression": 1.5586369299582237, "u2x_km_s": -385.38640217752925, "u2y_km_s": -14.432879774983329, "speed2_km_s": 385.6565661335736, "signed_deflection_degrees": 2.1447482644964158, "p2_over_p1": 2.5103327488221763, "B2_over_B1": 1.5583216632793417, "entropy_over_cv": 0.18072918617421344, "upstream_fast_Mach": 1.4381869473585487, "downstream_fast_Mach": 0.7374175233181631, "downstream_alfven_margin": 0.6117950291642058, "state_global_normalized": { "rho": "1.55863692995822370395718506193078631766412500160434812793014458471131353933506194021840786", "p": "0.101819096292227472921583666669148503335750764362546585557014715804446953148704136740069699", "u": [ "-0.642310670295882054596314457596842142565531949485581004497845640777944094566875583398414238", "-0.0240547996249722131694447329084859275272021062949923846249852813941152181999476672381731715", "-0E-91" ], "B": [ "0.0670346860982174788170891310264683340418642265736077870132954451885097857975658554255988509", "1.00239095524822845694521264905036051984270316581100002679121963768290502172884231655868144", "0E-91" ] }, "root_record": { "r": "1.55863692995822370395718506193078631766412500160434812793014458471131353933506194021840786", "b": "0.0405967869153863634716066899282972368826604498825761530398315812958741172745665489240827809", "h": "0.00135767565624935323039363075346745968257451829708720419961529355044939299583990374439340388", "A": "0.414640777799821437004271022244829096839566344715196727350238512195723579767372818926108027", "denominator": "0.997883876583264491426639284700363767403011034299629778406406367862744264760968976576184764", "polynomial_residual": "-8.6573422862960569182032E-67", "bracket_initial_signs": [ "1.46428763578559527740518960815942866928730734029745244611655197945182894908643364687480345", "-2.01641035692395778438724114303791470501486404160774575505011403003748624699325888522527636" ], "bracket_derivative_max": "-5.55595778827840141212162452042090735109919787399092509506181768522921167866424942568047517", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "-2E-91", "0E-182", "0E-90", "0E-182", "4.92000392429267400498250081611788522331124605666398933752125626827838092167806173553051557E-68", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.725", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.036740680423049996, 0.0 ], "rh_scaled_inf": 1.7819047660179792e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": -1.7819047660179792e-16, "t1_momentum": 3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.01119310203890691, "alfven_n": 0.029500452429857365, "fast": 0.869650450817091 }, "right": { "slow": 0.01377801668491214, "alfven_n": 0.03682995240119564, "fast": 0.6950047922932915 } }, "front_relative_normal_velocity": { "left": -0.6412954815940631, "right": -0.9995468206278512 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5586369299582237, "pressure_ratio": 2.5103327488221767, "entropy_over_cv": 0.18072918617421363, "tangential_field_ratio": 1.5598215815160639 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.7, "theta_Bn_degrees": 86.7, "compression": 1.5586658407649217, "u2x_km_s": -385.3720011806121, "u2y_km_s": -14.400615383213575, "speed2_km_s": 385.6409690597784, "signed_deflection_degrees": 2.1400380824482723, "p2_over_p1": 2.5104721177737805, "B2_over_B1": 1.5583457185296894, "entropy_over_cv": 0.18075378841253656, "upstream_fast_Mach": 1.438210037181452, "downstream_fast_Mach": 0.7374085475275057, "downstream_alfven_margin": 0.6115668294509575, "state_global_normalized": { "rho": "1.55866584076492156364060994275006334211759131428187247528332919241195983785795693500879615", "p": "0.101824749096904535318471965622323295153244872285949297276965115701615931980560596223778045", "u": [ "-0.642286668634353516358863542926913637333164504946373935375737608907805712145184038813296802", "-0.0240010256386892909316262115257395879002857817114276365479736124618913715644543142244935947", "-0E-91" ], "B": [ "0.0668781690484078669220044003245854609247561852941045702125415437610139860190274692675272698", "1.00241695260614737693586830173125837203065495216401292063263684544725764169134225650669015", "0E-91" ] }, "root_record": { "r": "1.55866584076492156364060994275006334211759131428187247528332919241195983785795693500879615", "b": "0.0405957277331851903543084536296584414923862720814746609260661756385124161591726026513601047", "h": "0.00137842366604272486142166568061487066590264734617435786709967797198299703087885366720515875", "A": "0.414609176267099401839134145793680557606549515121202122660910795653520845004719077535321416", "denominator": "0.997851498117637250791994692836158669577756825081072564754181263827215896929784398686823301", "polynomial_residual": "8.77878108875658668056999E-66", "bracket_initial_signs": [ "1.46437592079056572878025496481787556595158060906270891033978205243282123413274413275652300", "-2.01611588520027911502698429576937140943127518447687869319831171813503145130965000729348427" ], "bracket_derivative_max": "-5.55568775812269256887855566313647686519713195548920777719921933232996306105304292547655920", "iterations": 216 }, "flux_residuals": [ "-2E-90", "-8.02738235183879753221835148213799393885326354355991055535756040258578194091957731816885213E-90", "1E-91", "0E-182", "1E-90", "0E-182", "-4.98962264753854762536696163251279829669320035473970376466975171880435760853589931554539337E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.7", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03635546949978008, 0.0 ], "rh_scaled_inf": 2.1877618800738515e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1877618800738515e-16 }, "characteristics": { "left": { "slow": 0.011278480081650014, "alfven_n": 0.029725122920851662, "fast": 0.8696562502862616 }, "right": { "slow": 0.013883118280481258, "alfven_n": 0.03711078730800022, "fast": 0.6950027007726093 } }, "front_relative_normal_velocity": { "left": -0.6412919523718092, "right": -0.999559860119384 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5586658407649217, "pressure_ratio": 2.5104721177737805, "entropy_over_cv": 0.18075378841253653, "tangential_field_ratio": 1.5598687197632088 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.675, "theta_Bn_degrees": 86.675, "compression": 1.5586944822809266, "u2x_km_s": -385.3576949804671, "u2y_km_s": -14.368340178179574, "speed2_km_s": 385.62546892047294, "signed_deflection_degrees": 2.1353253891101747, "p2_over_p1": 2.5106102906337164, "B2_over_B1": 1.5583694672510446, "entropy_over_cv": 0.18077819967243258, "upstream_fast_Mach": 1.438232886161227, "downstream_fast_Mach": 0.7373996519785669, "downstream_alfven_margin": 0.611338625808018, "state_global_normalized": { "rho": "1.55869448228092646017411203735055560833500938121200344753435659044909240953285308212719494", "p": "0.101830353388103544591740250491779396206767200099722106683582365098837320256092412048690473", "u": [ "-0.642262824967445148142797007267920613748722510740308257197484863644745496300866183486280525", "-0.0239472336302992893051069644151025867861558108614167366995338525730957399003977905904285212", "-0E-91" ], "B": [ "0.0667216268956297090131911121093178703623431986263357940834649287574864241219165978415587215", "1.00244272871016827085632250443887714212337351879646988706374049957779954626560442268995424", "0E-91" ] }, "root_record": { "r": "1.55869448228092646017411203735055560833500938121200344753435659044909240953285308212719494", "b": "0.0405946840495415748448918451765910003115605524714307856783550896687354979042321526032814892", "h": "0.00139932846805435551166381250769587426953000351197427980384765958154091832975845863696707178", "A": "0.414577576757091634277776910015340472737439231923403679481499750653444356421826349674459685", "denominator": "0.997818874437945054394751955693203078976789823084765223288838095528312375481638167578689802", "polynomial_residual": "1.202332458643892208056935E-65", "bracket_initial_signs": [ "1.46446259274350548709025175089563038498158044586295187228119793660308059843337547794230829", "-2.01582279710768561308768014442956577944679243147237382575916699167440236831002427711857203" ], "bracket_derivative_max": "-5.55541775637997540895585493885827719562981923049518969466383250397196728813643017616513650", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-1E-91", "0E-182", "-1E-90", "0E-182", "-6.83456165199829866817053151503752443865576057252245380537339739669067859621091503870839296E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.675", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03597025472886002, 0.0 ], "rh_scaled_inf": 4.3754903838566356e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -4.3754903838566356e-16 }, "characteristics": { "left": { "slow": 0.011363857086796584, "alfven_n": 0.029949786175129074, "fast": 0.8696619401195306 }, "right": { "slow": 0.0139882181848128, "alfven_n": 0.03739161514943474, "fast": 0.695000593385664 } }, "front_relative_normal_velocity": { "left": -0.6412884119831471, "right": -0.999572709308829 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5586944822809266, "pressure_ratio": 2.510610290633717, "entropy_over_cv": 0.18077819967243258, "tangential_field_ratio": 1.559915728789586 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.65, "theta_Bn_degrees": 86.65, "compression": 1.5587228545083927, "u2x_km_s": -385.34348358188674, "u2y_km_s": -14.336054228960018, "speed2_km_s": 385.6100657268681, "signed_deflection_degrees": 2.1306101979319694, "p2_over_p1": 2.5107472671622126, "B2_over_B1": 1.5583929094478721, "entropy_over_cv": 0.18080241991920254, "upstream_fast_Mach": 1.4382554942919004, "downstream_fast_Mach": 0.7373908366618106, "downstream_alfven_margin": 0.6111104182161509, "state_global_normalized": { "rho": "1.55872285450839270638146251223572914821119523274101128779568193364406508238850680845639071", "p": "0.101835909156099346488261119297346868201643614072228864553621817462312964798996169874416576", "u": [ "-0.642239139303144605894798792671557309866838164825540619003767931966586172385407974972750135", "-0.0238934237149333617041868509424879803201156882155474352972720979923780979647550640061856599", "-0E-91" ], "B": [ "0.0665650598701061404078753723606515231443196185106728107763782079442723006918688760773566598", "1.00246828354414118065080134738552160865919954016261894173466580575257968596857401913772638", "0E-91" ] }, "root_record": { "r": "1.55872285450839270638146251223572914821119523274101128779568193364406508238850680845639071", "b": "0.0405936558628638257447682142308496522541377978719928758302298091928006967677170675703913389", "h": "0.00142039005813047481501511241171147022693214929500535556794141043804300567292893986092639478", "A": "0.414545979257641720376088241273057656321744366194431158444441797661549738949323089536804792", "denominator": "0.997786005554075524446194246976286787388236965138204004876479370579621480274057472455581520", "polynomial_residual": "-1.452617559887555745467897E-65", "bracket_initial_signs": [ "1.46454765184497860472684512681729511237661511520293384446361649269362094104838717306085497", "-2.01553109237431382819451471388331626956128861673179824013590031415940603951782080213308825" ], "bracket_derivative_max": "-5.55514778290905271618971149521914145277762317008307339809905917101386918218694326218319398", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "0E-91", "0E-182", "3E-90", "0E-182", "8.25828721774816769891313385621776159785286536891153406620448822651247634933429856134635154E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.65", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03558503614794672, 0.0 ], "rh_scaled_inf": 2.1877296241096705e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7818843252470797e-16, "t1_momentum": -3.469446951953614e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1877296241096705e-16 }, "characteristics": { "left": { "slow": 0.011449233053062217, "alfven_n": 0.030174442208250947, "fast": 0.8696675203173349 }, "right": { "slow": 0.014093316385069932, "alfven_n": 0.03767243587203353, "fast": 0.6949984701333387 } }, "front_relative_normal_velocity": { "left": -0.6412848604244018, "right": -0.9995853681937397 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5587228545083927, "pressure_ratio": 2.5107472671622126, "entropy_over_cv": 0.18080241991920254, "tangential_field_ratio": 1.559962608613789 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.625, "theta_Bn_degrees": 86.625, "compression": 1.5587509574493217, "u2x_km_s": -385.3293669896719, "u2y_km_s": -14.30375760464047, "speed2_km_s": 385.59475949015905, "signed_deflection_degrees": 2.125892522370854, "p2_over_p1": 2.5108830471209105, "B2_over_B1": 1.5584160451246425, "entropy_over_cv": 0.18082644911834728, "upstream_fast_Mach": 1.4382778615675034, "downstream_fast_Mach": 0.7373821015678296, "downstream_alfven_margin": 0.610882206656198, "state_global_normalized": { "rho": "1.55875095744932164146573021156597351713649500074367739100337378640287848959552873895051758", "p": "0.101841416391224132222292330205277567654666316169084935323225650925243727590735160415374564", "u": [ "-0.642215611649453165186753220766386695591788722483632100931124419908379671707395637156187394", "-0.0238395960077341150934519547326764553316838098933481041100146819317321541986777037392236281", "-0E-91" ], "B": [ "0.0664084682020660625286350380299057122627207769541600698584317233941045693831575864794829478", "1.00249361709203400122939324016499439508862103079328287113750144097334650904588242163206277", "0E-91" ] }, "root_record": { "r": "1.55875095744932164146573021156597351713649500074367739100337378640287848959552873895051758", "b": "0.0405926431715839458178373200292927951883841916102051710664607699603120082735378036143807493", "h": "0.00144160843235703540465860900622506704277429027156093662800069646444417349833910693171259936", "A": "0.414514383756596317079061467840521124717292794540679534498508887065155702442813972737395391", "denominator": "0.997752891475796455430128009707144619025091124138063721793575352805418576526244344413046763", "polynomial_residual": "-1.420079578189795333326518E-65", "bracket_initial_signs": [ "1.46463109829480230069924653634140906217523833543812352806409524517220933391449085742000509", "-2.01524077072751689373478803285263402749066129516464364405259785445724095471736467821412836" ], "bracket_derivative_max": "-5.55487783756672936999534114994804030851022427931405899940246632666809047916491305593318660", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-4E-91", "0E-182", "-4E-90", "0E-182", "8.07428293853639911384750529361073751218943707284540739421330515707452479286644114635675700E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-1.625", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.035199813794704174, 0.0 ], "rh_scaled_inf": 2.1877151765882898e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1877151765882898e-16 }, "characteristics": { "left": { "slow": 0.011534607979156482, "alfven_n": 0.030399091035774824, "fast": 0.8696729908801335 }, "right": { "slow": 0.014198412868415266, "alfven_n": 0.037953249422332316, "fast": 0.6949963310165235 } }, "front_relative_normal_velocity": { "left": -0.6412812976919728, "right": -0.9995978367717061 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5587509574493217, "pressure_ratio": 2.5108830471209105, "entropy_over_cv": 0.1808264491183471, "tangential_field_ratio": 1.560009359254135 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.6, "theta_Bn_degrees": 86.60000000000001, "compression": 1.5587787911055615, "u2x_km_s": -385.31534520863147, "u2y_km_s": -14.271450374313316, "speed2_km_s": 385.5795502215247, "signed_deflection_degrees": 2.1211723758913354, "p2_over_p1": 2.511017630272866, "B2_over_B1": 1.5584388742858328, "entropy_over_cv": 0.1808502872355672, "upstream_fast_Mach": 1.4382999879820726, "downstream_fast_Mach": 0.7373734466873451, "downstream_alfven_margin": 0.6106539911090805, "state_global_normalized": { "rho": "1.55877879110556160443200545112252556433885100149718928542263925953583349148918686578507547", "p": "0.101846875083867453779669551329799470853065122262350793213319424341303540487828551507544004", "u": [ "-0.642192242014385690833218000498030031099907916921838241940290780307385132931888179057736344", "-0.0237857506238555271183291262641192798993817517059413034728371174974797203439973222153109563", "-0E-91" ], "B": [ "0.0662518521217441630487551587341014238093758252467288332682744146569866825659200539639060714", "1.00251872933793248137595404298106928008773539644379734773342224230801609419130365637905012", "0E-91" ] }, "root_record": { "r": "1.55877879110556160443200545112252556433885100149718928542263925953583349148918686578507547", "b": "0.0405916459741576267068916268964036278512762785936080059131173643968118961221897839994993689", "h": "0.00146298358705967961086390604517937027453484563002632204840234553690569616576857248884830616", "A": "0.414482790241805133430992632235820042984169302892368988724089264618717949282530625930676551", "denominator": "0.997719532212755834476622499761396252533655074417267254066725970902919393516664534386766263", "polynomial_residual": "4.73941712548257328822156E-66", "bracket_initial_signs": [ "1.46471293229204716123126602768180279381456212198838111098382989782920376404241617640223698", "-2.01495183189386463550552055267301372212201142804881344396023731223564162045754796105908428" ], "bracket_derivative_max": "-5.55460792020781266984109636225814654781521716307965882376306330100295159302730298792646380", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.02738478532364504920955606419387031891204767988251168311127146055287588939629181242508859E-90", "-2E-91", "0E-182", "1E-90", "0E-182", "-2.69506219833955015073528885183241032266674540116971116717050465958357315803938436507384296E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.6", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03481458770680334, 0.0 ], "rh_scaled_inf": 2.1877018493366532e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1877018493366532e-16 }, "characteristics": { "left": { "slow": 0.01161998186378296, "alfven_n": 0.030623732673254533, "fast": 0.8696783518084077 }, "right": { "slow": 0.01430350762201085, "alfven_n": 0.03823405574686815, "fast": 0.6949941760361148 } }, "front_relative_normal_velocity": { "left": -0.6412777237823349, "right": -0.9996101150403544 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5587787911055615, "pressure_ratio": 2.511017630272866, "entropy_over_cv": 0.1808502872355673, "tangential_field_ratio": 1.5600559807286667 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.575, "theta_Bn_degrees": 86.575, "compression": 1.5588063554788079, "u2x_km_s": -385.30141824358236, "u2y_km_s": -14.239132607077718, "speed2_km_s": 385.56443793212816, "signed_deflection_degrees": 2.116449771965195, "p2_over_p1": 2.5111510163825503, "B2_over_B1": 1.5584613969359262, "entropy_over_cv": 0.18087393423676226, "upstream_fast_Mach": 1.4383218735296497, "downstream_fast_Mach": 0.7373648720112068, "downstream_alfven_margin": 0.6104257715557975, "state_global_normalized": { "rho": "1.55880635547880790765099909170589994830836674982703241257030270970435888313824924913899866", "p": "0.101852285224476239179324306728498733872084935761477815516747390825704662931721905532337249", "u": [ "-0.642169030405970606995989700442425364766110160267998988078273751078817983192736512913529419", "-0.0237318876784628632186194390737516144150500221102959076701844190983426277908178139745528861", "-0E-91" ], "B": [ "0.0660952118593809360277718420698282660390331968609637201888608384965209940897486341645323640", "1.00254362026604022446794234291880900411568827412226987237531917966301067179968525823194532", "0E-91" ] }, "root_record": { "r": "1.55880635547880790765099909170589994830836674982703241257030270970435888313824924913899866", "b": "0.0405906642690642439270773066419697322970696057767145326042286296885611558274319381439590397", "h": "0.00148451551880370693847687939076698593887329552378231263143191955212343228649738616701431457", "A": "0.414451198701120911795593756776041227535443145881270543129280936772405750174551104360561941", "denominator": "0.997685927774481861857310806067685875552938743352059424936650346576864103861524910730293061", "polynomial_residual": "4.98051562958629740906353E-66", "bracket_initial_signs": [ "1.46479315403503734477176741580882448913691142267400513342938422628619622786818569337039449", "-2.01466427559914366733701703027110216938385269963927153379433128353493173836794011280090088" ], "bracket_derivative_max": "-5.55433803068511264592803286485460717634671783985445174940502212858966887162964161044527430", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.02738921445038046588256854107666052517435659454066788690004709532598666034478418618423719E-90", "-4E-91", "0E-182", "-5E-90", "0E-182", "-2.83250530806489644340524222091198693819506025205507684589760984781484473426647222815603588E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.575", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03442935792192204, 0.0 ], "rh_scaled_inf": 1.781870799798455e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.781870799798455e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.011705354705639324, "alfven_n": 0.030848367136240267, "fast": 0.8696836031026594 }, "right": { "slow": 0.014408600633018171, "alfven_n": 0.038514854792179455, "fast": 0.694992005193016 } }, "front_relative_normal_velocity": { "left": -0.6412741386920376, "right": -0.9996222029973468 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5588063554788079, "pressure_ratio": 2.5111510163825503, "entropy_over_cv": 0.18087393423676235, "tangential_field_ratio": 1.560102473055149 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.55, "theta_Bn_degrees": 86.55, "compression": 1.5588336505706029, "u2x_km_s": -385.2875860993499, "u2y_km_s": -14.206804372039556, "speed2_km_s": 385.5494226331163, "signed_deflection_degrees": 2.111724724071445, "p2_over_p1": 2.5112832052158485, "B2_over_B1": 1.5584836130794129, "entropy_over_cv": 0.18089739008803188, "upstream_fast_Mach": 1.4383435182042816, "downstream_fast_Mach": 0.7373563775303931, "downstream_alfven_margin": 0.6101975479774266, "state_global_normalized": { "rho": "1.55883365057060281056340608320444331194759638418543265973207997695744684003477017165117646", "p": "0.101857646803554807692158057691418476862821974833556473244071677977732644065009088541778047", "u": [ "-0.642145976832249867775689907346418341799519613703033484286173919060692678092170964677066498", "-0.0236780072867325937248327172681632575425487026780900831258113663090723191901821892755390048", "-0E-91" ], "B": [ "0.0659385476452227020379765039191106616587516397652073780880947068316737465981906912937526060", "1.00256828986067868900813278113357020753190305342932942091490816458310516770933838876550440", "0E-91" ] }, "root_record": { "r": "1.55883365057060281056340608320444331194759638418543265973207997695744684003477017165117646", "b": "0.0405896980548068519363840792210762668938516337296670949441768358946030825037996613377426838", "h": "0.00150620422439404232387695679998142967790115708367555383351527520490361101050773441370630713", "A": "0.414419609122399409085959076838018644746197627942411756946641512335669189005575439186759407", "denominator": "0.997652078170382971602294685560757672584324690979116976142696961269981137915076470893533299", "polynomial_residual": "-1.159494976364706244180927E-65", "bracket_initial_signs": [ "1.46487176372135079141639344961501146540371648549764490859646087231706293946197732418007429", "-2.01437810156835747369879134211501894023323079055695688302517999465239444044606019232916140" ], "bracket_derivative_max": "-5.55406816884944235608097133535669397493713721681271850446802532535811131056697827483697413", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-3E-91", "0E-182", "3E-90", "0E-182", "6.59504633799540147926000098313862943777949169051299631108655856375382606328599855374302732E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.55", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03404412447774483, 0.0 ], "rh_scaled_inf": 2.1876785555429866e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1876785555429866e-16 }, "characteristics": { "left": { "slow": 0.011790726503417394, "alfven_n": 0.031072994440278737, "fast": 0.8696887447634137 }, "right": { "slow": 0.014513691888598156, "alfven_n": 0.038795646504806075, "fast": 0.6949898184881371 } }, "front_relative_normal_velocity": { "left": -0.6412705424177053, "right": -0.9996341006403823 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5588336505706029, "pressure_ratio": 2.5112832052158485, "entropy_over_cv": 0.18089739008803185, "tangential_field_ratio": 1.5601488362510714 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.525, "theta_Bn_degrees": 86.525, "compression": 1.5588606763823354, "u2x_km_s": -385.27384878076737, "u2y_km_s": -14.174465738311385, "speed2_km_s": 385.53450433561994, "signed_deflection_degrees": 2.106997245696293, "p2_over_p1": 2.5114141965400614, "B2_over_B1": 1.5585055227207887, "entropy_over_cv": 0.1809206547556748, "upstream_fast_Mach": 1.4383649220000199, "downstream_fast_Mach": 0.7373479632360106, "downstream_alfven_margin": 0.609969320355124, "state_global_normalized": { "rho": "1.55886067638233549352492484657142583159598012492760930674650728306858914416592728628126074", "p": "0.101862959811664885017303189924697162176007647788649546307947914368846842470650789655649923", "u": [ "-0.642123081301278928290303222186350859957473278997391547872398941463614251966000225516139434", "-0.0236241095638523109371452544015766338718507805201376128927976047009514035734409723434098998", "-0E-91" ], "B": [ "0.0657818597095216282826525450134357570344062915243184317760313499710276000931603163256341653", "1.00259273810628718896815494866442549843460197260067777511703818660556465853930673001250293", "0E-91" ] }, "root_record": { "r": "1.55886067638233549352492484657142583159598012492760930674650728306858914416592728628126074", "b": "0.0405887473299121792831364535504797659511264745895219323953592817427144282282690981138460218", "h": "0.00152804970087520517118273564420299455620371124398043110582448860763231975094600834467126830", "A": "0.414388021493499378004322311291518115544847105043376858959057165527646209470984613500966965", "denominator": "0.997617983409747852238696649638762693588532834241023641600060035868278095179694655384042671", "polynomial_residual": "-1.349991797463652223089832E-65", "bracket_initial_signs": [ "1.46494876154781943673849473856288225316763268868888338915202516655143322773737539993536174", "-2.01409330952572647929412910247657640866964707000733461627391623980192667916827204697480609" ], "bracket_derivative_max": "-5.55379833454961816885697879154488188029721632635114714405049577685178706821203947176837471", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "2E-91", "0E-182", "1E-90", "0E-182", "7.67949485061738592585889121068268664733077574390547865024897696185270463211318369898432055E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.525", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03365888741196289, 0.0 ], "rh_scaled_inf": 1.781865624563991e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": -1.781865624563991e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.011876097255803221, "alfven_n": 0.03129761460091325, "fast": 0.8696937767912168 }, "right": { "slow": 0.014618781375911152, "alfven_n": 0.03907643083128923, "fast": 0.6949876159223949 } }, "front_relative_normal_velocity": { "left": -0.6412669349560373, "right": -0.9996458079671954 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5588606763823354, "pressure_ratio": 2.5114141965400614, "entropy_over_cv": 0.18092065475567498, "tangential_field_ratio": 1.5601950703336478 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.5, "theta_Bn_degrees": 86.5, "compression": 1.558887432915242, "u2x_km_s": -385.260206292676, "u2y_km_s": -14.142116775012388, "speed2_km_s": 385.5196830507534, "signed_deflection_degrees": 2.1022673503330984, "p2_over_p1": 2.5115439901239056, "B2_over_B1": 1.5585271258645559, "entropy_over_cv": 0.18094372820618895, "upstream_fast_Mach": 1.4383860849109218, "downstream_fast_Mach": 0.7373396291192945, "downstream_alfven_margin": 0.6097410886701237, "state_global_normalized": { "rho": "1.55888743291524203179182603704608895014419786135576425599888009930164578975777910945871498", "p": "0.101868224239425618415801508865568855051412042057725489086127499252265122687866375481987425", "u": [ "-0.642100343821126716240601174141381854882330918369162044928580925050153496578643184921665299", "-0.0235701946250206461868028027290403811329631213048953608712290477267288965462830211066618677", "-0E-91" ], "B": [ "0.0656251482825357487068165801972601948570864780643679378671688581408857712134910492402812269", "1.00261696498742289394380498021918224009339312391479822391738672993124336339329544692116869", "0E-91" ] }, "root_record": { "r": "1.55888743291524203179182603704608895014419786135576425599888009930164578975777910945871498", "b": "0.0405878120929306238304593606588863622580460890900243234711547044288419972828245325109919532", "h": "0.00155005194553127916749106319600576664146964408777332071153847694765384907203643584693340011", "A": "0.414356435802282548291543094199573412110443819174594818407160272729234046758839744164533142", "denominator": "0.997583643501745467650903837802900735019652837045474049890479692270991133976587972821205937", "polynomial_residual": "1.340810558063731877082538E-65", "bracket_initial_signs": [ "1.46502414771052943002726273717041650566960407965110525431886235246040394420669302194127851", "-2.01380989919468810564943846369999902210929093478459497910954321930721322200943988999532869" ], "bracket_derivative_max": "-5.55352852763246003287708078229103062842451285313995693250295949232582385800376503782789723", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "0E-91", "0E-182", "2E-90", "0E-182", "-7.62818957697555041015818568203655606693222425784980280469527831246414205576963727139500460E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.5", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03327364676227388, 0.0 ], "rh_scaled_inf": 6.562979227651067e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.781864189449869e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 6.562979227651067e-16 }, "characteristics": { "left": { "slow": 0.01196146696147712, "alfven_n": 0.031522227633683786, "fast": 0.8696986991866366 }, "right": { "slow": 0.014723869082116946, "alfven_n": 0.03935720771817154, "fast": 0.6949853974967126 } }, "front_relative_normal_velocity": { "left": -0.6412633163038075, "right": -0.9996573249755573 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.558887432915242, "pressure_ratio": 2.5115439901239056, "entropy_over_cv": 0.18094372820618887, "tangential_field_ratio": 1.560241175319816 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.475, "theta_Bn_degrees": 86.47500000000001, "compression": 1.5589139201704054, "u2x_km_s": -385.2466586399254, "u2y_km_s": -14.109757551268313, "speed2_km_s": 385.504958789615, "signed_deflection_degrees": 2.097535051482337, "p2_over_p1": 2.5116725857375144, "B2_over_B1": 1.5585484225152233, "entropy_over_cv": 0.1809666104062715, "upstream_fast_Mach": 1.4384070069310495, "downstream_fast_Mach": 0.7373313751716086, "downstream_alfven_margin": 0.6095128529037379, "state_global_normalized": { "rho": "1.55891392017040536964696640815852237862302466157629353573457186704266698384014330037334546", "p": "0.101873440077513591801730677134507141643950332823363438158371396014148151131306697402506948", "u": [ "-0.642077764399875603962389061486677369034259517037028948185316882258399980532981420154653155", "-0.0235162625854471868797908673747751292291023633586160306107409470868311749069406796995908732", "-0E-91" ], "B": [ "0.0654684135945289841012364372895023150704665383630678020766377118832884976520035823145303738", "1.00264097048876082912207658672010177484403928104846987756698222475796780478591523693862253", "0E-91" ] }, "root_record": { "r": "1.55891392017040536964696640815852237862302466157629353573457186704266698384014330037334546", "b": "0.0405868923424362480576916014023384396179979345688434866795361835479221225493754868732153217", "h": "0.00157221095588588287693905663453445465083192078123429424829637836283310178615729641949605947", "A": "0.414324852036613607986260746157253259673676761733815446405371199644304953660364008333594195", "denominator": "0.997549058455425078062549313352223337665663460271055275656000373709610566543276062522601395", "polynomial_residual": "5.28665925915594405994035E-66", "bracket_initial_signs": [ "1.46509792240482135693113358315461397971190543157356545242957448946486074326033804041941934", "-2.01352787029789681470441307690878291621520932822077082239754044967026027394734680919578819" ], "bracket_derivative_max": "-5.55325874794279173238690191414582773023655527193181842308842759665174163888211544656840409", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "1E-91", "0E-182", "-1E-90", "0E-182", "-3.00806972080852482214476235431712467318661514720448489668227016585831788619160806990403543E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_-1.475", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03288840256638186, 0.0 ], "rh_scaled_inf": 2.1876520163078657e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1876520163078657e-16 }, "characteristics": { "left": { "slow": 0.012046835619113747, "alfven_n": 0.03174683355412715, "fast": 0.8697035119502632 }, "right": { "slow": 0.014828954994374725, "alfven_n": 0.039637977111997055, "fast": 0.6949831632120205 } }, "front_relative_normal_velocity": { "left": -0.641259686457865, "right": -0.9996686516632753 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5589139201704054, "pressure_ratio": 2.5116725857375144, "entropy_over_cv": 0.18096661040627127, "tangential_field_ratio": 1.5602871512262375 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.45, "theta_Bn_degrees": 86.45, "compression": 1.5589401381487553, "u2x_km_s": -385.23320582737284, "u2y_km_s": -14.077388136211438, "speed2_km_s": 385.4903315632865, "signed_deflection_degrees": 2.0928003626515608, "p2_over_p1": 2.5117999831524367, "B2_over_B1": 1.558569412677306, "entropy_over_cv": 0.18098930132281849, "upstream_fast_Mach": 1.43842768805447, "downstream_fast_Mach": 0.7373232013844447, "downstream_alfven_margin": 0.6092846130373567, "state_global_normalized": { "rho": "1.55894013814875529466614567238339606022578219081518320265390975880943612834277594230379404", "p": "0.101878607316662840790808860030108408553102375586102438660906156881790300872560862342265469", "u": [ "-0.642055343045621380965515656555005890217037150310260320035284787141446416022316618025926545", "-0.0234623135603523935225942920703579574383129693509581872978482814962613672173021786123114505", "-0E-91" ], "B": [ "0.0653116558757711622004982381813685222214486632935113280544908274186597494338079215129315830", "1.00266475459509387505985787863573217996241826708381406744088553071031666358210338755034951", "0E-91" ] }, "root_record": { "r": "1.55894013814875529466614567238339606022578219081518320265390975880943612834277594230379404", "b": "0.0405859880770267744387209608034928867932455891579223959310229430209106587065357001125090367", "h": "0.00159452672970214111338289047249373445050803684966889868752976786797819098488510819959631655", "A": "0.414293270184360184693653617565295508309319728855773733820879765151437535805857506957526034", "denominator": "0.997514228279716261140277515465730242786878267100242561750425647054524104708817589110416055", "polynomial_residual": "8.27833784433725282507654E-66", "bracket_initial_signs": [ "1.46517008582529046650459603716652719869957713054338510729679679281189091137925379671252130", "-2.01324722255722413940890488731690300224445434221679579500402205065029019352208624787251561" ], "bracket_derivative_max": "-5.55298899532344112905181880117981631386411332439229954711430823526786419276383932611628991", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "1E-91", "0E-182", "5E-90", "0E-182", "-4.71088210232479427148664376743833938596829954439692381424469624504708919954476562559770917E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.45", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.032503154861997154, 0.0 ], "rh_scaled_inf": 4.3752908204278914e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 3.5637272484294875e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": -0.0, "energy": -4.3752908204278914e-16 }, "characteristics": { "left": { "slow": 0.012132203227382177, "alfven_n": 0.03197143237777703, "fast": 0.8697082150827082 }, "right": { "slow": 0.014934039099843116, "alfven_n": 0.039918738959311244, "fast": 0.694980913069255 } }, "front_relative_normal_velocity": { "left": -0.6412560454151337, "right": -0.9996797880281931 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5589401381487553, "pressure_ratio": 2.511799983152437, "entropy_over_cv": 0.18098930132281854, "tangential_field_ratio": 1.5603329980692975 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.425, "theta_Bn_degrees": 86.42500000000001, "compression": 1.5589660868510684, "u2x_km_s": -385.21984785988394, "u2y_km_s": -14.04500859898051, "speed2_km_s": 385.4758013828333, "signed_deflection_degrees": 2.0880632973553537, "p2_over_p1": 2.5119261821416385, "B2_over_B1": 1.5585900963553254, "entropy_over_cv": 0.1810118009229251, "upstream_fast_Mach": 1.438448128275256, "downstream_fast_Mach": 0.7373151077494233, "downstream_alfven_margin": 0.6090563690524483, "state_global_normalized": { "rho": "1.55896608685106841212470643076668119840326369016607330644663297243043387619584081145762866", "p": "0.101883725947664867706507677000872763674561741451065991120762207495586276890439600266979750", "u": [ "-0.642033079766473226959588639626326406245717060424282057823682616395628741970616523305057055", "-0.0234083476649675167298680718149936574862440886367872188293616848440424282672271032870665752", "-0E-91" ], "B": [ "0.0651548753565380377758949758320517552102140406615390705068512152031279635877683132286097394", "1.00268831729133276727423994314787124867486659497285377677846656284500523788247224449527304", "0E-91" ] }, "root_record": { "r": "1.55896608685106841212470643076668119840326369016607330644663297243043387619584081145762866", "b": "0.0405850992953235808972152706787251360705511100427577300451897563914905012251434067638739143", "h": "0.00161699926498265709149152773119471879620935869655745256553682058847656985931846397338093528", "A": "0.414261690233392826863742289709254925648546982201750777419875539452640546047179976837011428", "denominator": "0.997479152983428933219341701725454341804672820370257368371448121502389391356074261807607462", "polynomial_residual": "-7.41803942013755190037220E-66", "bracket_initial_signs": [ "1.46524063816578690265660317973271151426310941867644753526610897087630602314644044783333693", "-2.01296795569375870133227822766000975305344549577295537689433325795872056926112504892249678" ], "bracket_derivative_max": "-5.55271926961524038999209615164170945076965413485990931250689540809209045589186864604970351", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.02744788393785311049924880348665411065765450853754404750275344375560024268013172716432916E-90", "0E-91", "0E-182", "3E-90", "0E-182", "4.22182984767156276102264625101818727555534560847807251704831402181431084131711293723901061E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.425", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.032117903686836216, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.012217569784945924, "alfven_n": 0.032196024120164125, "fast": 0.869712808584606 }, "right": { "slow": 0.015039121385680147, "alfven_n": 0.04019949320666101, "fast": 0.6949786470693599 } }, "front_relative_normal_velocity": { "left": -0.6412523931726124, "right": -0.9996907340681903 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5589660868510684, "pressure_ratio": 2.511926182141639, "entropy_over_cv": 0.18101180092292524, "tangential_field_ratio": 1.5603787158651068 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.4, "theta_Bn_degrees": 86.4, "compression": 1.5589917662779682, "u2x_km_s": -385.2065847423322, "u2y_km_s": -14.012619008720709, "speed2_km_s": 385.46136825930444, "signed_deflection_degrees": 2.0833238691152998, "p2_over_p1": 2.5120511824795035, "B2_over_B1": 1.5586104735538089, "entropy_over_cv": 0.18103410917388524, "upstream_fast_Mach": 1.4384683275874848, "downstream_fast_Mach": 0.7373070942582932, "downstream_alfven_margin": 0.6088281209305584, "state_global_normalized": { "rho": "1.55899176627796811954427942045582445424904620461650270968944668714136918207969447471995088", "p": "0.101888795961368656543703389183246107446735100883577853315670822204190246777352677560078504", "u": [ "-0.642010974570553685366341553916312753304308229325180061214855332557351351476410451620297215", "-0.0233543650145345142138412730900225155708758127300175087150981081922946457182012619685067123", "-0E-91" ], "B": [ "0.0649980722671113127239091071311467295704115376547293920979481983705032277523084211774816640", "1.00271165856250609564438274900648126536143370886930274927844241366339128273256294685998096", "0E-91" ] }, "root_record": { "r": "1.55899176627796811954427942045582445424904620461650270968944668714136918207969447471995088", "b": "0.0405842259959716963387241316033862184679981768801967611060297758665917066176565294101600318", "h": "0.00163962855996948535605791792236471734798872719978159898622343112875848142446224146388240065", "A": "0.414230112171584985079174972738531631228110568332608866902255835321679698855233229315062265", "denominator": "0.997443832575253370651082315115725104204819171879413563699405134851270594227769119537523216", "polynomial_residual": "-1.013235032630298482453285E-65", "bracket_initial_signs": [ "1.46530957961941593999885388518763138150303068064843895215962321267001930045227016535839836", "-2.01269006942780621529089055484539841958709322643115023322199804552274286727409027345472585" ], "bracket_derivative_max": "-5.55244957065702620206336340815050289894328904714152359436725245954483592001838477934141522", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "-2E-91", "0E-182", "-5E-90", "0E-182", "5.76732300559932479076976748213752504141346409222513518365511903650902769958147914252155621E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.4", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03173264907862154, 0.0 ], "rh_scaled_inf": 1.7818661323026763e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7818661323026763e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.012302935290463057, "alfven_n": 0.03242060879681624, "fast": 0.8697172924566118 }, "right": { "slow": 0.015144201839043253, "alfven_n": 0.04048023980059472, "fast": 0.6949763652132851 } }, "front_relative_normal_velocity": { "left": -0.6412487297273746, "right": -0.9997014897811831 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5589917662779682, "pressure_ratio": 2.5120511824795035, "entropy_over_cv": 0.18103410917388518, "tangential_field_ratio": 1.560424304629498 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.375, "theta_Bn_degrees": 86.37500000000001, "compression": 1.5590171764299245, "u2x_km_s": -385.1934164795992, "u2y_km_s": -13.980219434583582, "speed2_km_s": 385.4470322037323, "signed_deflection_degrees": 2.0785820914599378, "p2_over_p1": 2.5121749839418315, "B2_over_B1": 1.5586305442772905, "entropy_over_cv": 0.18105622604319158, "upstream_fast_Mach": 1.438488285985239, "downstream_fast_Mach": 0.7372991609029313, "downstream_alfven_margin": 0.6085998686533104, "state_global_normalized": { "rho": "1.55901717642992458137957850583066518052767428837924068706212686043248316223649487070870844", "p": "0.101893817348680687889896085375028536221221620649153340251211549364771067977345209217045890", "u": [ "-0.641989027465998637318601000779066594206952405694976703743609913921969174190265264233355603", "-0.0233003657243059677552758841215221582202335368818038923113543246921027821529436449521986572", "-0E-91" ], "B": [ "0.0648412468377786561510617931888976519613450382929242750087522688728957499329345884902367901", "1.00273477839376030362488356350228829026695030780993210571873706088014294723644677168673823", "0E-91" ] }, "root_record": { "r": "1.55901717642992458137957850583066518052767428837924068706212686043248316223649487070870844", "b": "0.0405833681776397962596264344368427030796914208348799141551677180164728027209553608448816767", "h": "0.00166241461314410548933452977367542450691638177244201745096900471669705795745268412451653017", "A": "0.414198535986812993352433492513332042321930922547122414741033307124029989595762784868718003", "denominator": "0.997408267063760231272336309772906370016903511853267586484500894002268433221296473629678692", "polynomial_residual": "4.42813120667536794728902E-66", "bracket_initial_signs": [ "1.46537691037853822409227641395785175910608779113771696371706543248831094099984627823835404", "-2.01241356347888948099921914735669066810285953083236581215702549687801298482851120288826257" ], "bracket_derivative_max": "-5.55217989828563997238767613731753651089088654711921229843242914332977089951680388573557388", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "1E-91", "0E-182", "-1E-90", "0E-182", "-2.52079214586759573199931427798661139512160027100873327525892876256720474960018941429174568E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.375", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03134739107508154, 0.0 ], "rh_scaled_inf": 2.1876323127053818e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7818685388476354e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1876323127053818e-16 }, "characteristics": { "left": { "slow": 0.012388299742586229, "alfven_n": 0.0326451864232584, "fast": 0.869721666699403 }, "right": { "slow": 0.015249280447089283, "alfven_n": 0.04076097868766217, "fast": 0.6949740675019874 } }, "front_relative_normal_velocity": { "left": -0.6412450550765688, "right": -0.9997120551651237 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5590171764299245, "pressure_ratio": 2.512174983941832, "entropy_over_cv": 0.18105622604319183, "tangential_field_ratio": 1.5604697643780299 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.35, "theta_Bn_degrees": 86.35, "compression": 1.5590423173072547, "u2x_km_s": -385.1803430765744, "u2y_km_s": -13.947809945727, "speed2_km_s": 385.4327932271327, "signed_deflection_degrees": 2.073837977924722, "p2_over_p1": 2.512297586305842, "B2_over_B1": 1.5586503085303105, "entropy_over_cv": 0.18107815149853548, "upstream_fast_Mach": 1.4385080034626063, "downstream_fast_Mach": 0.7372913076753432, "downstream_alfven_margin": 0.6083716122024053, "state_global_normalized": { "rho": "1.55904231730725470384515201587298963774379482332565947746957103373556407397221320774643145", "p": "0.101898790100564953804026461215425925817225626760357410724157909683662783680973671891365724", "u": [ "-0.641967238460957276145805720849177162866438679455394465172810302303944543505840206311268010", "-0.0232463499095450001558023561277794880251929808167455671049827245550591780451671489368023003", "-0E-91" ], "B": [ "0.0646843992988337244559015354935524440983975187812108977446419391675522600438605915933669811", "1.00275767677035968727059267632971885142143035261267730093396473539481359788350630404892039", "0E-91" ] }, "root_record": { "r": "1.55904231730725470384515201587298963774379482332565947746957103373556407397221320774643145", "b": "0.0405825258390201984328992505888065644399704282378295004751551310373423667671434887938556477", "h": "0.00168535742322739659620442969628528892650010602481662629659392458881780647060484096364203334", "A": "0.414166961666956050432398310811714176650135652022452285165169549911273799373783004515522460", "denominator": "0.997372456457400575996828570254302632282539899790376347765048296412936629358460105790570417", "polynomial_residual": "8.92108503712899365677369E-66", "bracket_initial_signs": [ "1.46544263063477001609011274445964119888062136795115538161757167283244364295427890654295368", "-2.01213843756574836175002714286211217975502373877708514856280411210193359240352395500847763" ], "bracket_derivative_max": "-5.55191025233592801514029321874367912093041728912023200527029607222844659567056200036463046", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "-1E-91", "0E-182", "-8E-90", "0E-182", "-5.07909929164795088628241732704929199118705776894066344696218879188936914799464091773331422E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-1.35", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.030962129713950383, 0.0 ], "rh_scaled_inf": 2.187630187097986e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7818717137319812e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.187630187097986e-16 }, "characteristics": { "left": { "slow": 0.012473663139962746, "alfven_n": 0.032869757015012914, "fast": 0.8697259313136791 }, "right": { "slow": 0.015354357196974472, "alfven_n": 0.04104170981441464, "fast": 0.6949717539364307 } }, "front_relative_normal_velocity": { "left": -0.6412413692174181, "right": -0.9997224302180006 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5590423173072547, "pressure_ratio": 2.512297586305842, "entropy_over_cv": 0.18107815149853534, "tangential_field_ratio": 1.5605150951259825 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.325, "theta_Bn_degrees": 86.325, "compression": 1.5590671889101222, "u2x_km_s": -385.16736453815525, "u2y_km_s": -13.915390611315116, "speed2_km_s": 385.4186513405048, "signed_deflection_degrees": 2.069091542051985, "p2_over_p1": 2.512418989350172, "B2_over_B1": 1.5586697663174154, "entropy_over_cv": 0.18109988550780684, "upstream_fast_Mach": 1.4385274800136796, "downstream_fast_Mach": 0.7372835345676626, "downstream_alfven_margin": 0.6081433515596215, "state_global_normalized": { "rho": "1.55906718891012210988199920754028951356772305793632882099839733270324744562829998280731917", "p": "0.101903714208042972652919618865516492078060194731455210698490676380255642618784274293417597", "u": [ "-0.641945607563592082346032133156430164273249323393040131385076015714002170706651118455724579", "-0.0231923176855251921714535315118803626541613806086094494385852175692043739943571587858385559", "-0E-91" ], "B": [ "0.0645275298805761814089050785401424331406683309150450945780611490253869851165499190461184620", "1.00278035367768639407282083521465654019276483895656255347202221303720548799591392708652767", "0E-91" ] }, "root_record": { "r": "1.55906718891012210988199920754028951356772305793632882099839733270324744562829998280731917", "b": "0.0405816989788288586706840889605761423415831683036111814600436853283429645472962952132313668", "h": "0.00170845698917961256700345827420520751589336482099589499145546583778562097400460467022785984", "A": "0.414135389199896201120211075563832063357131063521024445687584750341761634699977204767424170", "denominator": "0.997336400764505890528597659842302375668127008503812983414542672754623090294231263512418273", "polynomial_residual": "-1.610126398504616041217682E-65", "bracket_initial_signs": [ "1.46550674057898344177606850501390930410592331808515001206366014468366755556776659865832512", "-2.01186469140633975012883644548719052435166886412187850966822997219778624919356101746504131" ], "bracket_derivative_max": "-5.55164063264074172459718781109892964735619521676008528013493043100465193610561889214079982", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.02751756409885614142996340556372307798547922421777054067519618543589111678780818241914839E-90", "5E-91", "0E-182", "4E-90", "0E-182", "9.16814452839711223530767448814187571060471155708127816953529452887298696743733832936525002E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_-1.325", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.03057686503296795, 0.0 ], "rh_scaled_inf": 1.7818756569615085e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7818756569615085e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.01255902548123464, "alfven_n": 0.033094320587599535, "fast": 0.8697300863001611 }, "right": { "slow": 0.015459432075854476, "alfven_n": 0.041322433127404905, "fast": 0.6949694245175848 } }, "front_relative_normal_velocity": { "left": -0.641237672147221, "right": -0.9997326149378384 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5590671889101222, "pressure_ratio": 2.5124189893501723, "entropy_over_cv": 0.18109988550780698, "tangential_field_ratio": 1.5605602968883623 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.3, "theta_Bn_degrees": 86.3, "compression": 1.5590917912385371, "u2x_km_s": -385.15448086924727, "u2y_km_s": -13.8829615005183, "speed2_km_s": 385.40460655483116, "signed_deflection_degrees": 2.064342797390897, "p2_over_p1": 2.512539192854877, "B2_over_B1": 1.5586889176431578, "entropy_over_cv": 0.1811214280390941, "upstream_fast_Mach": 1.4385467156325569, "downstream_fast_Mach": 0.7372758415721514, "downstream_alfven_margin": 0.6079150867068148, "state_global_normalized": { "rho": "1.55909179123853711426396281223733417726362307558763578449425262604235293306819857935087966", "p": "0.101908589662193803905385147123615361677327846685396513915573567439764860616565406223060491", "u": [ "-0.641924134782078799044483830285489875545810568041188370457225073866291241077382009775318203", "-0.0231382691675304994272185865629700266936968282664096315271231098909260765918498434538943802", "-0E-91" ], "B": [ "0.0643706388133117182310635769880135133713357081754273712548360244413395559006321562368131129", "1.00280280910124042160688240803513785728911991789559167360341969788520946523353020359493893", "0E-91" ] }, "root_record": { "r": "1.55909179123853711426396281223733417726362307558763578449425262604235293306819857935087966", "b": "0.0405808875958053666636269460428203199305601481872636093517725769256402697183503250120411762", "h": "0.00173171331020035811781339659404132963639413292238945869143920560163483108376689645885535907", "A": "0.414103818573518317594373249606764616483858348379361026834323363422903017052713256334243311", "denominator": "0.997300099993288107197509234397863814269174925407849681697463523793840019613979579276823730", "polynomial_residual": "-8.99777615028725847676189E-66", "bracket_initial_signs": [ "1.46556924040130674499605956548237983433118631998859178792631554329050823706947020252895656", "-2.01159232471783752076784926894827113618665426757940011927172019970360415485143137980755773" ], "bracket_derivative_max": "-5.55137103903093773444819707331178074852012075605462648310432626469923028654157641436949174", "iterations": 216 }, "flux_residuals": [ "1E-90", "-1.60550776103412332160257718407336283157455237456140315447360142996666608452090861727570226E-89", "4E-91", "0E-182", "7E-90", "0E-182", "5.12399988096536484038136662169082045824939078739401748580431797564515117989106717122485910E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.3", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.030191597069879658, 0.0 ], "rh_scaled_inf": 2.1876292961962685e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1876292961962685e-16 }, "characteristics": { "left": { "slow": 0.012644386765038717, "alfven_n": 0.03331887715653551, "fast": 0.8697341316595925 }, "right": { "slow": 0.015564505070884312, "alfven_n": 0.04160314857318719, "fast": 0.6949670792464269 } }, "front_relative_normal_velocity": { "left": -0.6412339638633504, "right": -0.9997426093226983 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5590917912385371, "pressure_ratio": 2.512539192854877, "entropy_over_cv": 0.18112142803909403, "tangential_field_ratio": 1.5606053696798987 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.275, "theta_Bn_degrees": 86.275, "compression": 1.5591161242923568, "u2x_km_s": -385.14169207476385, "u2y_km_s": -13.8505226825131, "speed2_km_s": 385.3906588810775, "signed_deflection_degrees": 2.0595917574974254, "p2_over_p1": 2.5126581966014316, "B2_over_B1": 1.5587077625120966, "entropy_over_cv": 0.18114277906068402, "upstream_fast_Mach": 1.4385657103133411, "downstream_fast_Mach": 0.7372682286811998, "downstream_alfven_margin": 0.6076868176259183, "state_global_normalized": { "rho": "1.55911612429235669884381080002088486667764790980642880170058390550121811955595145313202824", "p": "0.101913416454154062884002574666840410264273745559835101425725781270084467171813683068435960", "u": [ "-0.641902820124606407938405453455414583451817755103978866202068679714975645307890240784300793", "-0.0230842044708551693124385444120950493448262051643826748967842974697306895388592298254531451", "-0E-91" ], "B": [ "0.0642137263273520736719271581465557887489410000851202127782119187887380236690973505789031662", "1.00282504302663961599091789576144588918148814697501061463981367952666230610611204823103051", "0E-91" ] }, "root_record": { "r": "1.55911612429235669884381080002088486667764790980642880170058390550121811955595145313202824", "b": "0.0405800916887129418969690039991032825498670667811175556786160161882835602478728285143213782", "h": "0.00175512638572856560805035206668093672693224027610415618150945329515223280807587603546136105", "A": "0.414072249775710080745019417931334358964728071877115841592622166057553336575982636100722295", "denominator": "0.997263554151839626916911559523835680128514027499551851674721593044920700414777666057395932", "polynomial_residual": "-1.278976266007326085289960E-65", "bracket_initial_signs": [ "1.46563013029112454548215250870195371014700167508560230654002286069591596546742249279067895", "-2.01132133721663247014433440382849885051606331934187402960054027272059218368780212042497015" ], "bracket_derivative_max": "-5.55110147133537806338060269061964460989944221289170263799016697624812745661903533052284313", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.02756157469324007530758863236899338191583787055547006894640217035374658996961381380212584E-90", "1E-91", "0E-182", "-2E-90", "0E-182", "7.28431716815576382693481536103861636275848027637398257913561886833896078213717076488538614E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-1.275", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.029806325862436367, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 2.220446049250313e-16, "normal_momentum": -1.7818858484863083e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1876305308992337e-16 }, "characteristics": { "left": { "slow": 0.012729746990006624, "alfven_n": 0.03354342673733571, "fast": 0.8697380673927381 }, "right": { "slow": 0.0156695761692184, "alfven_n": 0.04188385609831724, "fast": 0.6949647181239406 } }, "front_relative_normal_velocity": { "left": -0.641230244363254, "right": -0.9997524133706773 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5591161242923568, "pressure_ratio": 2.5126581966014316, "entropy_over_cv": 0.18114277906068388, "tangential_field_ratio": 1.5606503135150447 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.25, "theta_Bn_degrees": 86.25, "compression": 1.5591401880712845, "u2x_km_s": -385.1289981596263, "u2y_km_s": -13.818074226482196, "speed2_km_s": 385.37680833019255, "signed_deflection_degrees": 2.0548384359342946, "p2_over_p1": 2.51277600037273, "B2_over_B1": 1.5587263009287977, "entropy_over_cv": 0.18116393854106164, "upstream_fast_Mach": 1.4385844640501406, "downstream_fast_Mach": 0.7372606958873263, "downstream_alfven_margin": 0.6074585442989419, "state_global_normalized": { "rho": "1.55914018807128448793892267394159086274244199138801775648457430157825358623837914087827830", "p": "0.101918194575117935474621121981004208534559030443597245896698616794923742129451685074644653", "u": [ "-0.641881663599377105728384296992551668610882689237213614796567467009937005916154162249792076", "-0.0230301237108036578568648387491043751607464504381122217004750339287355805719717469514511240", "-0E-91" ], "B": [ "0.0640567926530150540878811486210417929574980361263742015510874382707266354494987243643596994", "1.00284705543961967015593902987799427819406195456564020503965070865380536313425784242775429", "0E-91" ] }, "root_record": { "r": "1.55914018807128448793892267394159086274244199138801775648457430157825358623837914087827830", "b": "0.0405793112563384296433652597151217482073350606882856161989736608002673571337359066094829570", "h": "0.00177869621544247263517692955678161167565799993276855706724567427461540752145243297403928832", "A": "0.414040682794361961517303924522529557179868681665142500720853139492696123015761740273777423", "denominator": "0.997226763248133341263488670291033601330976405594165560881184948202165217787280567884646015", "polynomial_residual": "-6.14930494957003870435575E-66", "bracket_initial_signs": [ "1.46568941043707810106736232415495802954609185732866595926639299738948571134617491576071558", "-2.01105172861833224342836870334027267972352629408872946217504974925964281794090502413962470" ], "bracket_derivative_max": "-5.55083192938093024693782139720656530439146438441709033565610045604117017698759608260081864", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-1E-91", "0E-182", "-1E-90", "0E-182", "3.50271512191669230689268282220867287434090063751871896595799680956320042234123177597557817E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.25", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.029421051448394256, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.012815106154764928, "alfven_n": 0.03376796934551274, "fast": 0.869741893500385 }, "right": { "slow": 0.01577464535801056, "alfven_n": 0.042164555649352314, "fast": 0.694962341151116 } }, "front_relative_normal_velocity": { "left": -0.6412265136444546, "right": -0.9997620270799091 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5591401880712845, "pressure_ratio": 2.51277600037273, "entropy_over_cv": 0.1811639385410615, "tangential_field_ratio": 1.560695128407978 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.225, "theta_Bn_degrees": 86.22500000000001, "compression": 1.5591639825748707, "u2x_km_s": -385.11639912876376, "u2y_km_s": -13.785616201614328, "speed2_km_s": 385.36305491310856, "signed_deflection_degrees": 2.050082846270947, "p2_over_p1": 2.5128926039530866, "B2_over_B1": 1.558744532897832, "entropy_over_cv": 0.1811849064489103, "upstream_fast_Mach": 1.4386029768370687, "downstream_fast_Mach": 0.7372532431831775, "downstream_alfven_margin": 0.6072302667079729, "state_global_normalized": { "rho": "1.55916398257487072385649778493613763617354520409849363313760399878171436969398732314044967", "p": "0.101922924016337192793602510523671882708157346782943974163137784065392467657062277786429323", "u": [ "-0.641860665214606281036005917097829719912378428393782246248527844789931540201060236561736807", "-0.0229760270026905465872023301449578351027954085676863640511239553287816257692684835561632183", "-0E-91" ], "B": [ "0.0638998380206245535214273772745929898964472904689339655571110800945577832149708799865047474", "1.00286884632603412192703929701581172700207828801006582240140393772426887976070497324832769", "0E-91" ] }, "root_record": { "r": "1.55916398257487072385649778493613763617354520409849363313760399878171436969398732314044967", "b": "0.0405785462974922970324087957512630235317311941077615126356079929022306949350505696762783103", "h": "0.00180242279925960040637108816849346228432700608232723367645720218290560073698157396879880365", "A": "0.414009117617367202263839540677975321905582147724099542906240050569101379719689591050696867", "denominator": "0.997189727290022654679367814516152764734616783317098728505751654805845669432855898294487570", "polynomial_residual": "1.38180889941614159792039E-66", "bracket_initial_signs": [ "1.46574708102706557429003675157525978370946778023571351130112024725154883072165604673814838", "-2.01078349863776124838469877058646118968037860642545720113735319352430916471750979740700001" ], "bracket_derivative_max": "-5.55056241299246745565777189822850512912812006508266712529292134768705935306964025187651510", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "0E-91", "0E-182", "2E-90", "0E-182", "-7.87189307268290575296838078589479904158969405828488743935937148371586233932181312045771304E-68", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.225", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.029035773865514695, 0.0 ], "rh_scaled_inf": 1.7818991134964606e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7818991134964606e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.012900464257935155, "alfven_n": 0.033992504996577, "fast": 0.8697456099833419 }, "right": { "slow": 0.01587971262441396, "alfven_n": 0.04244524717285116, "fast": 0.6949599483289501 } }, "front_relative_normal_velocity": { "left": -0.6412227717045499, "right": -0.9997714504485632 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5591639825748707, "pressure_ratio": 2.5128926039530866, "entropy_over_cv": 0.18118490644891028, "tangential_field_ratio": 1.5607398143726 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.2, "theta_Bn_degrees": 86.2, "compression": 1.5591875078025121, "u2x_km_s": -385.1038949871135, "u2y_km_s": -13.753148677104276, "speed2_km_s": 385.3493986407404, "signed_deflection_degrees": 2.045325002083501, "p2_over_p1": 2.513008007128235, "B2_over_B1": 1.5587624584237776, "entropy_over_cv": 0.18120568275311136, "upstream_fast_Mach": 1.438621248668244, "downstream_fast_Mach": 0.7372458705615285, "downstream_alfven_margin": 0.6070019848351753, "state_global_normalized": { "rho": "1.55918750780251224255820533594539850908386021026634981723322966929402592155474555762756631", "p": "0.101927604769121205812835420757724695432329138547554177821254113024685957916804659064034841", "u": [ "-0.641839824978522491807832945098355551309058645360520629551518132249995320754422996033209733", "-0.0229219144618404593639580947379979040814413193571863663700430321676548737259380600491421383", "-0E-91" ], "B": [ "0.0637428626605105737822441152794311485027118050287298445459766245751518817431293009660961282", "1.00289041567185435191571234231422501115164367479712844077953448581294194184805120985803757", "0E-91" ] }, "root_record": { "r": "1.55918750780251224255820533594539850908386021026634981723322966929402592155474555762756631", "b": "0.0405777968110086291968388319042409500545713613475216251912626130077185696529588700743600217", "h": "0.00182630613733673288698891697366139203202126168071664102401900577420825161507208278651217944", "A": "0.413977554232621798106126917124787720410538897742351493425153644194755133754188039455647406", "denominator": "0.997152446285241506796538922558183107017402229701042257316551886816502601779354711776211273", "polynomial_residual": "-1.60219023614381439752495E-66", "bracket_initial_signs": [ "1.46580314224824230338662275126715012616484934796071615178327288406869723314604403431620866", "-2.01051664698896055633336240023703156001554142779740653175576263574506349984244347281426563" ], "bracket_derivative_max": "-5.55029292199286859949537187304894077823395757967049217093376964485239495948447559266276341", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.02763905419032554374840361418237542800090444722829812000233603820589254180500807621759917E-90", "-2E-91", "0E-182", "0E-90", "0E-182", "9.12846354078173142250554172547936050511362290588377736225611980871408594341668112303252556E-68", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.2", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.02865049315156416, 0.0 ], "rh_scaled_inf": 2.1876409556511075e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1876409556511075e-16 }, "characteristics": { "left": { "slow": 0.012985821298133866, "alfven_n": 0.03421703370603685, "fast": 0.8697492168424399 }, "right": { "slow": 0.01598477795558117, "alfven_n": 0.0427259306153741, "fast": 0.6949575396584469 } }, "front_relative_normal_velocity": { "left": -0.6412190185412122, "right": -0.9997806834748455 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5591875078025121, "pressure_ratio": 2.513008007128235, "entropy_over_cv": 0.18120568275311155, "tangential_field_ratio": 1.560784371422535 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.175, "theta_Bn_degrees": 86.17500000000001, "compression": 1.5592107637534525, "u2x_km_s": -385.0914857396205, "u2y_km_s": -13.720671722152789, "speed2_km_s": 385.3358395239864, "signed_deflection_degrees": 2.040564916954716, "p2_over_p1": 2.513122209685329, "B2_over_B1": 1.5587800775112184, "entropy_over_cv": 0.1812262674227443, "upstream_fast_Mach": 1.4386392795377896, "downstream_fast_Mach": 0.737238578015282, "downstream_alfven_margin": 0.6067736986627901, "state_global_normalized": { "rho": "1.55921076375345244946419792246401672213973002759830102881714201449891382128532593736953456", "p": "0.101932236824836959942550023892945444037723884218261164202450061449238925106660174455298389", "u": [ "-0.641819142899367443205679230556168658231129808421601543870734240029017762543987421600697580", "-0.0228677862035879791984172195322554634117898710129829911270434520881539441125176099855333455", "-0E-91" ], "B": [ "0.0635858668030092445307983679421924737686258623537598744947560494319632379218199442449498583", "1.00291176346316958122322031153637887997502380307159504523766719995054046404901755828934243", "0E-91" ] }, "root_record": { "r": "1.55921076375345244946419792246401672213973002759830102881714201449891382128532593736953456", "b": "0.0405770627957451254954111236658757927783356373596700756976137134546165151927640012138611802", "h": "0.00185034623006989672566289434877129102539332135407927830498250362892213485001018508849811386", "A": "0.413945992628024478304913622344519584616873128680045064231999713136602166370728794506098918", "denominator": "0.997114920241404394883644948816698566744983477803907651154647020052473868382065358085178295", "polynomial_residual": "-1.07424541543396684265692E-66", "bracket_initial_signs": [ "1.46585759428702107767167659171784740107704229262247512758808953305489456260918631788393864", "-2.01025117338518779017358397730970480499738558661236976514969537894913279846015582060050169" ], "bracket_derivative_max": "-5.55002345620301841853350608732865396480574405935850078773843388334074771418513245761650483", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "3E-91", "0E-182", "3E-90", "0E-182", "6.12124139676689768045514980268310338523773732840841648842930632044582226676528667280171458E-68", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.175", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.028265209344314066, 0.0 ], "rh_scaled_inf": 2.1876466708026223e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1876466708026223e-16 }, "characteristics": { "left": { "slow": 0.013071177273972721, "alfven_n": 0.034441555489398645, "fast": 0.8697527140785314 }, "right": { "slow": 0.016089841338664108, "alfven_n": 0.04300660592348295, "fast": 0.6949551151406166 } }, "front_relative_normal_velocity": { "left": -0.6412152541521887, "right": -0.9997897261569982 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5592107637534525, "pressure_ratio": 2.5131222096853296, "entropy_over_cv": 0.1812262674227444, "tangential_field_ratio": 1.5608287995711325 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.15, "theta_Bn_degrees": 86.14999999999999, "compression": 1.5592337504267813, "u2x_km_s": -385.07917139123754, "u2y_km_s": -13.68818540596654, "speed2_km_s": 385.3223775737276, "signed_deflection_degrees": 2.0358026044739455, "p2_over_p1": 2.5132352114129457, "B2_over_B1": 1.5587973901647447, "entropy_over_cv": 0.18124666042708648, "upstream_fast_Mach": 1.4386570694398346, "downstream_fast_Mach": 0.7372313655374694, "downstream_alfven_margin": 0.6065454081731346, "state_global_normalized": { "rho": "1.55923375042678129539641263553686473304044915199621445219972555772641758179829089347202116", "p": "0.101936820174909069571960845478885197571957136644424095086877704149526489591314655432416075", "u": [ "-0.641798618985395965983154364716640039077245138185117997457621768592736314899175618062258536", "-0.0228136423432775650495667496195916711033042909629348802967646295429183241712010717205175079", "-0E-91" ], "B": [ "0.0634288506784628433652843921957215405368704759846604794343745578608642886657672238651426740", "1.00293288968618686895495380017840352290623919026871876381107752894789403050055678485630370", "0E-91" ] }, "root_record": { "r": "1.55923375042678129539641263553686473304044915199621445219972555772641758179829089347202116", "b": "0.0405763442505830958124097012671991733483950089524440104484556252500112185850539288417114842", "h": "0.00187454307809434195588152544605256390725187019648250381965662920216753918318161559334781621", "A": "0.413914432791476687639421619259194143947112509449322010602621133615723522392614774490047155", "denominator": "0.997077149166006396415203032568912322842823258405884565825365808413940055401529212131771365", "polynomial_residual": "-7.40051038634488482731600E-66", "bracket_initial_signs": [ "1.46591043732907241730404502452707666599371909469215397781239125040657741863689318204175197", "-2.00998707753891699947533276401563473135778677429612537939670784165235463416631035901461299" ], "bracket_derivative_max": "-5.54975401544180755998669405308481885453254694652895850775442169001467186224464663451212835", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.02769834987889971514099787840218742099075515589158176302565224515983190579114234041518210E-90", "1E-91", "0E-182", "1E-90", "0E-182", "4.21745107245970870573810645298608545900535045090962240418418144086629450082150596524261463E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.15", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.02787992248154069, 0.0 ], "rh_scaled_inf": 2.1876535060864317e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1876535060864317e-16 }, "characteristics": { "left": { "slow": 0.01315653218405853, "alfven_n": 0.034666070362166894, "fast": 0.8697561016924914 }, "right": { "slow": 0.016194902760814086, "alfven_n": 0.0432872730437411, "fast": 0.6949526747764763 } }, "front_relative_normal_velocity": { "left": -0.6412114785353016, "right": -0.9997985784932998 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5592337504267813, "pressure_ratio": 2.5132352114129457, "entropy_over_cv": 0.1812466604270866, "tangential_field_ratio": 1.5608730988314654 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.125, "theta_Bn_degrees": 86.125, "compression": 1.5592564678214353, "u2x_km_s": -385.0669519469256, "u2y_km_s": -13.65568979775808, "speed2_km_s": 385.3090128008279, "signed_deflection_degrees": 2.031038078237102, "p2_over_p1": 2.5133470121010797, "B2_over_B1": 1.5588143963889531, "entropy_over_cv": 0.18126686173561316, "upstream_fast_Mach": 1.4386746183685126, "downstream_fast_Mach": 0.7372242331212501, "downstream_alfven_margin": 0.6063171133486034, "state_global_normalized": { "rho": "1.55925646782143525266108593232155155830065150465331223843462982484427583294097936865428637", "p": "0.101941354810819792567766052401471856792803543439258301153391038513806347348508404887618798", "u": [ "-0.641778253244875995348456559847963291963964835039280276694770680716362331329476396681061818", "-0.0227594829962634686007888402742725837819551274302040520061011765869649176444069821061070296", "-0E-91" ], "B": [ "0.0632718145172198159126624781550289872691769689898089312344138961794490429050673036397121701", "1.00295379432723110954572468572922001822847442285649509726666619996942440049807407398833077", "0E-91" ] }, "root_record": { "r": "1.55925646782143525266108593232155155830065150465331223843462982484427583294097936865428637", "b": "0.0405756411744274569337793702176298538612323128267349468892438532250262290579553640851615302", "h": "0.00189889668228452347390058069934212130816195494352872224824890085326823178090991108638790289", "A": "0.413882874710882567795382081829046510218595457014820894946546399860149750537244252044489509", "denominator": "0.997039133066423191763317528470421610497879571485959508225068557867575379152637614422781868", "polynomial_residual": "-6.59069417952995516818203E-66", "bracket_initial_signs": [ "1.46596167155932485743821096266940819643378984796634868810615006491457637724712882367638471", "-2.00972435916183852264280781103805884659996525444723435802445424837799275711291388295935373" ], "bracket_derivative_max": "-5.54948459952613264150157315180818452008355952348200620681307541666518763857447147424020185", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.02773029061283411127950651878732459094894127781435189226534328314893324654650066509861771E-90", "2E-91", "0E-182", "6E-90", "0E-182", "3.75640070047415077333848323986189398125515850885111333341014969619010104515616526472499055E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_-1.125", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.02749463260102504, 0.0 ], "rh_scaled_inf": 2.1876614615147833e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1876614615147833e-16 }, "characteristics": { "left": { "slow": 0.013241886026993329, "alfven_n": 0.03489057833984431, "fast": 0.8697593796852162 }, "right": { "slow": 0.016299962209181746, "alfven_n": 0.043567931922713486, "fast": 0.6949502185670497 } }, "front_relative_normal_velocity": { "left": -0.6412076916884477, "right": -0.9998072404820648 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5592564678214353, "pressure_ratio": 2.5133470121010797, "entropy_over_cv": 0.18126686173561302, "tangential_field_ratio": 1.56091726921633 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.1, "theta_Bn_degrees": 86.1, "compression": 1.5592789159361973, "u2x_km_s": -385.0548274116531, "u2y_km_s": -13.623184966745791, "speed2_km_s": 385.2957452161341, "signed_deflection_degrees": 2.0262713518466144, "p2_over_p1": 2.51345761154115, "B2_over_B1": 1.5588310961884464, "entropy_over_cv": 0.18128687131799734, "upstream_fast_Mach": 1.438691926317963, "downstream_fast_Mach": 0.7372171807599113, "downstream_alfven_margin": 0.6060888141716669, "state_global_normalized": { "rho": "1.55927891593619729127041065874694516823088567037240624512197616689035443319974614883187092", "p": "0.101945840724109044730531088346369467439228053034730352947800558180623136090607011151784155", "u": [ "-0.641758045686088550313394785084112219514849288824891271590488248739163690508148725301553806", "-0.0227053082779096510161440710772157002589921662482985404491353809339730662250745395945068273", "-0E-91" ], "B": [ "0.0631147585496347959245722029396778659102457161514754018400279320794796118741852612268217950", "1.00297447737274502989593272685003309570104211563128080904588679212881334734029643398090208", "0E-91" ] }, "root_record": { "r": "1.55927891593619729127041065874694516823088567037240624512197616689035443319974614883187092", "b": "0.0405749535662067289998588212956219716659940304709112357568368984821310467827533958807663997", "h": "0.00192340704375408329284048519344527385200198297345175784771701072819768764328126793190738305", "A": "0.413851318374148938761816502164974051601229010141970466465265625377435323981817539020332266", "denominator": "0.997000871949911087011947059964805410291666234563558585001356979951041695596741566007835064", "polynomial_residual": "1.605934588349959111502778E-65", "bracket_initial_signs": [ "1.46601129716196523675986299155713617273049701720759414404447006603604280282892707464943720", "-2.00946301796485883615398811078881663990617992950195010011604016463782700291062023045991224" ], "bracket_derivative_max": "-5.54921520827089630075820067505676060466272498690577796876539165025389463639533350752605627", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "1E-91", "0E-182", "-1E-90", "0E-182", "-9.15421201833911268924914949914161071919157514087601982741883230438197102184834984015726722E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-1.1", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.02710933974055273, 0.0 ], "rh_scaled_inf": 6.938893903907228e-18, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.013327238801374442, "alfven_n": 0.035115079437932, "fast": 0.8697625480576248 }, "right": { "slow": 0.016405019670917127, "alfven_n": 0.04384858250696663, "fast": 0.6949477465133677 } }, "front_relative_normal_velocity": { "left": -0.641203893609599, "right": -0.9998157121216442 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5592789159361973, "pressure_ratio": 2.51345761154115, "entropy_over_cv": 0.18128687131799726, "tangential_field_ratio": 1.5609613107382472 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.075, "theta_Bn_degrees": 86.075, "compression": 1.5593010947696968, "u2x_km_s": -385.04279779039666, "u2y_km_s": -13.59067098215382, "speed2_km_s": 385.2825748304761, "signed_deflection_degrees": 2.02150243891139, "p2_over_p1": 2.5135670095259965, "B2_over_B1": 1.5588474895678333, "entropy_over_cv": 0.18130668914410977, "upstream_fast_Mach": 1.4387089932823292, "downstream_fast_Mach": 0.7372102084468688, "downstream_alfven_margin": 0.6058605106248725, "state_global_normalized": { "rho": "1.55930109476969685530326578852892224283209377911866200297126552525739222800573047188402841", "p": "0.101950277906374414208984416401882610144247900496990280026050972870229503195356641529400113", "u": [ "-0.641737996317327713528623984469171985615986173607958021978970730082935513556476842917354771", "-0.0226511183035896996760657800063608399886329042534147653052624243455577753898302218912065202", "-0E-91" ], "B": [ "0.0629576830060686253788945400705212324516049433216783431553932742911484485322913363658556205", "1.00299493880928918631854642054236638160610660962005593538694656515308281314672809971237253", "0E-91" ] }, "root_record": { "r": "1.55930109476969685530326578852892224283209377911866200297126552525739222800573047188402841", "b": "0.0405742814248730320346946248225735388759261843938915749391446097317570948048823125169068650", "h": "0.00194807416385583357282873424367170071091721871943914146508617982532206247006946443436782910", "A": "0.413819763769185280236503087466252478545537054799182872202912357582141708163331340121509988", "denominator": "0.996962365823607036893788851997383204060830646687071665354759601931095308759461031831138855", "polynomial_residual": "3.53364869615349915852472E-66", "bracket_initial_signs": [ "1.46605931432043899040481392419303548153945863426258157610296948874031237937905172865762532", "-2.00920305365810039088026156577128010639554531590796729989572246111251502328888994383503345" ], "bracket_derivative_max": "-5.54894584148900723137606583848438800871304879415645309298209316121302653116278568618856595", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.02779875801203942705997556654761442417789292118862114408075064002610202999509581318655345E-90", "0E-91", "0E-182", "-1E-90", "0E-182", "-2.01450726382112293623007663772319922506172135363879423322251678206371284255843857795970110E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.075", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.026724043937913868, 0.0 ], "rh_scaled_inf": 0.0, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.013412590505794533, "alfven_n": 0.03533957367192942, "fast": 0.8697656068106572 }, "right": { "slow": 0.01651007513316959, "alfven_n": 0.044129224743068615, "fast": 0.6949452586164669 } }, "front_relative_normal_velocity": { "left": -0.6412000842968019, "right": -0.999823993410425 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5593010947696968, "pressure_ratio": 2.5135670095259965, "entropy_over_cv": 0.18130668914410986, "tangential_field_ratio": 1.5610052234094602 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.05, "theta_Bn_degrees": 86.05, "compression": 1.5593230043204098, "u2x_km_s": -385.0308630881404, "u2y_km_s": -13.558147913212048, "speed2_km_s": 385.2695016546662, "signed_deflection_degrees": 2.016731353046772, "p2_over_p1": 2.5136752058498812, "B2_over_B1": 1.558863576531729, "entropy_over_cv": 0.18132631518401876, "upstream_fast_Mach": 1.438725819255761, "downstream_fast_Mach": 0.7372033161756661, "downstream_alfven_margin": 0.6056322026908433, "state_global_normalized": { "rho": "1.55932300432040983940495162286963764041623980478894302479828856389054529790155806156031724", "p": "0.101954666349271175872252961181111490222429604389264363885558724784867784709747443122358685", "u": [ "-0.641718105146900611605080128043734269159935141505215749107090773538393956845639058793119725", "-0.0225969131886867448922861727780623806894036591725730344084033264200192524443821292865594446", "-0E-91" ], "B": [ "0.0628005881168883745877373881572871882602277132578637510099240354423573838067897952720405427", "1.00301517862354196129683821535391165980393408880766998626948920196311513466289422760905522", "0E-91" ] }, "root_record": { "r": "1.55932300432040983940495162286963764041623980478894302479828856389054529790155806156031724", "b": "0.0405736247494020825519168107595369163176097122765073189897719713269997372426230679430798549", "h": "0.00197289804418174042705053467683646343698840978290145454192453383895124141073925740427791238", "A": "0.413788210883903713040067494457219706534537923144845367343970097419977725243008936646712345", "denominator": "0.996923614694528667849844702806190413707388869998764587083327175187753317859861652636026941", "polynomial_residual": "-9.9050462483687503753677E-67", "bracket_initial_signs": [ "1.46610572321745044726045946280227330389855358387033528066188276105989876154397382156142217", "-2.00894446595090143549002137380655683301230464495067760562931762358448217842439469841530837" ], "bracket_derivative_max": "-5.54867649899138020512859048786836324208961875033945897370528387873971910900102212038454933", "iterations": 216 }, "flux_residuals": [ "0E-90", "1.60556705694849879550959032172550993742626698584103396024985131706780819158148829228038961E-89", "-3E-91", "0E-182", "-6E-90", "0E-182", "5.64747498085564713627473526195623135125963329739451402928881075173997835475793030678776946E-68", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_-1.05", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.026338745230902946, 0.0 ], "rh_scaled_inf": 1.781969746330265e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.781969746330265e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.013497941138841674, "alfven_n": 0.03556406105733464, "fast": 0.8697685559452759 }, "right": { "slow": 0.01661512858308786, "alfven_n": 0.04440985857758912, "fast": 0.6949427548773917 } }, "front_relative_normal_velocity": { "left": -0.641196263748178, "right": -0.9998320843468308 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5593230043204098, "pressure_ratio": 2.5136752058498812, "entropy_over_cv": 0.18132631518401876, "tangential_field_ratio": 1.561049007241938 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.025, "theta_Bn_degrees": 86.025, "compression": 1.5593446445866586, "u2x_km_s": -385.01902330987645, "u2y_km_s": -13.525615829156026, "speed2_km_s": 385.25652569949943, "signed_deflection_degrees": 2.011958107874499, "p2_over_p1": 2.513782200308489, "B2_over_B1": 1.5588793570847548, "entropy_over_cv": 0.1813457494079902, "upstream_fast_Mach": 1.4387424042324124, "downstream_fast_Mach": 0.7371965039399752, "downstream_alfven_margin": 0.6054038903522792, "state_global_normalized": { "rho": "1.55934464458665856542586537557891515644389451408899390846189574667917861851615825798820350", "p": "0.101959006044512305640064676644988991513176290907068868699223688408286605011696584140011437", "u": [ "-0.641698372183127395921604772046728444502772143545440672012280934120100531563348784761784886", "-0.0225426930485933766018148566406744029964211809424211383479068098244008111274693257164747892", "-0E-91" ], "B": [ "0.0626434741124673623126192683069128273409144318315585704473132874742506222936757130287459890", "1.00303519680229956005281378532534987723903533014462114118475832686676075500481876211698960", "0E-91" ] }, "root_record": { "r": "1.55934464458665856542586537557891515644389451408899390846189574667917861851615825798820350", "b": "0.0405729835387931902371571627100297930988552733984780626660510717043415291628502506964273510", "h": "0.00199787868656290850357519411313581838870946266003205603597465878495623284088301839264538166", "A": "0.413756659706218980538636997015775957838375184977353912456457509625690921725666214882042307", "denominator": "0.996884618569574301211734058166273388059647254912310177570592670585845947674588818123723197", "polynomial_residual": "4.96288342108007462328063E-66", "bracket_initial_signs": [ "1.46615052403496313164903385061935142400482206032266865525928106731760132322101459907073090", "-2.00868725455181582693999353219201273791000365900092368291515099190288388101184424296608131" ], "bracket_derivative_max": "-5.54840718058693608046978493822832129593356572625048732874147038555868099051197555658320125", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-4E-91", "0E-182", "-4E-90", "0E-182", "-2.82998551604197112790941147739883085625299812515732168511190179931793097456827718590378303E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-1.025", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.025953443657318696, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.013583290699099406, "alfven_n": 0.03578854160964434, "fast": 0.8697713954624658 }, "right": { "slow": 0.016720180007820013, "alfven_n": 0.044690483957099424, "fast": 0.6949402352971923 } }, "front_relative_normal_velocity": { "left": -0.6411924319619235, "right": -0.9998399849293209 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5593446445866586, "pressure_ratio": 2.513782200308489, "entropy_over_cv": 0.1813457494079902, "tangential_field_ratio": 1.5610926622473722 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -1.0, "theta_Bn_degrees": 86.0, "compression": 1.5593660155666118, "u2x_km_s": -385.0072784606047, "u2y_km_s": -13.493074799226937, "speed2_km_s": 385.24364697575373, "signed_deflection_degrees": 2.007182717022668, "p2_over_p1": 2.5138879926989275, "B2_over_B1": 1.5588948312315385, "entropy_over_cv": 0.18136499178648738, "upstream_fast_Mach": 1.4387587482064428, "downstream_fast_Mach": 0.7371897717335956, "downstream_alfven_margin": 0.6051755735919557, "state_global_normalized": { "rho": "1.55936601556661175919905424912930281239072105547065778450027895014883368325725602807419086", "p": "0.101963296983868494770945499702658827043201424350558231093050699964292571419596747799735782", "u": [ "-0.641678797434341223918751729661292214217540436712801604122806661483931848824340082812270548", "-0.0224884579987115610397903383041411381831742590032336501631622235838141163229832660832872401", "-0E-91" ], "B": [ "0.0624863412231851758876261307027576181977349818181092254289216362231345363926853646483084897", "1.00305499333247600692627467570151248486247806537155509814027939918131722673287587452544731", "0E-91" ] }, "root_record": { "r": "1.55936601556661175919905424912930281239072105547065778450027895014883368325725602807419086", "b": "0.0405723577920692547069917802956382157825883259503130315765447280801549215647049951622159378", "h": "0.00202301609306956634283010205675698393251165842651884187503340499569290475687275561318283555", "A": "0.413725110224048430074997230362104840955655758906372106859878195450432834562003383170388253", "denominator": "0.996845377455522976506820755289450938673738367634495102685244580162275725119392215953930052", "polynomial_residual": "-6.6487147459878694350690E-67", "bracket_initial_signs": [ "1.46619371695420006939198518988686260207615250641909118233986235603792863262445022879253213", "-2.00843141916861282805793433349765005128296585173651376883756634029691124677811974569147389" ], "bracket_derivative_max": "-5.54813788608260179737661316843627688848139650041506141627910154185166638467787189667605195", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "1E-91", "0E-182", "-2E-90", "0E-182", "3.79175406189589554705513985581253430387666591224104115254574265158722432947985942023695353E-68", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-1", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.02556813925496401, 0.0 ], "rh_scaled_inf": 4.3754360827998163e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7819968435473752e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": -0.0, "energy": -4.3754360827998163e-16 }, "characteristics": { "left": { "slow": 0.013668639185146809, "alfven_n": 0.036013015344353944, "fast": 0.8697741253632331 }, "right": { "slow": 0.01682522939451345, "alfven_n": 0.04497110082817242, "fast": 0.6949376998769264 } }, "front_relative_normal_velocity": { "left": -0.6411885889363096, "right": -0.9998476951563913 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5593660155666118, "pressure_ratio": 2.5138879926989275, "entropy_over_cv": 0.18136499178648735, "tangential_field_ratio": 1.5611361884371775 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.975, "theta_Bn_degrees": 85.97500000000001, "compression": 1.5593871172582845, "u2x_km_s": -384.9956285453329, "u2y_km_s": -13.460524892671536, "speed2_km_s": 385.2308654941894, "signed_deflection_degrees": 2.0024051941256897, "p2_over_p1": 2.513992582819728, "B2_over_B1": 1.5589099989767137, "entropy_over_cv": 0.181384042290171, "upstream_fast_Mach": 1.438774851172017, "downstream_fast_Mach": 0.7371831195504551, "downstream_alfven_margin": 0.6049472523927246, "state_global_normalized": { "rho": "1.55938711725828452745658528830332211912544234341245511494205840177693136511920097218233272", "p": "0.101967539159168164108437783651271332287779727126748376678954417455612314881604814900161448", "u": [ "-0.641659380908888240878771379243722529943660933636791922315419431500525946401017017448104185", "-0.0224342081544525573910249127368865387745562474495665372046634676934853484656901185996974378", "-0E-91" ], "B": [ "0.0623291896794276913513164071339484182608289892110716760020596165389002303568918257985653547", "1.00307456820110314156445323740963744831945148873833419127994944203332658245485377764409963", "0E-91" ] }, "root_record": { "r": "1.55938711725828452745658528830332211912544234341245511494205840177693136511920097218233272", "b": "0.0405717475082767623443898905977637482653704428212886809121001716422390295196707715265546016", "h": "0.00204831026601105251059846684866484153292953553462153036484189525608501981748593951334661676", "A": "0.413693562425311994408190702508392055324754561678723351172747502673184769214383841373577593", "denominator": "0.996805891359034474886221107628427059133522976838459516321846468283384603221715250612337663", "polynomial_residual": "1.125250768135184187976434E-65", "bracket_initial_signs": [ "1.46623530215564409825485886650509121163123316999437511917093368255940833531100670647901931", "-2.00817695950827689222021196530830533347882570980268896527165965108551010709248897782243124" ], "bracket_derivative_max": "-5.54786861528331035851050943266344697210207664324732106965389394755439675614961030169382516", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "2E-91", "0E-182", "-2E-90", "0E-182", "-6.41806467346016904292021067898574930312869857933584518647280111470036413972080451678458317E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.975", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.025182832061645788, 0.0 ], "rh_scaled_inf": 3.564023090007336e-16, "rh_components": { "mass": 0.0, "normal_momentum": 3.564023090007336e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1877327180699588e-16 }, "characteristics": { "left": { "slow": 0.013753986595558562, "alfven_n": 0.03623748227695772, "fast": 0.8697767456486062 }, "right": { "slow": 0.016930276730314935, "alfven_n": 0.04525170913738261, "fast": 0.6949351486176577 } }, "front_relative_normal_velocity": { "left": -0.6411847346696823, "right": -0.9998552150265739 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5593871172582845, "pressure_ratio": 2.513992582819728, "entropy_over_cv": 0.18138404229017102, "tangential_field_ratio": 1.5611795858224935 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.95, "theta_Bn_degrees": 85.95, "compression": 1.5594079496595383, "u2x_km_s": -384.98407356907654, "u2y_km_s": -13.4279661787421, "speed2_km_s": 385.2181812655493, "signed_deflection_degrees": 1.99762555282425, "p2_over_p1": 2.514095970470845, "B2_over_B1": 1.55892486032492, "entropy_over_cv": 0.18140290088989902, "upstream_fast_Mach": 1.4387907131233046, "downstream_fast_Mach": 0.7371765473846098, "downstream_alfven_margin": 0.6047189267375135, "state_global_normalized": { "rho": "1.55940794965953833488467347962589249361865358338056646709142926121835957026252175100650399", "p": "0.101971732562297478285367139591567129246959327529284197598488735687777711994666791855705230", "u": [ "-0.641640122615127562191771062672852382463533935689984858201570685417988000026687657860370314", "-0.0223799436312368344200632531720308515191704605212084173786275781090623639162860549206435185", "-0E-91" ], "B": [ "0.0621720197115870935881496478942679443649470754365267796689260789137233145064890290156110940", "1.00309392139533061492215837293888031468776992992127739807673027115047502476390443273114708", "0E-91" ] }, "root_record": { "r": "1.55940794965953833488467347962589249361865358338056646709142926121835957026252175100650399", "b": "0.0405711526864857832106513154324243487518507007372101934238866800667864189026110170587623216", "h": "0.00207376120793580250642129155451520083828161204104072715377493513906157880422245502707267848", "A": "0.413662016297932173161496310659908697710038583455807484636939214959363532071126022328253122", "denominator": "0.996766160286649342675762106099266545651841750487840270220885909703343284279542910952354649", "polynomial_residual": "1.210669052828798372256932E-65", "bracket_initial_signs": [ "1.46627527981903818277214325906150417793164402066759198259828117404566839245768934255302912", "-2.00792387527700743512766163343083337403257466326824971658461816654670909370811955852889973" ], "bracket_derivative_max": "-5.54759936799200079670137624545254417447837271923831862457247203269406711205351493416810138", "iterations": 216 }, "flux_residuals": [ "0E-90", "-1.60559933587301401620090007223283054925798218047039696966385990151359043069452882627818823E-89", "0E-91", "0E-182", "6E-90", "0E-182", "-6.90609443817783767523491515816969922476492627346536540476695545112765113456926906433829628E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.95", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.02479752211517484, 0.0 ], "rh_scaled_inf": 2.1877485150289033e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1877485150289033e-16 }, "characteristics": { "left": { "slow": 0.013839332928904996, "alfven_n": 0.0364619424229489, "fast": 0.8697792563196353 }, "right": { "slow": 0.01703532200237054, "alfven_n": 0.04553230883130615, "fast": 0.6949325815204569 } }, "front_relative_normal_velocity": { "left": -0.6411808691604624, "right": -0.9998625445384374 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5594079496595383, "pressure_ratio": 2.514095970470845, "entropy_over_cv": 0.18140290088989908, "tangential_field_ratio": 1.561222854414183 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.925, "theta_Bn_degrees": 85.925, "compression": 1.559428512768081, "u2x_km_s": -384.9726135368588, "u2y_km_s": -13.395398726696392, "speed2_km_s": 385.2055943005589, "signed_deflection_degrees": 1.9928438067652716, "p2_over_p1": 2.514198155453658, "B2_over_B1": 1.5589394152808038, "entropy_over_cv": 0.18142156755672667, "upstream_fast_Mach": 1.4388063340544806, "downstream_fast_Mach": 0.7371700552302435, "downstream_alfven_margin": 0.6044905966093257, "state_global_normalized": { "rho": "1.55942851276808098131751174671025917176621688809720918545642042558418377089386355340792788", "p": "0.101975877185200359886184448116474952515854960915885179498549884830341966758580529746322040", "u": [ "-0.641621022561431256108052952376038102954625109956419489821560978235983439598194181640152360", "-0.0223256645444939870795748928372986058214876228045824604802948870639549517808992989121888943", "-0E-91" ], "B": [ "0.0620148315500618964802142884234180940127841644060584403955570413674046683404125088593458704", "1.00311305290242588507237022153150756326398631476764864084185736968591682292864455298984607", "0E-91" ] }, "root_record": { "r": "1.55942851276808098131751174671025917176621688809720918545642042558418377089386355340792788", "b": "0.0405705733257899680338154271491006223472208438886310494018520326842593215395780375521175593", "h": "0.00209936892163133644728838969084619862330136551319789498199277815187418320431611415851429006", "A": "0.413630471829834014278729146905034722116901701495840267375027057038826727335726087529039349", "denominator": "0.996726184244788915049959616717456852481151685600437057943822955445383383519531196038200812", "polynomial_residual": "-1.437910470745350368503448E-65", "bracket_initial_signs": [ "1.46631365012338573345159762107280537332208113710454163155704941417610719297894279197799131", "-2.00767216618021859368297900154942253817643490671134093415440813578299233364536620161121628" ], "bracket_derivative_max": "-5.54733014400961812875728164800489023035948323190637593217234295379196212711671836722080554", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.02804085013797969315170261500577024100764462547541860537414277542784612295914630689718534E-90", "0E-91", "0E-182", "4E-90", "0E-182", "8.20334938330570844579695557067012350073959933856353880764051940856565127414283317308527995E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.925", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.02441220945336576, 0.0 ], "rh_scaled_inf": 0.0, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.013924678183752162, "alfven_n": 0.036686395797819744, "fast": 0.869781657377393 }, "right": { "slow": 0.017140365197825677, "alfven_n": 0.045812899856520796, "fast": 0.6949299985864017 } }, "front_relative_normal_velocity": { "left": -0.6411769924071454, "right": -0.9998696836905859 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559428512768081, "pressure_ratio": 2.514198155453658, "entropy_over_cv": 0.18142156755672678, "tangential_field_ratio": 1.5612659942228317 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.9, "theta_Bn_degrees": 85.9, "compression": 1.5594488065814667, "u2x_km_s": -384.9612484537106, "u2y_km_s": -13.362822605797593, "speed2_km_s": 385.19310460992614, "signed_deflection_degrees": 1.9880599696018695, "p2_over_p1": 2.514299137570969, "B2_over_B1": 1.5589536638490173, "entropy_over_cv": 0.18144004226190624, "upstream_fast_Mach": 1.4388217139597248, "downstream_fast_Mach": 0.7371636430816678, "downstream_alfven_margin": 0.6042622619912403, "state_global_normalized": { "rho": "1.55944880658146657906974867399543439741616856471549990398319763472441755236281477476144509", "p": "0.101979973019878503567409637815253847168084225572127681916406954817340271248414670981358112", "u": [ "-0.641602080756184326976633691759988375872232269664413471658474991353925570876586928787507794", "-0.0222713710096626530969006656552090214523829199360273399557864780668892290638805877401550600", "-0E-91" ], "B": [ "0.0618576254252569630700303033324676855768336648642438040982001690436468831890772281430479741", "1.00313196270977421282722151651016247351141143229669754538396388287084205770329140235812133", "0E-91" ] }, "root_record": { "r": "1.55944880658146657906974867399543439741616856471549990398319763472441755236281477476144509", "b": "0.0405700094253065452735248514228515440209674982376518252459037144727875897287072414319182428", "h": "0.00212513341012424752650755837035358763336332068394485293529731536103149510438228375047828761", "A": "0.413598929008945095488799923837021797874172844126689367361243943227397667072906583086089245", "denominator": "0.996685963239755339829087559337769668258449455900128257311897537149497881177976619430309455", "polynomial_residual": "2.00503639161648705830427E-66", "bracket_initial_signs": [ "1.46635041324695093035764771109473462874490541964929676325666718058815529112007960739593388", "-2.00742183192253897197279217867411165792174318683163458470996227713730732725888831544994265" ], "bracket_derivative_max": "-5.54706094313511329560296166829111908113878064585958382878319326986202276271725665200841025", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "-3E-91", "0E-182", "0E-90", "0E-182", "-1.14402075264900788603293988409959118973662058749125567393615421698352262869564558551863528E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.9", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.024026894114036815, 0.0 ], "rh_scaled_inf": 2.187783469931553e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.187783469931553e-16 }, "characteristics": { "left": { "slow": 0.014010022358661908, "alfven_n": 0.036910842417061676, "fast": 0.8697839488229733 }, "right": { "slow": 0.017245406303825095, "alfven_n": 0.04609348215960599, "fast": 0.6949273998165758 } }, "front_relative_normal_velocity": { "left": -0.641173104408302, "right": -0.9998766324816606 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5594488065814667, "pressure_ratio": 2.514299137570969, "entropy_over_cv": 0.18144004226190613, "tangential_field_ratio": 1.5613090052587504 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.875, "theta_Bn_degrees": 85.875, "compression": 1.5594688310970954, "u2x_km_s": -384.94997832467084, "u2y_km_s": -13.330237885314258, "speed2_km_s": 385.1807122043413, "signed_deflection_degrees": 1.9832740549933126, "p2_over_p1": 2.5143989166270067, "B2_over_B1": 1.558967606034219, "entropy_over_cv": 0.18145832497688716, "upstream_fast_Mach": 1.4388368528332225, "downstream_fast_Mach": 0.7371573109333229, "downstream_alfven_margin": 0.604033922866412, "state_global_normalized": { "rho": "1.55946883109709553040756197413062519697812591086258957638787960263962946524212194188722773", "p": "0.101984020058391390136203661463346539700712284056987601579313158367104032956287107675891166", "u": [ "-0.641583297207784698969953040232600146555787561718099591254517112276335405617594138903862347", "-0.0222170631421904295385730464504817807875349226363253407093970891717126899283325570632815418", "-0E-91" ], "B": [ "0.0617004015675835257352027230422063241788486913918553735937210248766075036872361866857725826", "1.00315065080487865716930295211008301657950465948196835087450975950063369257015952358969175", "0E-91" ] }, "root_record": { "r": "1.55946883109709553040756197413062519697812591086258957638787960263962946524212194188722773", "b": "0.0405694609841763182623276011449305866906584144460654242857707178914202721867237380116738601", "h": "0.00215105467668019124764534200890400261028326692160388936599126292911734771158435581698844294", "A": "0.413567387823195505778473396713927540145584094101851052609686087987067716452114913313652147", "denominator": "0.996645497277731601399410157094597105271294878935300333349309486904900309067053923312409512", "polynomial_residual": "9.50420950178734969835787E-66", "bracket_initial_signs": [ "1.46638556936725905107350040680089282399928055621314135649347021384027247133498602163383857", "-2.00717287220781137435742798763375694500280664814017736023621218098458250466734649929147553" ], "bracket_derivative_max": "-5.54679176516544308875012194569449629638372146032339914152053854755071939339206864219100366", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "1E-91", "0E-182", "-4E-90", "0E-182", "-5.42350337545596082964446896334296424769255891348914386719388476338067433912486567246458098E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.875", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.023641576135009817, 0.0 ], "rh_scaled_inf": 2.18780262793953e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.782078037123138e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.18780262793953e-16 }, "characteristics": { "left": { "slow": 0.014095365452191913, "alfven_n": 0.03713528229616539, "fast": 0.8697861306574929 }, "right": { "slow": 0.017350445307512844, "alfven_n": 0.046374055687142826, "fast": 0.6949247852120702 } }, "front_relative_normal_velocity": { "left": -0.6411692051625774, "right": -0.9998833909103383 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5594688310970954, "pressure_ratio": 2.5143989166270067, "entropy_over_cv": 0.1814583249768873, "tangential_field_ratio": 1.5613518875319718 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.85, "theta_Bn_degrees": 85.85000000000001, "compression": 1.5594885863122145, "u2x_km_s": -384.9388031547859, "u2y_km_s": -13.297644634520275, "speed2_km_s": 385.16841709447704, "signed_deflection_degrees": 1.9784860766049837, "p2_over_p1": 2.5144974924274237, "B2_over_B1": 1.5589812418410731, "entropy_over_cv": 0.18147641567331577, "upstream_fast_Mach": 1.4388517506691638, "downstream_fast_Mach": 0.7371510587797765, "downstream_alfven_margin": 0.6038055792180708, "state_global_normalized": { "rho": "1.55948858631221450515827789748082349509519178406994037111822308394969837225074350935363862", "p": "0.101988018292856300587094935175964184490151938342245495947586078402238119438040715847316677", "u": [ "-0.641564671924643200294781680778475226692016167636099257765312895114861813945068368920916182", "-0.0221627410575337893526302010482113711235720769073416229665896967588206960555122196947011471", "-0E-91" ], "B": [ "0.0615431602074592063757022111704243146310309433546074370423504511653121204196422128526741176", "1.00316911717536007049322950135299149275655975314080864814031209696028851692387420512245314", "0E-91" ] }, "root_record": { "r": "1.55948858631221450515827789748082349509519178406994037111822308394969837225074350935363862", "b": "0.0405689280015636624234017510145367587668800003299360900891858232973716969889767779136380240", "h": "0.00217713272480387543343713421971005038083476299115647014358018236141559269290888589985454588", "A": "0.413535848260517826873265204385585826644901259773471826061152981809276420714064122056197870", "denominator": "0.996604786364781544756650451255061271185497188530415421971243962673507812618036998901241032", "polynomial_residual": "4.24936831629963358179397E-66", "bracket_initial_signs": [ "1.46641911866109680304169417710573485252924495330972316172661540363790981593071343322871069", "-2.00692528673909252567126381196256521821395276100954481394622447824439394026376846369433393" ], "bracket_derivative_max": "-5.54652260989557006310242060093994310433360726620084922006374489347241100711315539696984181", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.02818253620520995617908199142809788312490430436853433923834886033000087210011799954758036E-90", "-2E-91", "0E-182", "-4E-90", "0E-182", "-2.42516085774410436075542023857863096498420671774878088153190127395486640508548308975627286E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.85", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.02325625555411001, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.01418070746289577, "alfven_n": 0.037359715450620896, "fast": 0.86978820288209 }, "right": { "slow": 0.0174554821960323, "alfven_n": 0.04665462038571405, "fast": 0.6949221547739826 } }, "front_relative_normal_velocity": { "left": -0.6411652946686917, "right": -0.9998899589753325 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5594885863122145, "pressure_ratio": 2.5144974924274237, "entropy_over_cv": 0.18147641567331574, "tangential_field_ratio": 1.561394641052254 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.825, "theta_Bn_degrees": 85.825, "compression": 1.5595080722239165, "u2x_km_s": -384.92772294911015, "u2y_km_s": -13.265042922694798, "speed2_km_s": 385.15621929098825, "signed_deflection_degrees": 1.973696048108337, "p2_over_p1": 2.514594864779298, "B2_over_B1": 1.5589945712742506, "entropy_over_cv": 0.1814943143230354, "upstream_fast_Mach": 1.438866407461744, "downstream_fast_Mach": 0.7371448866157244, "downstream_alfven_margin": 0.6035772310295223, "state_global_normalized": { "rho": "1.55950807222391641845848896590114155210205691915043897313666677222403895481670394359768998", "p": "0.101991967715448330096886340289376333933225694869409505461400107530520844212479068146623498", "u": [ "-0.641546204915183547889341275178569701115400361104100190443218985685531689228220539102309592", "-0.0221084048711579978885434230473623869238884183021337456340927269774765782359766195166900192", "-0E-91" ], "B": [ "0.0613859015753080366145491290343517354472223151378928335063153091533293797336310720544738851", "1.00318736180895709365740423028338587842367520782922276909590657655403946365979514301734400", "0E-91" ] }, "root_record": { "r": "1.55950807222391641845848896590114155210205691915043897313666677222403895481670394359768998", "b": "0.0405684104766565225646871877967560104310470498747663009292358636667236064629005959928902590", "h": "0.00220336755823905100956867896049537034537344760293562798482381549254428022824531618998460952", "A": "0.413504310308847114726416596498098695050239240909093317260748785610272943727707996561603858", "denominator": "0.996563830506849899672769381519671852728692387343898804591301078338609841693908594076806588", "polynomial_residual": "7.21263206096099694905697E-66", "bracket_initial_signs": [ "1.46645106130451266028286790181213115409168183434951382176773924248078887843448551436312816", "-2.00667907521865277853643194346741277212122397841475680841942233165815485748411715980989169" ], "bracket_derivative_max": "-5.54625347711846243609790259291356780703654204008546721886706617688231593396642554727168171", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.02823282296034790230025358322303592675805190421535804862222416415470761331725988510926039E-90", "-3E-91", "0E-182", "-8E-90", "0E-182", "-4.11682307924189287554341139243535580764123796167683048847839590058088641835945686742092567E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.825", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.022870932409165955, 0.0 ], "rh_scaled_inf": 1.7821158953893065e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7821158953893065e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.014266048389323053, "alfven_n": 0.03758414189591771, "fast": 0.8697901654979249 }, "right": { "slow": 0.01756051695652615, "alfven_n": 0.04693517620190412, "fast": 0.6949195085034169 } }, "front_relative_normal_velocity": { "left": -0.64116137292544, "right": -0.9998963366753925 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5595080722239165, "pressure_ratio": 2.514594864779298, "entropy_over_cv": 0.1814943143230353, "tangential_field_ratio": 1.5614372658290758 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.8, "theta_Bn_degrees": 85.80000000000001, "compression": 1.5595272888291405, "u2x_km_s": -384.9167377127054, "u2y_km_s": -13.232432819122218, "speed2_km_s": 385.14411880451223, "signed_deflection_degrees": 1.9689039831808586, "p2_over_p1": 2.5146910334911343, "B2_over_B1": 1.559007594338428, "entropy_over_cv": 0.18151202089808616, "upstream_fast_Mach": 1.438880823205164, "downstream_fast_Mach": 0.7371387944359903, "downstream_alfven_margin": 0.6033488782841472, "state_global_normalized": { "rho": "1.55952728882914040864062459706906263961287135371138266544666688521643406857848966584396262", "p": "0.101995868318400401977768722295816581107538212006788597803443926236140299542375735264793241", "u": [ "-0.641527896187842332606652779476179635635672448930957910734692155189707489337931091314800327", "-0.0220540546985370293945774970075544931499974135220248415983760342401227754285184691324883724", "-0E-91" ], "B": [ "0.0612286259015604780126777471902236963600205552318356055322484147016170610736562401161920086", "1.00320538469352615084591575728095644149111442989173984205897537785607969006806288354367905", "0E-91" ] }, "root_record": { "r": "1.55952728882914040864062459706906263961287135371138266544666688521643406857848966584396262", "b": "0.0405679084086664102494093964428058375490462565181075819482959129802015668588475011457405036", "h": "0.00222975918096850356323534443421603392385935882638775523972379066966360977594899485915386598", "A": "0.413472773956120881015886559427529231809287826099413975641655611969144525428077011744118266", "denominator": "0.996522629709762304986130837332321776204771778604319724855897653155621479946887435291353584", "polynomial_residual": "2.76334262781440699729154E-66", "bracket_initial_signs": [ "1.46648139747281720449259612200367978643842952523890584758989109727807785103457331690036138", "-2.00643423734797580779251903719114712745924127633249192529878411098425450481387753809472022" ], "bracket_derivative_max": "-5.54598436662509397319154401450158953476116247070883540916532884235371342060270118777352887", "iterations": 216 }, "flux_residuals": [ "-2E-90", "-8.02828463882710477599610703085133942334178337989915342894304802532150168947236574589433100E-90", "3E-91", "0E-182", "2E-90", "0E-182", "-1.57744927620765879409887716885222976356849197205119289068909067889318874363429782959759752E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.8", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.022485606738009412, 0.0 ], "rh_scaled_inf": 6.938893903907228e-18, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.014351388230019354, "alfven_n": 0.037808561647544876, "fast": 0.86979201850618 }, "right": { "slow": 0.017665549576136398, "alfven_n": 0.04721572308229916, "fast": 0.6949168464014843 } }, "front_relative_normal_velocity": { "left": -0.641157439931692, "right": -0.9999025240093042 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5595272888291405, "pressure_ratio": 2.5146910334911343, "entropy_over_cv": 0.18151202089808605, "tangential_field_ratio": 1.5614797618716427 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.775, "theta_Bn_degrees": 85.775, "compression": 1.559546236124672, "u2x_km_s": -384.90584745064143, "u2y_km_s": -13.199814393092089, "speed2_km_s": 385.1321156456684, "signed_deflection_degrees": 1.9641098955060259, "p2_over_p1": 2.514785998372862, "B2_over_B1": 1.5590203110382885, "entropy_over_cv": 0.18152953537070496, "upstream_fast_Mach": 1.4388949978936292, "downstream_fast_Mach": 0.7371327822355259, "downstream_alfven_margin": 0.6031205209654015, "state_global_normalized": { "rho": "1.55954623612467181525793137028702754818248402546389076734577446374701908153317658312350004", "p": "0.101999720094003281588666655793715843332010424586039506982518895215999078350418738845422759", "u": [ "-0.641509745751069004884131960219903409112836147574357567427417766284074721776643881574976332", "-0.0219996906551534834924033872909149493451069147762141632586781165870774876022629522377350037", "-0E-91" ], "B": [ "0.0610713334166534422987575028158760463824155592683742574139180161540264756073032260793055330", "1.00322318581704144424050510915763554729752482327412996736629207540332059198482415153335216", "0E-91" ] }, "root_record": { "r": "1.55954623612467181525793137028702754818248402546389076734577446374701908153317658312350004", "b": "0.0405674217968284012429806673720071431252629466890759036195069028898338134906642519421260081", "h": "0.00225630759721404567638985470966289383737054916458126508825953064673592891171428988790482305", "A": "0.413441239190279074649300897995624076561221026500349023485549390688378402679524648788727961", "denominator": "0.996481183979225333015129191490651485830693521766224180284362033468756278306711056105300821", "polynomial_residual": "-9.28982119607815400703854E-66", "bracket_initial_signs": [ "1.46651012734058347051620437737887822774041091964738308620820923115304170047201194787929339", "-2.00619077282775829204477902305563892882358963221514262463103905809654959649646760571272237" ], "bracket_derivative_max": "-5.54571527820444385968045303863955738425159801161844888570582512151793219038576638293131880", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.02833798385481858930691653153821327562508006373552204987652874794997371265416842800828121E-90", "3E-91", "0E-182", "4E-90", "0E-182", "5.30371590455875246426951122406041802475485139654704148210822531789569281701536001891404500E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.775", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.022100278578475213, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.014436726983526372, "alfven_n": 0.03803297472099111, "fast": 0.8697937619080597 }, "right": { "slow": 0.017770580042004335, "alfven_n": 0.047496260973487005, "fast": 0.6949141684693023 } }, "front_relative_normal_velocity": { "left": -0.6411534956863927, "right": -0.9999085209758897 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559546236124672, "pressure_ratio": 2.514785998372862, "entropy_over_cv": 0.18152953537070493, "tangential_field_ratio": 1.5615221291888812 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.75, "theta_Bn_degrees": 85.75000000000001, "compression": 1.5595649141071422, "u2x_km_s": -384.8950521679955, "u2y_km_s": -13.167187713899102, "speed2_km_s": 385.12020982505845, "signed_deflection_degrees": 1.9593137987732658, "p2_over_p1": 2.514879759235838, "B2_over_B1": 1.559032721378521, "entropy_over_cv": 0.1815468577133254, "upstream_fast_Mach": 1.4389089315213504, "downstream_fast_Mach": 0.7371268500094108, "downstream_alfven_margin": 0.6028921590568163, "state_global_normalized": { "rho": "1.55956491410714215724782186978618510408090391618555118328305933188408404104847193564871436", "p": "0.102003523034605590204842079122522888804016935871706544288215526566349366799918011001848245", "u": [ "-0.641491753613325860899453980392065034713585599750245120704990207855850766598513826163790206", "-0.0219453128564985016287825078528919550434600112429479403648455145874311018792700224874535243", "-0E-91" ], "B": [ "0.0609140243510303116147484459571759315543832942587981808242431386285127989201430002220085889", "1.00324076516759494850253732833716504323503991860225299174025673878436014411218955196741383", "0E-91" ] }, "root_record": { "r": "1.55956491410714215724782186978618510408090391618555118328305933188408404104847193564871436", "b": "0.0405669506404011330362645351940884162109788476440954419480125078865933318576090291853312811", "h": "0.00228301281143651003359347456172101107307713799276668334057152918563062888260866084799617042", "A": "0.413409705999264063276797874281877911341103134702961972224997472767890246360186292117507706", "denominator": "0.996439493320826514095356933276961025192016349452959940593533566004605754389451340639200628", "polynomial_residual": "-7.30904096366920362563941E-66", "bracket_initial_signs": [ "1.46653725108164729620154383984047502791312305885540835980075663431921455305603323525818047", "-2.00594868135790958233325362282929191796185082842571992734486709830733948985801621891877206" ], "bracket_derivative_max": "-5.54544621164349655887416253222913036058291504599288065300365825551780285795773561652309443", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-1E-91", "0E-182", "1E-90", "0E-182", "4.17335679016798401123351077741634444176675131507841659631174607730957318271360601173794188E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.75", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.02171494796840116, 0.0 ], "rh_scaled_inf": 2.1879152250198413e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7821784488164265e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1879152250198413e-16 }, "characteristics": { "left": { "slow": 0.014522064648381969, "alfven_n": 0.03825738113174492, "fast": 0.8697953957047905 }, "right": { "slow": 0.017875608341270575, "alfven_n": 0.04777678982205721, "fast": 0.6949114747079951 } }, "front_relative_normal_velocity": { "left": -0.6411495401885612, "right": -0.999914327574007 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5595649141071422, "pressure_ratio": 2.5148797592358383, "entropy_over_cv": 0.18154685771332546, "tangential_field_ratio": 1.5615643677894424 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.725, "theta_Bn_degrees": 85.725, "compression": 1.5595833227730291, "u2x_km_s": -384.88435186985276, "u2y_km_s": -13.13455285084301, "speed2_km_s": 385.1084013532661, "signed_deflection_degrees": 1.954515706677915, "p2_over_p1": 2.5149723158928454, "B2_over_B1": 1.5590448253638207, "entropy_over_cv": 0.18156398789857772, "upstream_fast_Mach": 1.4389226240825432, "downstream_fast_Mach": 0.7371209977528524, "downstream_alfven_margin": 0.6026637925419973, "state_global_normalized": { "rho": "1.55958332277302911123355322718920168785601294992008108195428382957082703016497342031792291", "p": "0.102007277132613818845781237128545861166843500524140425534384642246241083158358042476734858", "u": [ "-0.641473919783088029212711852791065889198528578659973229679188047710227826141149171988987132", "-0.0218909214180716835041416808741943467765036037157709680544724576471125632429320796645128159", "-0E-91" ], "B": [ "0.0607566989351409587779682672077911535627458419757621315349207015393976667741694707181521403", "1.00325812273339640506491278759182927565432638934399918615453703592933617666986991197594848", "0E-91" ] }, "root_record": { "r": "1.55958332277302911123355322718920168785601294992008108195428382957082703016497342031792291", "b": "0.0405664949386668024451896840090924694392478105931178159240730630435854525366683146748975383", "h": "0.00230987482833574330438995266886793332092863067082224588384498756398008646329267828476580833", "A": "0.413378174371020614811710048768446890926848964618856381958919927552018829885743892099722734", "denominator": "0.996397557740034361240391124456586498958683420668472493897003515735419060017181816888832190", "polynomial_residual": "-6.48862600687389737052485E-66", "bracket_initial_signs": [ "1.46656276886910767662976998681048246511679092206578045857225841181315297667578768953851956", "-2.00570796263755135792507047586985376853128351055610952941997552846963079259089980031627012" ], "bracket_derivative_max": "-5.54517716672724165661233770831762551428095516470919739742006408166852476317335628466534366", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.02844926159775337231638839657007555447708636777685717831910211454663045778920125456384182E-90", "-1E-91", "0E-182", "0E-90", "0E-182", "3.70535714162167399902839509732012172884977226822154566009985000330184584057765707288732825E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.725", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.02132961494562789, 0.0 ], "rh_scaled_inf": 2.1879411061349064e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1879411061349064e-16 }, "characteristics": { "left": { "slow": 0.014607401223120205, "alfven_n": 0.03848178089529463, "fast": 0.8697969198976206 }, "right": { "slow": 0.017980634461075007, "alfven_n": 0.04805730957460102, "fast": 0.6949087651186939 } }, "front_relative_normal_velocity": { "left": -0.641145573437292, "right": -0.9999199438025509 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5595833227730291, "pressure_ratio": 2.5149723158928454, "entropy_over_cv": 0.18156398789857753, "tangential_field_ratio": 1.5616064776817005 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.7, "theta_Bn_degrees": 85.7, "compression": 1.5596014621186565, "u2x_km_s": -384.8737465613061, "u2y_km_s": -13.101909873228603, "speed2_km_s": 385.09669024085713, "signed_deflection_degrees": 1.9497156329211778, "p2_over_p1": 2.515063668158095, "B2_over_B1": 1.5590566229988887, "entropy_over_cv": 0.18158092589928868, "upstream_fast_Mach": 1.4389360755714293, "downstream_fast_Mach": 0.7371152254611864, "downstream_alfven_margin": 0.6024354214046256, "state_global_normalized": { "rho": "1.55960146211865648996419867093926231779064152678651300579594209173403015628506967650783690", "p": "0.102010982380492342061390205352928820173037581469946300883378910860159688858870216849144586", "u": [ "-0.641456244268843457894896488010996676414250768195129384522845527988005138879054573015705001", "-0.0218365164553810034778577412682405276966416041355510224335542071856362322245034907395553786", "-0E-91" ], "B": [ "0.0605993573994417675604485542772148179224900405703016126630348829896020816949603606282715986", "1.00327525850277331623385277056794135018126974127424958102882633891331719624882566304023098", "0E-91" ] }, "root_record": { "r": "1.55960146211865648996419867093926231779064152678651300579594209173403015628506967650783690", "b": "0.0405660546909311632866999791639182993205928513086115156094364550335529140016447860544731114", "h": "0.00233689365285060080012583708430127002497818603312534410164475146350518155727690658022950947", "A": "0.413346644293495878959022012637696792304236927980154755682722533010845296034614894270735009", "denominator": "0.996355377242198394926278507812661452284989096747909158467024811325085353246446812621547570", "polynomial_residual": "-7.60115674348233489340988E-66", "bracket_initial_signs": [ "1.46658668087532712272423557384065199349833185458685862256353201885366248942139082478026797", "-2.00546861636501726923206478599855197053369274317536787197362493548055767680614223678690061" ], "bracket_derivative_max": "-5.54490814323867369213211058481311228207710138940823802873218108321287227718588085771155385", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "1E-91", "0E-182", "2E-90", "0E-182", "4.34119427152517887462789126171461467033328526777512598569152751535615435097176163582764749E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.7", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.020944279547998768, 0.0 ], "rh_scaled_inf": 2.1879681079230528e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1879681079230528e-16 }, "characteristics": { "left": { "slow": 0.01469273670627146, "alfven_n": 0.03870617402712859, "fast": 0.8697983344878206 }, "right": { "slow": 0.018085658388556816, "alfven_n": 0.04833782017771145, "fast": 0.6949060397025367 } }, "front_relative_normal_velocity": { "left": -0.6411415954317542, "right": -0.999925369660452 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5596014621186565, "pressure_ratio": 2.5150636681580956, "entropy_over_cv": 0.18158092589928876, "tangential_field_ratio": 1.561648458873752 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.675, "theta_Bn_degrees": 85.675, "compression": 1.5596193321401943, "u2x_km_s": -384.86323624745575, "u2y_km_s": -13.069258850365637, "speed2_km_s": 385.08507649837946, "signed_deflection_degrees": 1.9449135912100868, "p2_over_p1": 2.5151538158472246, "B2_over_B1": 1.5590681142884328, "entropy_over_cv": 0.18159767168848154, "upstream_fast_Mach": 1.4389492859822348, "downstream_fast_Mach": 0.7371095331298758, "downstream_alfven_margin": 0.6022070456284568, "state_global_normalized": { "rho": "1.55961933214019422089287757718732493581929876846249880886190795141360934763985416071739992", "p": "0.102014638770763431676524103842942447267038227966267878879513036130577871553078731008019561", "u": [ "-0.641438727079092902142728994084340644606513957509301953406182358655007973841364993966565829", "-0.0217820980839427269500705897823874938699993746645223233951950356383677127258126873400625740", "-0E-91" ], "B": [ "0.0604419999743956529863581851270779356289850825256943405169005921995994439083090804533974396", "1.00329217246417093910049347766156782460573589935730022922002959115416622361422876537684570", "0E-91" ] }, "root_record": { "r": "1.55961933214019422089287757718732493581929876846249880886190795141360934763985416071739992", "b": "0.0405656298965235241310277099730016503579987991992579222351087061326784238493738841175482576", "h": "0.00236406929015894190514508485353508667183838537583353548418577497441348710226706499490904839", "A": "0.413315115754639368751543743286905195250920234054840996854370445960839682337764715778028268", "denominator": "0.996312951832549167999800204401129086007229042282072031925503031650158872701142990334446572", "polynomial_residual": "2.79360509545647533854465E-66", "bracket_initial_signs": [ "1.46660898727193202423767366503046146442611109555653648386387634443506739917350158608944363", "-2.00523064223785256785574636352067182292712556339491309267106329439093842655781748273320653" ], "bracket_derivative_max": "-5.54463914095879197528714145989387990108041239035721654332816959397979462959210547308943146", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-2E-91", "0E-182", "-5E-90", "0E-182", "-1.59568344611962102089400732447894583483083603600699201834465404034710332341615337255621397E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.675", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.020558941813359766, 0.0 ], "rh_scaled_inf": 1.7822479223992643e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7822479223992643e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.014778071096362424, "alfven_n": 0.03893056054273517, "fast": 0.8697996394766828 }, "right": { "slow": 0.018190680110854486, "alfven_n": 0.048618321577983244, "fast": 0.6949032984606676 } }, "front_relative_normal_velocity": { "left": -0.641137606171192, "right": -0.9999306051466773 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5596193321401943, "pressure_ratio": 2.5151538158472246, "entropy_over_cv": 0.1815976716884814, "tangential_field_ratio": 1.5616903113734186 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.65, "theta_Bn_degrees": 85.65, "compression": 1.5596369328336583, "u2x_km_s": -384.85282093341, "u2y_km_s": -13.036599851568797, "speed2_km_s": 385.0735601363631, "signed_deflection_degrees": 1.9401095952574599, "p2_over_p1": 2.5152427587772994, "B2_over_B1": 1.5590792992371658, "entropy_over_cv": 0.18161422523937604, "upstream_fast_Mach": 1.4389622553091908, "downstream_fast_Mach": 0.737103920754512, "downstream_alfven_margin": 0.6019786651973211, "state_global_normalized": { "rho": "1.55963693283365832489321170386384011999889601100727923789549399406612079489193442319242169", "p": "0.102018246296007270493874943761095962411086274905495224954065462405027930494015101935042207", "u": [ "-0.641421368222349912379878815356498125553816711939404629419888465391649572674599011960220467", "-0.0217276664192813267198433396344323183350999939397744736240510443939810273965507121419063455", "-0E-91" ], "B": [ "0.0602846268904720816482720309236702496396667274671946016324820747766224478319540876754217150", "1.00330886460615227926222221770160802217156170196228819046987865695388974397870624984613463", "0E-91" ] }, "root_record": { "r": "1.55963693283365832489321170386384011999889601100727923789549399406612079489193442319242169", "b": "0.0405652205547967461302775524294277625507147945660861738588082167539939844372780840501920312", "h": "0.00239140174567762628229019482202043146576424681461538222831281235395066676859872603199243915", "A": "0.413283588742402942093739358031192820753881991562791001312782887375439393779484012555596936", "denominator": "0.996270281516198290710598042415429699298906442128273641177375978499217142899683345660932198", "polynomial_residual": "1.81447139348272097282697E-66", "bracket_initial_signs": [ "1.46662968822981301711791196245017574552193046308547930309435383399853971978301378693709536", "-2.00499403995281372376150994947655922871143943164205140569705727341415567301763470287109730" ], "bracket_derivative_max": "-5.54437015966660039012039609903526885481568753052089706332327904652124720216327188759614953", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.02862764823655727495994209393778569191602961306867035025786478364900063639748612319020388E-90", "-2E-91", "0E-182", "-4E-90", "0E-182", "-1.03653514953728314085274223113245942814426650312745401628907761617550199235672759548917367E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.65", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.020173601779559347, 0.0 ], "rh_scaled_inf": 2.1880254737204371e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7822726182666764e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1880254737204371e-16 }, "characteristics": { "left": { "slow": 0.014863404391916215, "alfven_n": 0.03915494045760296, "fast": 0.869800834865522 }, "right": { "slow": 0.018295699615105774, "alfven_n": 0.048898813722012886, "fast": 0.6949005413942378 } }, "front_relative_normal_velocity": { "left": -0.6411336056549242, "right": -0.9999356502602301 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5596369328336583, "pressure_ratio": 2.5152427587772994, "entropy_over_cv": 0.18161422523937587, "tangential_field_ratio": 1.5617320351882436 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.625, "theta_Bn_degrees": 85.625, "compression": 1.559654264194911, "u2x_km_s": -384.84250062428447, "u2y_km_s": -13.00393294615764, "speed2_km_s": 385.06214116531964, "signed_deflection_degrees": 1.9353036587818615, "p2_over_p1": 2.515330496766814, "B2_over_B1": 1.5590901778498076, "entropy_over_cv": 0.1816305865253882, "upstream_fast_Mach": 1.4389749835465337, "downstream_fast_Mach": 0.737098388330814, "downstream_alfven_margin": 0.6017502800951235, "state_global_normalized": { "rho": "1.55965426419491089511397747745805984498597492087587615660869094182887261230461726485759854", "p": "0.102021804948861965955242885001044982919390889081308890948818353241162640332836832935783878", "u": [ "-0.641404167707140822844604229276938616706592346781818680837888202199730308837929303549691060", "-0.0216732215769293993194880403860336272971324435114240264072009343920641150641024853594310495", "-0E-91" ], "B": [ "0.0601272383781470920430634129683935912095038976037279831631885172675925992903252255728296995", "1.00332533491739808435368914635147708155634053135044587262318698133870385149598863358853401", "0E-91" ] }, "root_record": { "r": "1.55965426419491089511397747745805984498597492087587615660869094182887261230461726485759854", "b": "0.0405648266651272409233091853454874284893489108183815330111011596095917062418436067531797041", "h": "0.00241889102506251085264639909794348600309575438600206141137244163693047213650041291582545958", "A": "0.413252063244740783313151083534501912375509042712373023939934106428865004422847182913202720", "denominator": "0.996227366298138455867245667444127600055292176914518249660479699993178441552286977524642906", "polynomial_residual": "-1.99859377988599637842643E-66", "bracket_initial_signs": [ "1.46664878391912535525242514309524563379242384890912631500797866834387559626711144185494362", "-2.00475880920586802958386277234251088129298761771314821487123568770384779610176289802676750" ], "bracket_derivative_max": "-5.54410119913910718479251585508954783698689934294878671912296631687951282887319046677925905", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.02869016934770214978206243608482270713715472829022003011947577748807988664583931331114292E-90", "4E-91", "0E-182", "6E-90", "0E-182", "1.14185409295353768572867734625613551478671219630759733539277688729619896580129145651999095E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.625", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.019788259484448345, 0.0 ], "rh_scaled_inf": 4.3761116756716777e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.782298083211322e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 4.3761116756716777e-16 }, "characteristics": { "left": { "slow": 0.014948736591452422, "alfven_n": 0.0393793137872208, "fast": 0.8698019206556745 }, "right": { "slow": 0.01840071688844772, "alfven_n": 0.04917929655639864, "fast": 0.6948977685044054 } }, "front_relative_normal_velocity": { "left": -0.6411295938823444, "right": -0.9999405050001497 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559654264194911, "pressure_ratio": 2.515330496766814, "entropy_over_cv": 0.1816305865253881, "tangential_field_ratio": 1.561773630325494 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.6, "theta_Bn_degrees": 85.60000000000001, "compression": 1.55967132621966, "u2x_km_s": -384.83227532520283, "u2y_km_s": -12.971258203456548, "speed2_km_s": 385.050819595743, "signed_deflection_degrees": 1.9304957955075603, "p2_over_p1": 2.5154170296356893, "B2_over_B1": 1.5591007501310838, "entropy_over_cv": 0.18164675552013032, "upstream_fast_Mach": 1.4389874706885055, "downstream_fast_Mach": 0.7370929358546288, "downstream_alfven_margin": 0.6015218903058432, "state_global_normalized": { "rho": "1.55967132621966007597192639040127974161866543030945627346418753247815249170022097520496045", "p": "0.102025314722023563761215518112753644948293475632388914065912868976670222444293246504999098", "u": [ "-0.641387125542004740663854651553829861658373142131963234114418513908209996056852538333137433", "-0.0216187636724275813248752980493268434266945541987248985832992953630817211474061808850258613", "-0E-91" ], "B": [ "0.0599698346679033149281990340308147834760136414459850331678023346687090367389528077216309312", "1.00334158338670683738742751214603817292459533285009391047493043240650074880722043675988813", "0E-91" ] }, "root_record": { "r": "1.55967132621966007597192639040127974161866543030945627346418753247815249170022097520496045", "b": "0.0405644482269149686169069176719404699660015632180594566363684430429444407781160528728760494", "h": "0.00244653713420844754946975434444088238354887073731615258557941004635150841133029349762019483", "A": "0.413220539249609384719358300739731009888138373901196633582578682720961201890968445595388130", "denominator": "0.996184206183243464117348690984527628071372711358145310631909699419353954519906314016498457", "polynomial_residual": "1.561262341855385693231906E-65", "bracket_initial_signs": [ "1.46666627450928928659209736476972973963953039692016084541061783312825383535382215113265084", "-2.00452494969219319206431939926091411418797564130803675157559103711804655119556433760547532" ], "bracket_derivative_max": "-5.54383225915132474786754650998690698704924971695016887599279712507313738762108553283829275", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.02875422000596825494140339258039080695421068854108268919045472168244135333748875383353095E-90", "-5E-91", "0E-182", "-7E-90", "0E-182", "-8.92101212717556835745958535144206869026614312137364537921086925358388536772258553320874925E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.6", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.01940291496587984, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.015034067693487158, "alfven_n": 0.03960368054707791, "fast": 0.8698028968484992 }, "right": { "slow": 0.018505731918016636, "alfven_n": 0.04945977002774052, "fast": 0.6948949797923348 } }, "front_relative_normal_velocity": { "left": -0.6411255708529211, "right": -0.9999451693655121 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.55967132621966, "pressure_ratio": 2.5154170296356893, "entropy_over_cv": 0.18164675552013032, "tangential_field_ratio": 1.5618150967921602 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.575, "theta_Bn_degrees": 85.575, "compression": 1.5596881189034602, "u2x_km_s": -384.8221450412961, "u2y_km_s": -12.938575692794679, "speed2_km_s": 385.03959543810885, "signed_deflection_degrees": 1.9256860191644873, "p2_over_p1": 2.5155023572052775, "B2_over_B1": 1.559111016085726, "entropy_over_cv": 0.18166273219741103, "upstream_fast_Mach": 1.438999716729353, "downstream_fast_Mach": 0.737087563321931, "downstream_alfven_margin": 0.601293495813534, "state_global_normalized": { "rho": "1.55968811890346004228274775591344754484796110571552479888161732301950326385589692164121915", "p": "0.102028775608246061449279618989743998310744632106825247367926491170097795106834890103423290", "u": [ "-0.641370241735493535413877132559806947401306368369072044384632804279000578168858334963356497", "-0.0215642928213244656415459422495788459838792626416542603027293725828108053296571767746319835", "-0E-91" ], "B": [ "0.0598124159902299936992153861243660725491723007010286205324703116573360497638838118434280091", "1.00335761000299474990401497062984324423002177658855609123813805025956998499258350314559986", "0E-91" ] }, "root_record": { "r": "1.55968811890346004228274775591344754484796110571552479888161732301950326385589692164121915", "b": "0.0405640852395834358432251089566454197310914236622171177143675539720010455474108390282653169", "h": "0.00247434007924928184624427910864138773720895461435795871675728229703761137143409081968291245", "A": "0.413189016744967528170411566963334500100852953199251275484780198760135063328436245066575974", "denominator": "0.996140801176268249351759241338724266079594425161493696341088550963172461495509957726179638", "polynomial_residual": "-7.44919757335622178838923E-66", "bracket_initial_signs": [ "1.46668216016899043365463254160970126066094285529774753663874666638381958037146784090816221", "-2.00429246110617691062349010312207158595562082038723845363089123442729429302668582904904558" ], "bracket_derivative_max": "-5.54356333947626937095768023324964643019071770187355295531540497489108499794880916040680268", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-2E-91", "0E-182", "-2E-90", "0E-182", "4.25696316799443083922833480111590953554192153075227572409976951309823491421904840540819167E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.575", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.019017568261709063, 0.0 ], "rh_scaled_inf": 2.1881199287811805e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 1.782351320519754e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1881199287811805e-16 }, "characteristics": { "left": { "slow": 0.015119397696533138, "alfven_n": 0.03982804075266401, "fast": 0.8698037634453765 }, "right": { "slow": 0.018610744690948106, "alfven_n": 0.04974023408264035, "fast": 0.6948921752591976 } }, "front_relative_normal_velocity": { "left": -0.641121536566198, "right": -0.9999496433554291 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5596881189034602, "pressure_ratio": 2.515502357205278, "entropy_over_cv": 0.18166273219741103, "tangential_field_ratio": 1.5618564345949548 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.55, "theta_Bn_degrees": 85.55000000000001, "compression": 1.559704642241711, "u2x_km_s": -384.81210977770314, "u2y_km_s": -12.90588548350591, "speed2_km_s": 385.0284687028745, "signed_deflection_degrees": 1.9208743434881959, "p2_over_p1": 2.5155864792983587, "B2_over_B1": 1.5591209757184714, "entropy_over_cv": 0.18167851653123498, "upstream_fast_Mach": 1.4390117216633276, "downstream_fast_Mach": 0.7370822707288236, "downstream_alfven_margin": 0.6010650966023237, "state_global_normalized": { "rho": "1.55970464224171097853015025673909342900728726732313114850626059120341041011165312869119050", "p": "0.102032187600341421930389659976405724110338226409194594355613471774549449331463428024055486", "u": [ "-0.641353516296171829167372361028945394778048977876869869673360966329862588084201664994436107", "-0.0215098091391765177664427196226568942185719694498948288879008560670580048368732737452694469", "-0E-91" ], "B": [ "0.0596549825756230047891559237359372333548635650770220204338056651513587811058200337038128383", "1.00337341475529575493170812614892007401719954874127200901581582319920957585623259438362633", "0E-91" ] }, "root_record": { "r": "1.55970464224171097853015025673909342900728726732313114850626059120341041011165312869119050", "b": "0.0405637377025796938934985890193557260340210653482485439218230361565761901658563095006515465", "h": "0.00250229986655785205881758778878285091255334245136914084517912520127301137587335316791918739", "A": "0.413157495718776266646681558377157910205039663655338089700728287905019516948503342625779167", "denominator": "0.996097151281848904232991388463182914737098063925680285434425924677258976257314343855421706", "polynomial_residual": "4.41632705825275773833370E-66", "bracket_initial_signs": [ "1.46669644106618017840811541661150666650934666433093224193557959744023334380834919486079127", "-2.00406134314141644306876517210607729484881853583149342929747507076686401403154696184828897" ], "bracket_derivative_max": "-5.54329443988496099772855369749992157192397467775867581629038856082007984700172498009120284", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.02888691020930675294177164070502660649190485772089811442198817713714428681324303980539670E-90", "-1E-91", "0E-182", "-4E-90", "0E-182", "-2.52408381815606384596951544846885255077012865102079688336015176016354369780263018341518020E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.55", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.018632219409793253, 0.0 ], "rh_scaled_inf": 2.1881536557298569e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1881536557298569e-16 }, "characteristics": { "left": { "slow": 0.015204726599099732, "alfven_n": 0.04005239441946938, "fast": 0.8698045204477092 }, "right": { "slow": 0.01871575519437698, "alfven_n": 0.05002068866770172, "fast": 0.6948893549061714 } }, "front_relative_normal_velocity": { "left": -0.6411174910217929, "right": -0.999953926969049 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559704642241711, "pressure_ratio": 2.5155864792983587, "entropy_over_cv": 0.181678516531235, "tangential_field_ratio": 1.561897643740315 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.525, "theta_Bn_degrees": 85.52499999999999, "compression": 1.5597208962296591, "u2x_km_s": -384.8021695395702, "u2y_km_s": -12.873187644928795, "speed2_km_s": 385.0174394004792, "signed_deflection_degrees": 1.9160607822198217, "p2_over_p1": 2.515669395739142, "B2_over_B1": 1.5591306290340643, "entropy_over_cv": 0.18169410849580303, "upstream_fast_Mach": 1.439023485484687, "downstream_fast_Mach": 0.7370770580715368, "downstream_alfven_margin": 0.6008366926564144, "state_global_normalized": { "rho": "1.55972089622965905827304091438207249293716316630110628747262953985182265825523663494087169", "p": "0.102035550691179586984017196311117892729299190846396994542431769415407789432744000848830604", "u": [ "-0.641336949232616987027248424981822001308143922272743088338458489509952180465734895304192493", "-0.0214553127415479920250798175087219317308432802222045288313143608445030154185145285527606003", "-0E-91" ], "B": [ "0.0594975346545848780907485838510692684647884047444188906988236152614158852811948235216038922", "1.00338899763276149975548205946402560652817495888716151533076931995471052381257717398489327", "0E-91" ] }, "root_record": { "r": "1.55972089622965905827304091438207249293716316630110628747262953985182265825523663494087169", "b": "0.0405634056153743369280077069439752030727664882195562133934972290890877464043375480208751518", "h": "0.00253041650274598942156877563174059578537784214813811706346473741512284209587411541168181623", "A": "0.413125976158998905832062917321359119661062887841794670121568455215126087901545248812845374", "denominator": "0.996053256504502705847925021966525891005384780242301002122032454667049660863975688197037547", "polynomial_residual": "-5.24782524184846012159241E-66", "bracket_initial_signs": [ "1.46670911736807605153529187342269048425017530775078275218274975375754722682780169990903099", "-2.00383159549071815843887383828250104756178185528216457992888238998597819998311677112424270" ], "bracket_derivative_max": "-5.54302556014642295926653407336734004908505404281200532129445665416812775315849282328947704", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.02895554988074527279497376518374313393668423997318609829649318610013135646063196787982161E-90", "-4E-91", "0E-182", "-7E-90", "0E-182", "2.99967389656439200382323066122869343751268287585663971133665607775640350508950400310700903E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.525", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.01824686844799154, 0.0 ], "rh_scaled_inf": 1.7824076347135017e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7824076347135017e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.015290054399693026, "alfven_n": 0.04027674156298499, "fast": 0.869805167856922 }, "right": { "slow": 0.018820763415437376, "alfven_n": 0.050301133729530045, "fast": 0.6948865187344413 } }, "front_relative_normal_velocity": { "left": -0.6411134342193994, "right": -0.9999580202055561 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5597208962296591, "pressure_ratio": 2.515669395739142, "entropy_over_cv": 0.18169410849580303, "tangential_field_ratio": 1.5619387242343994 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.5, "theta_Bn_degrees": 85.5, "compression": 1.5597368808623964, "u2x_km_s": -384.79232433205146, "u2y_km_s": -12.84048224640651, "speed2_km_s": 385.00650754134404, "signed_deflection_degrees": 1.9112453491060388, "p2_over_p1": 2.5157511063532665, "B2_over_B1": 1.5591399760372542, "entropy_over_cv": 0.181709508065512, "upstream_fast_Mach": 1.4390350081876933, "downstream_fast_Mach": 0.7370719253464291, "downstream_alfven_margin": 0.6006082839600824, "state_global_normalized": { "rho": "1.55973688086239642369078229626274200834458678507930895287339812711437156146165443114003486", "p": "0.102038864873688490711705082129224066850717800749651335003054186209812593413992998066589439", "u": [ "-0.641320540553419108147023514489632143920825677223702875343806151925715091608301234971558198", "-0.0214008037440108477839678434101834945645257083239848676024110093211967275207947101653849740", "-0E-91" ], "B": [ "0.0593400724576248174021035318097269053193336558988531126353227996897788698471202866026157844", "1.00340435862466133849540619749120313262799320353350515543914526695423917469938395018470364", "0E-91" ] }, "root_record": { "r": "1.55973688086239642369078229626274200834458678507930895287339812711437156146165443114003486", "b": "0.0405630889774615002622880634260116429493427951505722161092245104062152679812048037829209587", "h": "0.00255868999466451893756661237820746615422305657334739170617308687037233148094815641929376125", "A": "0.413094458053600985702473029777311709481633664078610618637752065275118603632879566096745410", "denominator": "0.996009116848628141484886869250333240419355788050081624808257728466749002422923582935547764", "polynomial_residual": "7.12065126733689666736762E-66", "bracket_initial_signs": [ "1.46672018924116212607920233368346197297994641453389179311518014144907161448827258826281988", "-2.00360321784609707698647279521998892575264170848546634749059117904649019338324060726847099" ], "bracket_derivative_max": "-5.54275670002768169580931334454037530726402898420931370671307375565056079927794756070007431", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "2E-91", "0E-182", "3E-90", "0E-182", "-4.07067586774297828826440000968068984211212446486580275403946328937187109299379184806298441E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.5", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.017861515414164857, 0.0 ], "rh_scaled_inf": 2.188224472891782e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.782436945770066e-16, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.188224472891782e-16 }, "characteristics": { "left": { "slow": 0.015375381096815901, "alfven_n": 0.04050108219870262, "fast": 0.8698057056744617 }, "right": { "slow": 0.01892576934126266, "alfven_n": 0.05058156921473254, "fast": 0.6948836667451986 } }, "front_relative_normal_velocity": { "left": -0.641109366158785, "right": -0.9999619230641713 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5597368808623964, "pressure_ratio": 2.5157511063532665, "entropy_over_cv": 0.181709508065512, "tangential_field_ratio": 1.5619796760830897 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.475, "theta_Bn_degrees": 85.475, "compression": 1.559752596134861, "u2x_km_s": -384.7825741603086, "u2y_km_s": -12.8077693572868, "speed2_km_s": 384.9956731358716, "signed_deflection_degrees": 1.9064280578990194, "p2_over_p1": 2.5158316109678025, "B2_over_B1": 1.5591490167327966, "entropy_over_cv": 0.18172471521495476, "upstream_fast_Mach": 1.4390462897666136, "downstream_fast_Mach": 0.7370668725499865, "downstream_alfven_margin": 0.6003798704976777, "state_global_normalized": { "rho": "1.55975259613486116526651096967952190024492844814816646930799677302766459718710550193426599", "p": "0.102042130140854072949150305606573837568628073543297066978987683005261995538194380999282720", "u": [ "-0.641304290267181017237931686372544161733741596640080575852358387291070149828280446500645772", "-0.0213462822621446656381117036097950914878430082734922901120677449528771557666756525203609987", "-0E-91" ], "B": [ "0.0591825962152587208967113150873053930642156767820443398226186108395956200180596202869041305", "1.00341949772038232449428747912835758270910206698417518880131427761858224343288802596794813", "0E-91" ] }, "root_record": { "r": "1.55975259613486116526651096967952190024492844814816646930799677302766459718710550193426599", "b": "0.0405627877883588587295754043649693374268406572624970993444517601500709659253540072921899678", "h": "0.00258712034940326100268040486804762820544565353765652319804553813558358155361501430379119552", "A": "0.413062941390550262121585798878746865152484608252800868965333867427104995256885008982220806", "denominator": "0.995964732318504934535198448762114040334163652688665526733978106305405908877349390054614514", "polynomial_residual": "-1.149459188664518142394938E-65", "bracket_initial_signs": [ "1.46672965685118941547086748027150037616524908437458703707311735742169534318352816958383732", "-2.00337620989877639729979560993958152073738038334267584986364107042247333710444968702123483" ], "bracket_derivative_max": "-5.54248785929376646484102013702974966616370108920451062039201715027682767636472033430123348", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "-3E-91", "0E-182", "-1E-90", "0E-182", "6.57192318862644685377640314862970247539215641642512033077211152652941615804580889377283433E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.475", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.01747616034617578, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.015460706688968073, "alfven_n": 0.04072541634211492, "fast": 0.8698061339017974 }, "right": { "slow": 0.019030772958985465, "alfven_n": 0.05086199506991825, "fast": 0.6948807989396416 } }, "front_relative_normal_velocity": { "left": -0.6411052868397926, "right": -0.9999656355441514 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559752596134861, "pressure_ratio": 2.5158316109678025, "entropy_over_cv": 0.1817247152149547, "tangential_field_ratio": 1.562020499291992 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.45, "theta_Bn_degrees": 85.45, "compression": 1.5597680420418374, "u2x_km_s": -384.77291902951094, "u2y_km_s": -12.77504904692194, "speed2_km_s": 384.9849361944462, "signed_deflection_degrees": 1.9016089223563941, "p2_over_p1": 2.5159109094112497, "B2_over_B1": 1.5591577511254537, "entropy_over_cv": 0.18173972991892, "upstream_fast_Mach": 1.4390573302157208, "downstream_fast_Mach": 0.7370618996788232, "downstream_alfven_margin": 0.6001514522536244, "state_global_normalized": { "rho": "1.55976804204183730160850240357291152182397786888543731631302393829983705980002657164622460", "p": "0.102045346485720292636839068227268103310375150991776879730312873379817731719714464205765831", "u": [ "-0.641288198382518256562788747254688119910201457700824803881175025004317126190985094377272637", "-0.0212917484115365635733986387909847042827426221472273930297576060054896928099233091683895267", "-0E-91" ], "B": [ "0.0590251061580092016185219155253035470785193417945022967541816623027390436738238125742827452", "1.00343441490942920251451136828711470361154614613175819670866005933220340231344104596931188", "0E-91" ] }, "root_record": { "r": "1.55976804204183730160850240357291152182397786888543731631302393829983705980002657164622460", "b": "0.0405625020476076251194765773625795671013792652055549153097770709850701435443703830712824436", "h": "0.00261570757429103380361019112055962327501016381575855572260528455576015034123443937948861029", "A": "0.413031426157816688443740520553409048537454893840196778759830648780168139236239890966638052", "denominator": "0.995920102918294070519281861475796151909616775809661476700731379614661014902586361431816994", "polynomial_residual": "-9.91116347307504958230393E-66", "bracket_initial_signs": [ "1.46673752036317627593979093180010734914486817141416009806155874144928543726779979860520960", "-2.00315057133918701056427071061784125203455102288958432512143018486831381580322022417522040" ], "bracket_derivative_max": "-5.54221903770770903555294704389810923042829480797928093203161095877238987918093470500819065", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "2E-91", "0E-182", "4E-90", "0E-182", "5.66729303962690135706208721937443051985627452108353539033237584301103869672391618232818063E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.45", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.017090803281888445, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.015546031174646159, "alfven_n": 0.04094974400871552, "fast": 0.8698064525404199 }, "right": { "slow": 0.01913577425573766, "alfven_n": 0.05114241124169805, "fast": 0.6948779153189749 } }, "front_relative_normal_velocity": { "left": -0.64110119626234, "right": -0.9999691576447897 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5597680420418374, "pressure_ratio": 2.5159109094112497, "entropy_over_cv": 0.18173972991891985, "tangential_field_ratio": 1.562061193866433 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.425, "theta_Bn_degrees": 85.42500000000001, "compression": 1.5597832185779548, "u2x_km_s": -384.7633589448355, "u2y_km_s": -12.742321384668667, "speed2_km_s": 384.9742967274341, "signed_deflection_degrees": 1.8967879562412082, "p2_over_p1": 2.515989001513539, "B2_over_B1": 1.559166179219993, "entropy_over_cv": 0.18175455215239236, "upstream_fast_Mach": 1.4390681295292922, "downstream_fast_Mach": 0.7370570067296808, "downstream_alfven_margin": 0.5999230292124204, "state_global_normalized": { "rho": "1.55978321857795475940956971187757389963385230840017872507434996217321505224378982775802672", "p": "0.102048513901389141149257568606291245992511566353529977314680448263985738205707693246443381", "u": [ "-0.641272264908059078416678248601292062104165403898991157864610481647647075038707500639779050", "-0.0212372023077811131036934854642013857744800812598550540330025148908363333787296560685560478", "-0E-91" ], "B": [ "0.0588676025164056080028855043397344510073136564513016581235331530963053122097897234913786876", "1.00344911018142440074401086191016368566999119978493536503260539419540607675585014011739889", "0E-91" ] }, "root_record": { "r": "1.55978321857795475940956971187757389963385230840017872507434996217321505224378982775802672", "b": "0.0405622317547725486928578764816827644711590648053755605564398625137057034873841583435459228", "h": "0.00264445167689565648980723015007553729524679235726546812497053789115254999739212733852027545", "A": "0.412999912343372397123966007266519631018073881321129888504440213941632275051986956017636426", "denominator": "0.995875228652037823237415432030754910660524278143482046124194205935618058741224699178978766", "polynomial_residual": "-2.06222284535283119617632E-66", "bracket_initial_signs": [ "1.46674377994140881330810887054635095383128867132905044992992019150755730448284355973744341", "-2.00292630185696700196489204687286792953392661643611669747121804066543968714523048553100260" ], "bracket_derivative_max": "-5.54195023503054336967088024663459742528883228277274854744753957636722260457508583182790405", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-1E-91", "0E-182", "-6E-90", "0E-182", "1.17933916636997860531083324772744344044150835162734384081103013144434776424466263036630325E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.425", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.01670544425916841, 0.0 ], "rh_scaled_inf": 0.0, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.015631354552343758, "alfven_n": 0.04117406521399916, "fast": 0.8698066615918421 }, "right": { "slow": 0.019240773218650368, "alfven_n": 0.051422817676684655, "fast": 0.6948750158844103 } }, "front_relative_normal_velocity": { "left": -0.6410970944264195, "right": -0.9999724893654156 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5597832185779548, "pressure_ratio": 2.515989001513539, "entropy_over_cv": 0.18175455215239233, "tangential_field_ratio": 1.5621017598114642 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.4, "theta_Bn_degrees": 85.4, "compression": 1.5597981257376894, "u2x_km_s": -384.75389391146666, "u2y_km_s": -12.709586439888154, "speed2_km_s": 384.96375474518265, "signed_deflection_degrees": 1.8919651733218819, "p2_over_p1": 2.516065887106032, "B2_over_B1": 1.5591743010211883, "entropy_over_cv": 0.18176918189055216, "upstream_fast_Mach": 1.439078687701611, "downstream_fast_Mach": 0.7370521936994289, "downstream_alfven_margin": 0.5996946013586367, "state_global_normalized": { "rho": "1.55979812573768935354448582572067462198844547200867505771095052892824239167639509561199824", "p": "0.102051632381020655582701786786748931634818894085791395047053334710690530726768738756970320", "u": [ "-0.641256489852444438094520525475405249958210367880426136288277210647936259441213020057059491", "-0.0211826440664802553824580394772489902193120446559685015082684759570742797181216346131310418", "-0E-91" ], "B": [ "0.0587100855209840444241360234166903612708064941215444381127185904542199093534331878704481267", "1.00346358352610802261129323690829800482559220350327916478504617629072312146885429076062171", "0E-91" ] }, "root_record": { "r": "1.55979812573768935354448582572067462198844547200867505771095052892824239167639509561199824", "b": "0.0405619769094419137729425242408459786527149366814289799471866396821867465752464206539267185", "h": "0.00267335266502395311926005310303235141601120931602690062592144561495410141369971568891443545", "A": "0.412968399935191681335060145381700543912813114775326350325978617851149856817930525292173835", "denominator": "0.995830109523659781045232319443182292854433468965414627959210768886959258234731564082472984", "polynomial_residual": "-7.7436906058025110279465E-67", "bracket_initial_signs": [ "1.46674843574944129416928199553875365653643697188595166295500894809338213439568185505538970", "-2.00270340114096113923000297291290630585170547796924446604396069043887816351648490679727027" ], "bracket_derivative_max": "-5.54168145102130528864990708589212312432831439715388638340810630765062663192341771679648902", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-1E-91", "0E-182", "-4E-90", "0E-182", "4.42897480725008845707827373907076732132516753361267810661786516431819729549457127162100196E-68", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.4", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.016320083315882545, 0.0 ], "rh_scaled_inf": 6.565138686469047e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -3.5651237686532335e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 6.565138686469047e-16 }, "characteristics": { "left": { "slow": 0.015716676820551494, "alfven_n": 0.041398379973461796, "fast": 0.8698067610575994 }, "right": { "slow": 0.019345769834853956, "alfven_n": 0.05170321432149264, "fast": 0.694872100637166 } }, "front_relative_normal_velocity": { "left": -0.6410929813320986, "right": -0.9999756307053947 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5597981257376894, "pressure_ratio": 2.516065887106032, "entropy_over_cv": 0.18176918189055213, "tangential_field_ratio": 1.5621421971318588 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.375, "theta_Bn_degrees": 85.37500000000001, "compression": 1.5598127635153627, "u2x_km_s": -384.74452393459677, "u2y_km_s": -12.676844281945929, "speed2_km_s": 384.9533102580211, "signed_deflection_degrees": 1.8871405873721683, "p2_over_p1": 2.516141566021522, "B2_over_B1": 1.559182116533819, "entropy_over_cv": 0.1817836191087756, "upstream_fast_Mach": 1.439089004726965, "downstream_fast_Mach": 0.7370474605850651, "downstream_alfven_margin": 0.5994661686769187, "state_global_normalized": { "rho": "1.55981276351536276730542087589591040091908415272120791905513548629067439941212310778677510", "p": "0.102054701917832932001709400460322566678514789551969539873579467070886913672281136399202445", "u": [ "-0.641240873224327987345590649805313972826765099173634038779766917566489431232612250255821009", "-0.0211280738032432172887112018712417247816256391630603029873693659168166928953212168825622131", "-0E-91" ], "B": [ "0.0585525554022873917705990409674496959220034654614041042146761459591858383890552538630659450", "1.00347783493333783840945387559115643113523855344755322264330620813312921084303022829085948", "0E-91" ] }, "root_record": { "r": "1.55981276351536276730542087589591040091908415272120791905513548629067439941212310778677510", "b": "0.0405617375112275384126094633700225092852717094229413896618489595795027382725777074880918329", "h": "0.00270241054672175737812564224491217492157063243119513797905122222008231599202881265062884502", "A": "0.412936888921250976591665110865042599104910609517978111250551693248586847668605554886461491", "denominator": "0.995784745536964873254056325951110416245929282824915296517795691111770547891258995558793788", "polynomial_residual": "-1.185551913062228309383648E-65", "bracket_initial_signs": [ "1.46675148795009656145229053570983522148267919031023934383448568624495868037213799524581913", "-2.00248186887922034831703039395926861538169128548669905886989686878070469390447825619088209" ], "bracket_derivative_max": "-5.54141268543703212723746611633664664383819327725173991367026828180692083833592831514410170", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "0E-91", "0E-182", "0E-90", "0E-182", "6.78153289657613333438752946464186120253574099362083847102159366482794675641209671929078302E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.375", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.01593472048989891, 0.0 ], "rh_scaled_inf": 1.7825950428336197e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7825950428336197e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.015801997977757085, "alfven_n": 0.04162268830260066, "fast": 0.8698067509392485 }, "right": { "slow": 0.019450764091478015, "alfven_n": 0.05198360112273845, "fast": 0.6948691695784672 } }, "front_relative_normal_velocity": { "left": -0.6410888569795193, "right": -0.9999785816641292 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598127635153627, "pressure_ratio": 2.5161415660215223, "entropy_over_cv": 0.18178361910877583, "tangential_field_ratio": 1.562182505832112 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.35, "theta_Bn_degrees": 85.35000000000001, "compression": 1.5598271319051424, "u2x_km_s": -384.7352490194256, "u2y_km_s": -12.644094980211856, "speed2_km_s": 384.94296327626, "signed_deflection_degrees": 1.882314212171112, "p2_over_p1": 2.516216038094234, "B2_over_B1": 1.5591896257626716, "entropy_over_cv": 0.18179786378263443, "upstream_fast_Mach": 1.4390990805996475, "downstream_fast_Mach": 0.7370428073837145, "downstream_alfven_margin": 0.5992377311519845, "state_global_normalized": { "rho": "1.55982713190514253277538876192622567986106806417480480967893998123490257571622518536939365", "p": "0.102057722505102138644136800126166355299916487641790172096941765735231593344661352999619005", "u": [ "-0.641225415032376068315054108982108598238650149675099898088575071418198134447127910210736878", "-0.0210734916336864274871463878338599588926586280588983942977747042780323616602894839452562473", "-0E-91" ], "B": [ "0.0583950123908653280478056595641100033170008669914035027391369577729823400218984117803646294", "1.00349186439308927672910610428390721246218930784872887952042607073857552814071502953038442", "0E-91" ] }, "root_record": { "r": "1.55982713190514253277538876192622567986106806417480480967893998123490257571622518536939365", "b": "0.0405615135597647731378860543363343382234264436069647730472947432695003113665735545508559106", "h": "0.00273162533027391807418960492078796750916948370279044570202208125960404822002552374374279070", "A": "0.412905379289528842381278506934043450123155638284621821558288424451051352402532759016706897", "denominator": "0.995739136695639396656170241364263868879949209498685973755575622778334258669880836486509037", "polynomial_residual": "-1.615692003073761106947548E-65", "bracket_initial_signs": [ "1.46675293670546645437235841571375253032178181772882818861828701670333267504773929521410321", "-2.00226170475900117624058274183927043786029871023545741855863562165178293831571463644899842" ], "bracket_derivative_max": "-5.54114393803276237340529309175973617776423237434636952730592383231779970696877587782842308", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.02947886582122218808746472177347949384959053742394826889053205696560224527808230333883431E-90", "5E-91", "0E-182", "3E-90", "0E-182", "9.24310620880066878619651864572428969294215348109413137789718384365261070097898610102578153E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.35", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.01554935581908664, 0.0 ], "rh_scaled_inf": 2.1884638354101606e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1884638354101606e-16 }, "characteristics": { "left": { "slow": 0.0158873180224454, "alfven_n": 0.041846990216914355, "fast": 0.8698066312383692 }, "right": { "slow": 0.019555755975651384, "alfven_n": 0.05226397802704038, "fast": 0.6948662227095456 } }, "front_relative_normal_velocity": { "left": -0.6410847213688989, "right": -0.9999813422410571 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598271319051424, "pressure_ratio": 2.5162160380942344, "entropy_over_cv": 0.18179786378263463, "tangential_field_ratio": 1.5622226859164432 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.325, "theta_Bn_degrees": 85.325, "compression": 1.559841230901042, "u2x_km_s": -384.72606917116065, "u2y_km_s": -12.611338604060059, "speed2_km_s": 384.9327138101917, "signed_deflection_degrees": 1.8774860615030073, "p2_over_p1": 2.5162893031598257, "B2_over_B1": 1.559196828712537, "entropy_over_cv": 0.18181191588789614, "upstream_fast_Mach": 1.439108915313957, "downstream_fast_Mach": 0.7370382340926303, "downstream_alfven_margin": 0.5990092887686261, "state_global_normalized": { "rho": "1.55984123090104201133969907963774778854665597141704171763436836791169039541228111892467830", "p": "0.102060694136162529084904005805675159226783986545491058758706259060762143321461196604722765", "u": [ "-0.641210115285267707972591961642866681793981198769516256826276530974202882474275656928047382", "-0.0210188976734334324622224764948516245473029555909206387779580473516339014442070608172018972", "-0E-91" ], "B": [ "0.0582374567172743490106945899150279965861247460821047849976099200313655888109471556686803287", "1.00350567189545541570015557441148638896212628068464568023074427941874677988485733457893668", "0E-91" ] }, "root_record": { "r": "1.55984123090104201133969907963774778854665597141704171763436836791169039541228111892467830", "b": "0.0405613050547124997676276980699786726459489815989846011727408467879826524737328136232887305", "h": "0.00276099702420430540414350989815302074410970144294852102488069197851644144416947546362635586", "A": "0.412873871028005943802140725795518334167772815488772003010751255234138971413775689319184983", "denominator": "0.995693283003251042175113169259735418503069738211156181910719988059723982799853340859964349", "polynomial_residual": "-5.39065652400555693276284E-66", "bracket_initial_signs": [ "1.46675278217691223276929802011946284834368111755141066823852408019363342183752235361122208", "-2.00204290846676524104320190514815864210734928107402510803078340759172398251009170319997235" ], "bracket_derivative_max": "-5.54087520856153529465080526625665995360239414288845934236761988355083689411231273059752315", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.02955974584437644884299636175738301972279250253465411863239052958803613573461579126196081E-90", "-4E-91", "0E-182", "-7E-90", "0E-182", "3.08427497732822984202949602535578562430363544546007172813329605450589553233276997285774461E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.325", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.015163989341315826, 0.0 ], "rh_scaled_inf": 2.1885076544607851e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7826636689081782e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1885076544607851e-16 }, "characteristics": { "left": { "slow": 0.015972636953098536, "alfven_n": 0.04207128573190305, "fast": 0.8698064019565624 }, "right": { "slow": 0.01966074547450212, "alfven_n": 0.05254434498101864, "fast": 0.6948632600316396 } }, "front_relative_normal_velocity": { "left": -0.6410805745005292, "right": -0.9999839124356527 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559841230901042, "pressure_ratio": 2.5162893031598257, "entropy_over_cv": 0.18181191588789614, "tangential_field_ratio": 1.562262737388793 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.3, "theta_Bn_degrees": 85.3, "compression": 1.5598550604969204, "u2x_km_s": -384.7169843950167, "u2y_km_s": -12.578575222868887, "speed2_km_s": 384.92256187008957, "signed_deflection_degrees": 1.8726561491573575, "p2_over_p1": 2.516361361055386, "B2_over_B1": 1.5592037253882134, "entropy_over_cv": 0.18182577540052372, "upstream_fast_Mach": 1.4391185088641962, "downstream_fast_Mach": 0.737033740709193, "downstream_alfven_margin": 0.5987808415117086, "state_global_normalized": { "rho": "1.55985506049692037433541277551663507884611178304935715853868211721376431463985655527753124", "p": "0.102063616804406455358430123566204523070611098049815055128526287714850112014872155024411425", "u": [ "-0.641194973991694613028190164571561521930913962930937254745502254750124334076950709439105905", "-0.0209642920381148125260443728019941263333162426967580190516118324757792014942310329517189574", "-0E-91" ], "B": [ "0.0580798886120777888255848444715007133335164294818301077517055427442694889514586494513704308", "1.00351925743064697404234730938516001723517785175112586902020356758924650282791779250014222", "0E-91" ] }, "root_record": { "r": "1.55985506049692037433541277551663507884611178304935715853868211721376431463985655527753124", "b": "0.0405611119957531303093778266819231681773978719523325961387647171396334062564616532954307938", "h": "0.00279052563727581799467185351177347218017174290936899932427660159479921087997092399741422649", "A": "0.412842364124665033207938874825630040387727533367239487676473134413149423589541460084340653", "denominator": "0.995647184463248921641104390491864103405022277794183188984798138959040464646213929799211355", "polynomial_residual": "-1.234505796545288541715423E-65", "bracket_initial_signs": [ "1.46675102452506500583463235111112826702956089562359940136479041755457346517033378985979656", "-2.00182547968817866890893583156971626924687685049674017087065249733308397164608848013618672" ], "bracket_derivative_max": "-5.54060649677439055066835536405166149354856950507507447440644555393208913555290368863720006", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-2E-91", "0E-182", "-5E-90", "0E-182", "7.06409637745253005730898853539841131123655154157553257265276282460910865395140669006094174E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.3", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.014778621094457395, 0.0 ], "rh_scaled_inf": 2.1885525952350419e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1885525952350419e-16 }, "characteristics": { "left": { "slow": 0.01605795476819587, "alfven_n": 0.04229557486306848, "fast": 0.8698060630954516 }, "right": { "slow": 0.01976573257515752, "alfven_n": 0.05282470193129531, "fast": 0.6948602815459942 } }, "front_relative_normal_velocity": { "left": -0.6410764163747771, "right": -0.9999862922474267 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598550604969204, "pressure_ratio": 2.516361361055386, "entropy_over_cv": 0.1818257754005237, "tangential_field_ratio": 1.5623026602528254 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.275, "theta_Bn_degrees": 85.275, "compression": 1.5598686206864827, "u2x_km_s": -384.7079946962167, "u2y_km_s": -12.545804906020859, "speed2_km_s": 384.91250746620875, "signed_deflection_degrees": 1.8678244889288318, "p2_over_p1": 2.5164322116194375, "B2_over_B1": 1.5592103157945039, "entropy_over_cv": 0.18183944229667567, "upstream_fast_Mach": 1.4391278612446745, "downstream_fast_Mach": 0.7370293272309114, "downstream_alfven_margin": 0.5985523893661701, "state_global_normalized": { "rho": "1.55986862068648258383880209322300097123270317110054754644277862985259739082547888861445852", "p": "0.102066490503284381039781815773790666690386750950486568615244640200513803363727007606094912", "u": [ "-0.641179991160361165335170707800093738227137380198990333689866690632213115900440552902167394", "-0.0209096748433680977998490427057199113693521808275220748416601403054841200147477650675149848", "-0E-91" ], "B": [ "0.0579223083058458407627018510873634103307845542703004742650193681691914507685460769273104822", "1.00353262098899230192451313413578457209801070118651488636882472385405487139704575675335535", "0E-91" ] }, "root_record": { "r": "1.55986862068648258383880209322300097123270317110054754644277862985259739082547888861445852", "b": "0.0405609343825926059314021282710551580829781445346099320667590669072625992805641082471141248", "h": "0.00282021117849039071734542280399659081228218665022518481751180386978742000911355741017749254", "A": "0.412810858567490931859267645421217423805854966807207734673869848861823766866429751166103556", "denominator": "0.995600841078963594691692428767242152509244228494813663459621606956549066171918290646982135", "polynomial_residual": "-1.198450084657026496840263E-65", "bracket_initial_signs": [ "1.46674766390982616522871672145551732575040350815488112545208535024858888077040524330869876", "-2.00160941810811151841977514349223732234587628870768070376619463114754746286113805345940305" ], "bracket_derivative_max": "-5.54033780242036779239067556333969448223262018012572119423580563572541206038051476244081124", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "4E-91", "0E-182", "6E-90", "0E-182", "6.85860002074282383231964334382873175824969013143336652304554693278664651575970026906425280E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.275", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.014393251116383003, 0.0 ], "rh_scaled_inf": 2.1885986578164176e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.782735374150421e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1885986578164176e-16 }, "characteristics": { "left": { "slow": 0.016143271466214103, "alfven_n": 0.04251985762591409, "fast": 0.8698056146566825 }, "right": { "slow": 0.019870717264744077, "alfven_n": 0.05310504882449439, "fast": 0.6948572872538615 } }, "front_relative_normal_velocity": { "left": -0.6410722469920841, "right": -0.9999884816759264 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598686206864827, "pressure_ratio": 2.5164322116194375, "entropy_over_cv": 0.1818394422966756, "tangential_field_ratio": 1.5623424545119264 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.25, "theta_Bn_degrees": 85.25, "compression": 1.5598819114632794, "u2x_km_s": -384.6991000799906, "u2y_km_s": -12.51302772290261, "speed2_km_s": 384.90255060878565, "signed_deflection_degrees": 1.8629910946172263, "p2_over_p1": 2.5165018546919353, "B2_over_B1": 1.559216599936218, "entropy_over_cv": 0.181852916552706, "upstream_fast_Mach": 1.4391369724497054, "downstream_fast_Mach": 0.7370249936554221, "downstream_alfven_margin": 0.5983239323170217, "state_global_normalized": { "rho": "1.55988191146327937359081757550553244012820488232678854131218141066500750099808582979682922", "p": "0.102069315226304894284557094691059119492155277146576205656599875553712596226669781153525605", "u": [ "-0.641165166799984417780545139248800880965314265657269058710978056844841922070496270165097550", "-0.0208550462048376841689126693639680237198242530132451871256813084815945513936035493284970015", "-0E-91" ], "B": [ "0.0577647160291555779200401384858209962506309250896762873499125302128513456881759547840809804", "1.00354576256093737163244679709683537394682221294190372293061977054067134126008086205805086", "0E-91" ] }, "root_record": { "r": "1.55988191146327937359081757550553244012820488232678854131218141066500750099808582979682922", "b": "0.0405607722149603960108912951723827369849545859112165044319662153960105672976896060002203784", "h": "0.00285005365708900327732212242678259599242156305239016205978327735346633086752463168082819645", "A": "0.412779354344470511581787540294945819346082632053991324224794932078744218900086042048893097", "denominator": "0.995554252853607095797729092471079667529652404445819679767228671842704744570947603170042452", "polynomial_residual": "1.057247892287762730833773E-65", "bracket_initial_signs": [ "1.46674270049036782258914746922638675665679358893063181530101592649435909014166496809984370", "-2.00139472341063719195487376162949067055677661992568738139285302400829774031004020037940297" ], "bracket_derivative_max": "-5.54006912524650624740072085719022617465020992175834411665400040639393238967363250740989226", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "-5E-91", "0E-182", "-3E-90", "0E-182", "-6.05124015099160021276960971195224360845087014093656061077919665950718125739690024508649397E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.25", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.014007879444964896, 0.0 ], "rh_scaled_inf": 2.1886458422904997e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7827723816223117e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1886458422904997e-16 }, "characteristics": { "left": { "slow": 0.016228587045627362, "alfven_n": 0.04274413403594514, "fast": 0.8698050566419224 }, "right": { "slow": 0.01997569953038752, "alfven_n": 0.053385385607241785, "fast": 0.6948542771565004 } }, "front_relative_normal_velocity": { "left": -0.641068066352967, "right": -0.9999904807207345 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598819114632794, "pressure_ratio": 2.5165018546919353, "entropy_over_cv": 0.18185291655270597, "tangential_field_ratio": 1.5623821201692039 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.225, "theta_Bn_degrees": 85.22500000000001, "compression": 1.5598949328207072, "u2x_km_s": -384.6903005515764, "u2y_km_s": -12.480243742904849, "speed2_km_s": 384.89269130803785, "signed_deflection_degrees": 1.8581559800274186, "p2_over_p1": 2.5165702901142684, "B2_over_B1": 1.5592225778181714, "entropy_over_cv": 0.1818661981451641, "upstream_fast_Mach": 1.4391458424736079, "downstream_fast_Mach": 0.7370207399804889, "downstream_alfven_margin": 0.5980954703493482, "state_global_normalized": { "rho": "1.55989493282070723006056708341055651796815899385246425287820653533715038317556335393731440", "p": "0.102072090967034720827526584759685901498802764220819488339082464787114111152014064259738285", "u": [ "-0.641150500919294090662774005642473307086011652368973851150654968957495516899369911078236420", "-0.0208004062381747492106943610521426485136398409633784620825032298647169382643041712490683350", "-0E-91" ], "B": [ "0.0576071120125909739793461022272600656799583819374820764100510981666943972392175751078824817", "1.00355868213704576804533368684069545451903083280359691378578176069451059026844121753078384", "0E-91" ] }, "root_record": { "r": "1.55989493282070723006056708341055651796815899385246425287820653533715038317556335393731440", "b": "0.0405606254926094972583270082033434704507591428039315741152122677288640122496229784586842957", "h": "0.00288005308255168957586063148020986634270172775746494830443132330906866864247126609878640375", "A": "0.412747851443592676431020912197776658989661696994067831993298167596242076325327719497366488", "denominator": "0.995507419790272961414769376516798778867981090356027972348618749112021239595669436471902208", "polynomial_residual": "1.130797072166761789892762E-65", "bracket_initial_signs": [ "1.46673613442513325143181052450349904134167579236207832455621558819140674691406568693455906", "-2.00118139527903183423235021362547671115078589825625665715322808419493880634280292875679800" ], "bracket_derivative_max": "-5.53980046499784429171401019600477608948630916816269468724304264065368476539345620608050817", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.02989857048258934518546191808042567048763627556039681851085516775355619523412398235955992E-90", "0E-91", "0E-182", "0E-90", "0E-182", "-6.47297995248045346819498707370922097757386979286905786045635940303125310396501781451689031E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.225", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.01362250611807581, 0.0 ], "rh_scaled_inf": 4.377388297489947e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 4.377388297489947e-16 }, "characteristics": { "left": { "slow": 0.016313901504907226, "alfven_n": 0.042968404108668805, "fast": 0.8698043890528614 }, "right": { "slow": 0.020080679359212785, "alfven_n": 0.053665712226165334, "fast": 0.6948512512551759 } }, "front_relative_normal_velocity": { "left": -0.6410638744580169, "right": -0.9999922893814706 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598949328207072, "pressure_ratio": 2.5165702901142684, "entropy_over_cv": 0.18186619814516414, "tangential_field_ratio": 1.5624216572274894 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.2, "theta_Bn_degrees": 85.2, "compression": 1.5599076847520084, "u2x_km_s": -384.6815961162195, "u2y_km_s": -12.447453035422301, "speed2_km_s": 384.88292957416456, "signed_deflection_degrees": 1.853319158969329, "p2_over_p1": 2.516637517729259, "B2_over_B1": 1.5592282494451855, "entropy_over_cv": 0.18187928705079479, "upstream_fast_Mach": 1.439154471310706, "downstream_fast_Mach": 0.737016566204004, "downstream_alfven_margin": 0.5978670034483061, "state_global_normalized": { "rho": "1.55990768475200837364681399412382509732675641767885921506162328795082217943809885768557829", "p": "0.102074817719098736940054234654843405477556982683496454588845959980282174421334409834908244", "u": [ "-0.641135993527032568557018683007361651293529741620846845476518054871645230402731887428177852", "-0.0207457550590371680960316209228625901709570610280046460205395762317171271265189861472063579", "-0E-91" ], "B": [ "0.0574494964867429239950047222224757943338706811894569678121697693303956845374281318501197236", "1.00357137970799867892066163740647301897890888871538792529742688917738907508447934656583483", "0E-91" ] }, "root_record": { "r": "1.55990768475200837364681399412382509732675641767885921506162328795082217943809885768557829", "b": "0.0405604942153164329180062926258528772433580371432735496677928839195006418719396788324447012", "h": "0.00291020946459754784665655574283492866336351450964543787131074933158396482370246372991314149", "A": "0.412716349852848344363726303931173374415113485985186362736616085151245743227113457736257594", "denominator": "0.995460341891936257259999217724290318364977237905723436268878562152767717419349714142354173", "polynomial_residual": "5.2595064332326633767515E-67", "bracket_initial_signs": [ "1.46672796587183733344598800188413694940889368735089590251808007257986769777279104744184987", "-2.00096943339577371799334301425827119104970527833662774453416837713061537477885990742143735" ], "bracket_derivative_max": "-5.53953182141741900793145288011721483816175633888752398234777793148389251759085128044594285", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.02998710318199611003317521876314480684845921932053058665923472174487782626973755241715195E-90", "1E-91", "0E-182", "4E-90", "0E-182", "-3.01104048062369555985784075128090896993638343320311008724247475867371433944294284941589274E-68", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.2", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.013237131173588846, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.016399214842522825, "alfven_n": 0.043192667859594254, "fast": 0.8698036118912108 }, "right": { "slow": 0.020185656738344018, "alfven_n": 0.0539460286278948, "fast": 0.69484820955116 } }, "front_relative_normal_velocity": { "left": -0.6410596713079004, "right": -0.9999939076577904 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599076847520084, "pressure_ratio": 2.516637517729259, "entropy_over_cv": 0.1818792870507948, "tangential_field_ratio": 1.5624610656893352 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.175, "theta_Bn_degrees": 85.17500000000001, "compression": 1.5599201672502707, "u2x_km_s": -384.6729867791729, "u2y_km_s": -12.414655669853657, "speed2_km_s": 384.8732654173459, "signed_deflection_degrees": 1.8484806452578786, "p2_over_p1": 2.5167035373811633, "B2_over_B1": 1.559233614822087, "entropy_over_cv": 0.18189218324653808, "upstream_fast_Mach": 1.4391628589553294, "downstream_fast_Mach": 0.7370124723239871, "downstream_alfven_margin": 0.5976385315991257, "state_global_normalized": { "rho": "1.55992016725027074001750393903589873059496871346718521186828717139556473992951039232599084", "p": "0.102077495476179982346319295969881785241860764052429328470153387514031299810986805604941100", "u": [ "-0.641121644631954897667975017829992307135572435235717805941240060536143114998991255282777612", "-0.0206910927830894294632025647029336895804271305217921885568132495197025310001244365383911627", "-0E-91" ], "B": [ "0.0572918696822092652166144706022384932298382847403610486981950291578539178175687735415117716", "1.00358385526459488498753890761936091718835933978764371265907920303426163644609091583342838", "0E-91" ] }, "root_record": { "r": "1.55992016725027074001750393903589873059496871346718521186828717139556473992951039232599084", "b": "0.0405603783828812520447198046610121707280023574929290309345355794333882038756882219571498701", "h": "0.00294052281318475156601503993856925248508533528436910990349169213958691690361362672325095129", "A": "0.412684849560230428915791616058639363297230984921527315257537836633128794457615191708875407", "denominator": "0.995413019161453605714794207111316983702424676769432628883530319016808962210760838960519719", "polynomial_residual": "4.75941842122959779901203E-66", "bracket_initial_signs": [ "1.46671819498746700918500633705264544178532941080171036345776976410207293212825428884964787", "-2.00075883744254261682787023953378802156038409793568515526706414439124061140098021539809615" ], "bracket_derivative_max": "-5.53926319424626572976253675675662120447616157984164576326661489227483998812202028887231605", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.03007716666383674528426768091598503660753789244918161431690143720247482752143172410834731E-90", "4E-91", "0E-182", "4E-90", "0E-182", "-2.72506897255205487858470275487608737322559378946113447523594022731510729554897492126697471E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.175", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.012851754649377356, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 2.220446049250313e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.016484527056940847, "alfven_n": 0.04341692530423281, "fast": 0.8698027251587048 }, "right": { "slow": 0.02029063165490456, "alfven_n": 0.0542263347590619, "fast": 0.6948451520457317 } }, "front_relative_normal_velocity": { "left": -0.6410554569033585, "right": -0.9999953355493857 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599201672502707, "pressure_ratio": 2.5167035373811637, "entropy_over_cv": 0.18189218324653833, "tangential_field_ratio": 1.5625003455570168 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.15, "theta_Bn_degrees": 85.15, "compression": 1.559932380308428, "u2x_km_s": -384.66447254569727, "u2y_km_s": -12.38185171560153, "speed2_km_s": 384.86369884774354, "signed_deflection_degrees": 1.843640452712946, "p2_over_p1": 2.5167683489156722, "B2_over_B1": 1.5592386739537096, "entropy_over_cv": 0.18190488670952937, "upstream_fast_Mach": 1.439171005401812, "downstream_fast_Mach": 0.737008458338586, "downstream_alfven_margin": 0.5974100547871093, "state_global_normalized": { "rho": "1.55993238030842796158733164469643625140286902943301630400721302594529670747959311106918731", "p": "0.102080124232019673098361221180921785700412530759915552728217440569282067386465808185176414", "u": [ "-0.641107454242828783670381148972925149155107830578711360029946893005890951626371592483930449", "-0.0206364195260025512646696448370662599010814988085569250158928728724594637510793749907411845", "-0E-91" ], "B": [ "0.0571342318295947979460350219410435296392243841391400270181388867014665934704520910362595669", "1.00359610879775074984834501038287259760611976738097433197396922838808864634675093078936633", "0E-91" ] }, "root_record": { "r": "1.55993238030842796158733164469643625140286902943301630400721302594529670747959311106918731", "b": "0.0405602779951275288565800304749850645767945372882211090655436534232574423330792952718075250", "h": "0.00297099313851056113687810381916201136652289043438132725600567856720925803487199194922177009", "A": "0.412653350553733820886586664941931667758653758082793282679343978235402448853869622513294661", "denominator": "0.995365451601563213353013472504651123628729377517832135543897155640881707031503455693312847", "polynomial_residual": "1.498231652523492714506828E-65", "bracket_initial_signs": [ "1.46670682192828173315397483174345357680189423194412239360924695602517547807969298321113436", "-2.00054960710021916514192017734729377009249111868207633378151489283186555695662797916993501" ], "bracket_derivative_max": "-5.53899458322341757291864388163932594535587069560528405201758110913100822340958327937516093", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-3E-91", "0E-182", "-2E-90", "0E-182", "-8.57935382355956009042258562873322510363869364929138539954329163221987655458695873638772141E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.15", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.012466376583314814, 0.0 ], "rh_scaled_inf": 2.1888458008991105e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1888458008991105e-16 }, "characteristics": { "left": { "slow": 0.01656983814662566, "alfven_n": 0.043641176458097966, "fast": 0.8698017288570992 }, "right": { "slow": 0.020395604096016953, "alfven_n": 0.05450663056630029, "fast": 0.6948420787401763 } }, "front_relative_normal_velocity": { "left": -0.6410512312452074, "right": -0.9999965730559848 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559932380308428, "pressure_ratio": 2.5167683489156727, "entropy_over_cv": 0.18190488670952942, "tangential_field_ratio": 1.5625394968325306 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.125, "theta_Bn_degrees": 85.125, "compression": 1.5599443239192594, "u2x_km_s": -384.65605342106073, "u2y_km_s": -12.349041242072397, "speed2_km_s": 384.85422987550015, "signed_deflection_degrees": 1.8387985951593266, "p2_over_p1": 2.5168319521799116, "B2_over_B1": 1.5592434268448923, "entropy_over_cv": 0.18191739741709917, "upstream_fast_Mach": 1.4391789106444937, "downstream_fast_Mach": 0.7370045242460755, "downstream_alfven_margin": 0.5971815729976322, "state_global_normalized": { "rho": "1.55994432391925934913336164123267079967605959925547587039104895675998071081050172975787969", "p": "0.102082703980417214409968969350921312465355873011006698097627098575332478715408456201665378", "u": [ "-0.641093422368434590037294830729028177136302579538519280685995875408948773697040881074590919", "-0.0205817354034539965863194084856245517004681255427820886245059333915474082500932892351637562", "-0E-91" ], "B": [ "0.0569765831595113064296927564449393554935426591232452987247284835285446540438852199040094927", "1.00360814029850020968863965801878197751819711462905072238654872623219216444613823656582525", "0E-91" ] }, "root_record": { "r": "1.55994432391925934913336164123267079967605959925547587039104895675998071081050172975787969", "b": "0.0405601930519023621639958026020383063884415533157825895029257466978059874714019519492353436", "h": "0.00300162045101133634672926495744717881854142794403437083315233251997880646523393977533100095", "A": "0.412621852821355370029715729611918492290440150839718626987151826859705286815738492033143401", "denominator": "0.995317639214884898595134055040248633090155463973243084475861126464739807793339225255308433", "polynomial_residual": "-9.15085875539350270347986E-66", "bracket_initial_signs": [ "1.46669384684981393329622882009986623519067654701275386487070974655347401309151597499396011", "-2.00034174204888420526507672116204810562719540991719188156962131163959921486111690572177439" ], "bracket_derivative_max": "-5.53872598808590495237614843080281435448196276109701722667251460085752559580057365883941065", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "0E-91", "0E-182", "-2E-90", "0E-182", "5.24070185996228217798816159884184313611718548910773231791402984774141045682333384692597326E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.125", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.012080997013274712, 0.0 ], "rh_scaled_inf": 2.1888985961940165e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1888985961940165e-16 }, "characteristics": { "left": { "slow": 0.016655148110039337, "alfven_n": 0.043865421336705575, "fast": 0.8698006229881718 }, "right": { "slow": 0.02050057404880295, "alfven_n": 0.054786915996245626, "fast": 0.6948389896357864 } }, "front_relative_normal_velocity": { "left": -0.6410469943343378, "right": -0.9999976201773518 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599443239192594, "pressure_ratio": 2.5168319521799116, "entropy_over_cv": 0.1819173974170991, "tangential_field_ratio": 1.5625785195175967 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.1, "theta_Bn_degrees": 85.1, "compression": 1.5599559980753899, "u2x_km_s": -384.6477294105392, "u2y_km_s": -12.316224318676554, "speed2_km_s": 384.84485851073987, "signed_deflection_degrees": 1.8339550864266905, "p2_over_p1": 2.516894347022441, "B2_over_B1": 1.5592478735004793, "entropy_over_cv": 0.18192971534677327, "upstream_fast_Mach": 1.4391865746777195, "downstream_fast_Mach": 0.7370006700448593, "downstream_alfven_margin": 0.5969530862161418, "state_global_normalized": { "rho": "1.55995599807538987354871880556661612943217846602840068634822732334703438854514160288236015", "p": "0.102085234715230213449436043858979036403700335866995928399953454683960022271091912823262564", "u": [ "-0.641079549017565336856238528987566470644610870768910626194846565168862456901920185475692672", "-0.0205270405311275894390125821534037525592467460006454198163654454055356954481735131629584120", "-0E-91" ], "B": [ "0.0568189239025775797869294307552941046280877860443735516484665160380450748193993658935963296", "1.00361994975799476279525467922784524708573943994513629556483941456236989112523580611924601", "0E-91" ] }, "root_record": { "r": "1.55995599807538987354871880556661612943217846602840068634822732334703438854514160288236015", "b": "0.0405601235530763748747899617877111514750895028485281604982334138043549905676352092272750586", "h": "0.00303240476136254959940231028071878968303343418619354816401018357445017289002364151024412694", "A": "0.412590356351093866750110721537854389496676966319260335727905877671652511748104728748359488", "denominator": "0.995269582003920119488332213422631141397989270534589573181534283850328239718080576680011988", "polynomial_residual": "-9.81598765814071484277009E-66", "bracket_initial_signs": [ "1.46667926990686947488015702156921627813780638778382286243222559482801266739082165277161716", "-2.00013524196781812169785997898424892059848567657348090663797500642522838736993752256244730" ], "bracket_derivative_max": "-5.53845740856875508600884079182307387448165573229048259854609624171540244224710884891028096", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "2E-91", "0E-182", "1E-90", "0E-182", "5.62229445720237226849584533187394555743655946622099167204540132111947312967273703678084820E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.1", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.011695615977130437, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.016740456945641725, "alfven_n": 0.0440896599555739, "fast": 0.8697994075537235 }, "right": { "slow": 0.020605541500383472, "alfven_n": 0.05506719099553551, "fast": 0.6948358847338607 } }, "front_relative_normal_velocity": { "left": -0.6410427461717157, "right": -0.9999984769132877 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599559980753899, "pressure_ratio": 2.516894347022441, "entropy_over_cv": 0.18192971534677327, "tangential_field_ratio": 1.562617413613656 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.075, "theta_Bn_degrees": 85.075, "compression": 1.5599674027692902, "u2x_km_s": -384.63950051941606, "u2y_km_s": -12.283401014828058, "speed2_km_s": 384.83558476356745, "signed_deflection_degrees": 1.8291099403495399, "p2_over_p1": 2.5169555332932565, "B2_over_B1": 1.5592520139253219, "entropy_over_cv": 0.18194184047627243, "upstream_fast_Mach": 1.439193997495839, "downstream_fast_Mach": 0.7369968957334678, "downstream_alfven_margin": 0.5967245944281583, "state_global_normalized": { "rho": "1.55996740276929014773436691038785183329598310553480287707555556980638150921800142885878762", "p": "0.102087716430374492091202422281005993833843091782969145830262414652585914440075381178354532", "u": [ "-0.641065834199026700133313515415591705462841775683219866107539082142426145647665191559353393", "-0.0204723350247134305222585375642865716826642629331421069613605798599980781283998896739771774", "-0E-91" ], "B": [ "0.0566612542894194329751797804971031050658031981460942072839363059159563088756389270680831420", "1.00363153716750345888249335213996601696918099696970257063871428401661095192071707425669082", "0E-91" ] }, "root_record": { "r": "1.55996740276929014773436691038785183329598310553480287707555556980638150921800142885878762", "b": "0.0405600694985437135754574152251260108704386049608202083392254615606370249284268323277124041", "h": "0.00306334608047879992082537756243315440778941490931922264043802052025761914191853228768413663", "A": "0.412558861130950023807405646582135662354516674972595886562384566822485745932115762059861328", "denominator": "0.995221279971052001612619200250216764241782650905499483099236343089789097073769272519632902", "polynomial_residual": "-1.493246541345852623046643E-65", "bracket_initial_signs": [ "1.46666309125352812878815800197918192686616845861191186391312975015084407928863770834266921", "-1.99993010653550016249783939647587926634823296839720349896739396448282094251711778764869992" ], "bracket_derivative_max": "-5.53818884440499148458911092415290390151542434444559813251836422541993290439649285405085425", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "-3E-91", "0E-182", "-6E-90", "0E-182", "8.55387844258842448017526307994455149795468073203936751570124493262441789564774361089213753E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_-0.075", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.011310233512755145, 0.0 ], "rh_scaled_inf": 1.7830529976156506e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7830529976156506e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.016825764651890528, "alfven_n": 0.04431389233022372, "fast": 0.8697980825555758 }, "right": { "slow": 0.020710506437878647, "alfven_n": 0.05534745551080954, "fast": 0.6948327640357049 } }, "front_relative_normal_velocity": { "left": -0.641038486758382, "right": -0.9999991432636292 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599674027692902, "pressure_ratio": 2.516955533293257, "entropy_over_cv": 0.1819418404762725, "tangential_field_ratio": 1.5626561791218712 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.05, "theta_Bn_degrees": 85.05, "compression": 1.5599785379932765, "u2x_km_s": -384.6313667529822, "u2y_km_s": -12.250571399944686, "speed2_km_s": 384.8264086440693, "signed_deflection_degrees": 1.8242631707671684, "p2_over_p1": 2.5170155108437893, "B2_over_B1": 1.5592558481242766, "entropy_over_cv": 0.18195377278351266, "upstream_fast_Mach": 1.4392011790932075, "downstream_fast_Mach": 0.7369932013105599, "downstream_alfven_margin": 0.5964960976192737, "state_global_normalized": { "rho": "1.55997853799327640862899555433784429364791066157071889595625648760071070260579205666428519", "p": "0.102090149119824099626404374400281114857666099232459884178465895789018880490382832619076921", "u": [ "-0.641052277921637011585387138859982233277162113653593778830433546659454744085409187610236704", "-0.0204176189999078129598279516987762379649821466344325417073465130748284194633038346751130174", "-0E-91" ], "B": [ "0.0565035745506697277927642136168981875696302411969388457523193769527098691424600852255700997", "1.00364290251841288822636118620794589712470965735953427730837311816992498272052152727448627", "0E-91" ] }, "root_record": { "r": "1.55997853799327640862899555433784429364791066157071889595625648760071070260579205666428519", "b": "0.0405600308882220481885612651241664615000682180418527630501124906516897324899004999178973255", "h": "0.00309444441951382773873580737039399343488831533306604382241615724356698775395583874824019764", "A": "0.412527367148926458025533063320669255401385258068400570892014724802390166897378550687067661", "denominator": "0.995172733118545366113140165283136946923680385260811253513097921895141046214724325179508069", "polynomial_residual": "1.163115638337110239310491E-65", "bracket_initial_signs": [ "1.46664531104314404420953602620456675792144672927877676473998807328383961760518638730355380", "-1.99972633542960774780345353901704998068615789701606863326174318609123573614256570794399223" ], "bracket_derivative_max": "-5.53792029532563342815721325486627398913528044495599128966880054997371368092963575378433307", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-3E-91", "0E-182", "-4E-90", "0E-182", "-6.66356159242583325348755819702126381401719426883358722923507840832804360000444598369785325E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.05", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.010924849658021653, 0.0 ], "rh_scaled_inf": 2.1890637171839534e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7830961670209878e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1890637171839534e-16 }, "characteristics": { "left": { "slow": 0.016911071227241333, "alfven_n": 0.044538118476178445, "fast": 0.8697966479955735 }, "right": { "slow": 0.02081546884840777, "alfven_n": 0.05562770948870931, "fast": 0.6948296275426314 } }, "front_relative_normal_velocity": { "left": -0.6410342160954521, "right": -0.9999996192282494 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599785379932765, "pressure_ratio": 2.5170155108437897, "entropy_over_cv": 0.18195377278351266, "tangential_field_ratio": 1.5626948160431275 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": -0.025, "theta_Bn_degrees": 85.025, "compression": 1.5599894037395106, "u2x_km_s": -384.62332811653636, "u2y_km_s": -12.217735543447883, "speed2_km_s": 384.8173301623127, "signed_deflection_degrees": 1.819414791523619, "p2_over_p1": 2.5170742795269065, "B2_over_B1": 1.5592593761022058, "entropy_over_cv": 0.18196551224660484, "upstream_fast_Mach": 1.4392081194641855, "downstream_fast_Mach": 0.7369895867749221, "downstream_alfven_margin": 0.5962675957751524, "state_global_normalized": { "rho": "1.55998940373951049937703805425144380971825168796654951706734914604310154701785276590438329", "p": "0.102092532777611325432353000188658113044966757825810277901032772592202538408303033459127793", "u": [ "-0.641038880194227258920460408882256479787134035263640531933068624011046571041286309845820840", "-0.0203628925724131380071172286739115375931694627392990121518542823657393940764550460227452131", "-0E-91" ], "B": [ "0.0563458849169683939200831539165144532560222312246220945489032924517618066535496667418663373", "1.00365404580222717060675177336689415762970865478804068491039156963212498297733180379463485", "0E-91" ] }, "root_record": { "r": "1.55998940373951049937703805425144380971825168796654951706734914604310154701785276590438329", "b": "0.0405600077220525717062651045002198704731133525981008274698380139957115045534753853120440449", "h": "0.00312569978986053043640552537714852265761246855079795866144771129563233291422188602127193481", "A": "0.412495874393027672008483276472137309055215471450927803901087245423673126707073317292959081", "denominator": "0.995123941448546757858745951230626627268658704047558666803159275737455640909557396229951939", "polynomial_residual": "-1.585289129902534557706147E-65", "bracket_initial_signs": [ "1.46662592942834622573921195375290533421335914648504747587545569903438875469849627858282978", "-1.99952392832701576549434754158256880809341570787477216004922906383277636273342513703150540" ], "bracket_derivative_max": "-5.53765176105969542875782456747810834262783611483163800090383314469894391032925757189629486", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.03064969889317587776498508518903884845984622853015988741426746342689490957503650518936734E-90", "0E-91", "0E-182", "-1E-90", "0E-182", "9.08330629511087578359026088870139341841819532227808295595988603389464627257775517898338048E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_-0.025", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.01053946445080232, 0.0 ], "rh_scaled_inf": 2.1891210028903115e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7831401070082605e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1891210028903115e-16 }, "characteristics": { "left": { "slow": 0.016996376670147688, "alfven_n": 0.04476233840896422, "fast": 0.8697951038755833 }, "right": { "slow": 0.020920428719089328, "alfven_n": 0.0559079528758784, "fast": 0.6948264752559594 } }, "front_relative_normal_velocity": { "left": -0.6410299341841167, "right": -0.9999999048070578 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599894037395106, "pressure_ratio": 2.5170742795269065, "entropy_over_cv": 0.18196551224660473, "tangential_field_ratio": 1.5627333243780317 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.0, "theta_Bn_degrees": 85.0, "compression": 1.5599999999999998, "u2x_km_s": -384.61538461538464, "u2y_km_s": -12.184893514762697, "speed2_km_s": 384.808349328346, "signed_deflection_degrees": 1.8145648164676402, "p2_over_p1": 2.517131839196911, "B2_over_B1": 1.5592625978639778, "entropy_over_cv": 0.18197705884385498, "upstream_fast_Mach": 1.4392148186031382, "downstream_fast_Mach": 0.7369860521254686, "downstream_alfven_margin": 0.596039088881531, "state_global_normalized": { "rho": "1.55999999999999985163484508659523960798288248572455028384726922324826736009571409862749629", "p": "0.102094867397826711600962155469156982968501619921040585108040740505336073661254642223353742", "u": [ "-0.641025641025641086606325983483224236692158025059558580018431779045556854744866568796353048", "-0.0203081558579378307300780023639536378481354426228758558857113591579760305727098679397069354", "-0E-91" ], "B": [ "0.05618818561896245000000000000000000000000000000000000000000000000000000000000000000000000", "1.00366496701056794405751091592429512407082944759545601036732719011638822337212757539948282", "0E-89" ] }, "root_record": { "r": "1.55999999999999985163484508659523960798288248572455028384726922324826736009571409862749629", "b": "0.04056", "h": "0.0031571122031509786804210145100025", "A": "0.41246438285126003586216703841296", "denominator": "0.995074904963084473726948658463891652621213553516219186457284867644472817050965946710336082", "polynomial_residual": "4.26620789379558404096923E-66", "bracket_initial_signs": [ "1.4666049465610390148841902035651344922634427332289025207088930087767081050000", "-1.9993228849037958539869161161098875338604281485915538870929762622683450650000" ], "bracket_derivative_max": "-5.537383241334186679542995546615423231621018349723445450642509846001827450000", "iterations": 216 }, "flux_residuals": [ "0E-89", "0E-54", "0E-91", "0E-180", "-2E-90", "0E-180", "-2.44472176952271555555107043410610778492391897003132426061389778086390958548403362213422952E-67", "0E-89" ], "diagnosis": { "case_id": "R95_phi_0", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.010154077928968915, 0.0 ], "rh_scaled_inf": 4.3783588229215367e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 4.3783588229215367e-16 }, "characteristics": { "left": { "slow": 0.017081680979061195, "alfven_n": 0.04498655214411002, "fast": 0.8697934501974935 }, "right": { "slow": 0.02102538603704097, "alfven_n": 0.05618818561896245, "fast": 0.6948233071770148 } }, "front_relative_normal_velocity": { "left": -0.6410256410256411, "right": -1.0 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599999999999998, "pressure_ratio": 2.517131839196911, "entropy_over_cv": 0.18197705884385496, "tangential_field_ratio": 1.5627717041269118 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.025, "theta_Bn_degrees": 84.97500000000001, "compression": 1.5600103267665975, "u2x_km_s": -384.60753625484085, "u2y_km_s": -12.152045383317752, "speed2_km_s": 384.7994661521985, "signed_deflection_degrees": 1.8097132594526462, "p2_over_p1": 2.517188189709543, "B2_over_B1": 1.5592655134144664, "entropy_over_cv": 0.1819884125537639, "upstream_fast_Mach": 1.4392212765044363, "downstream_fast_Mach": 0.7369825973612414, "downstream_alfven_margin": 0.595810576924218, "state_global_normalized": { "rho": "1.56001032676659746801504107245464562175849574723322625008059974603504425680760040377293068", "p": "0.102097152974619065526146268846199800081153426313368586281780179839859975292904221743280012", "u": [ "-0.641012560424734797127629611690937874550088537465528034985368962868499986803929411670720665", "-0.0202534089721962556555247863314406150210421763629311732674398277642077032917508277144318529", "-0E-91" ], "B": [ "0.0560304768873060247582000761169971251006156190981470971581909573505208993619400671164703104", "1.00367566613517435342430182505618173627200299091346801115287898488959593407573687338709910", "0E-91" ] }, "root_record": { "r": "1.56001032676659746801504107245464562175849574723322625008059974603504425680760040377293068", "b": "0.0405600077220525717062651045002198704731133525981008274698380139957115045534753853120440449", "h": "0.00318868167125643352256623619034397892624316475768157273010095570056345348569273673354457703", "A": "0.412432892511631768922322565658941852786584775244044189832434001018742006135602466580686437", "denominator": "0.995025623664068591015372966014946725349232177357845235165246655858432647444847187241000680", "polynomial_residual": "-9.80013814391204312688321E-66", "bracket_initial_signs": [ "1.46658236259240257597978819723845502939882237011670170457210655983137406813750329329706335", "-1.99912320483521567216361690228399283997358829172132108029485910531041596536262133073456090" ], "bracket_derivative_max": "-5.53711473587411049024048585903052138373443488772144734404284481019385605913036378856316399", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "1E-91", "0E-182", "-1E-90", "0E-182", "5.61657498539684085315671372456503226041912877760797896262284543331133637990769300819162460E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.025", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.009768690130392523, 0.0 ], "rh_scaled_inf": 1.783230299051293e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.783230299051293e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.017166984152431515, "alfven_n": 0.045210759697147745, "fast": 0.8697916869632147 }, "right": { "slow": 0.02113034078937952, "alfven_n": 0.05646840766460909, "fast": 0.6948201233071303 } }, "front_relative_normal_velocity": { "left": -0.6410213366213657, "right": -0.9999999048070578 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600103267665975, "pressure_ratio": 2.517188189709543, "entropy_over_cv": 0.18198841255376397, "tangential_field_ratio": 1.5628099552898178 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.05, "theta_Bn_degrees": 84.95, "compression": 1.5600203840310018, "u2x_km_s": -384.5997830402264, "u2y_km_s": -12.119191218545179, "speed2_km_s": 384.7906806438806, "signed_deflection_degrees": 1.804860134336674, "p2_over_p1": 2.5172433309219793, "B2_over_B1": 1.5592681227585516, "entropy_over_cv": 0.18199957335502748, "upstream_fast_Mach": 1.4392274931624558, "downstream_fast_Mach": 0.7369792224814103, "downstream_alfven_margin": 0.5955820598890935, "state_global_normalized": { "rho": "1.56002038403100190466909250856573350740810857828536856976804235773464266204505055402563458", "p": "0.102099389502195472450208389368682438194165051820417220040055264651476299734750357314894344", "u": [ "-0.640999638400377352731451041806572211956949039204494754756026689011327536273504449334439384", "-0.0201986520309086323926335817576158855982130053436091629474534293687491988572750809794278594", "-0E-91" ], "B": [ "0.0558727589526603781643133681122372681687009388925054824956070506912161132082110527764881591", "1.00368614316790303873019376955535819894772719377397323471723207969600487951512341032972444", "0E-91" ] }, "root_record": { "r": "1.56002038403100190466909250856573350740810857828536856976804235773464266204505055402563458", "b": "0.0405600308882220481885612651241664615000682180418527630501124906516897324899004999178973255", "h": "0.00322040820628736427586115992134409757201308153240901610277774384942987550450343589497421541", "A": "0.412401403362152921488407710769719151264260491869057598611653138196527279146830953540333643", "denominator": "0.994976097553290995979816307299775607150490174023196671013138590004173329461478799458121240", "polynomial_residual": "-7.17535804256082849322154E-66", "bracket_initial_signs": [ "1.46655817767289338651770008162656954872643053502658629876253273173424279370048608007445772", "-1.99892488779573815643449585802647425897091596897918927129462314057119143056885766569365130" ], "bracket_derivative_max": "-5.53684624440246370898636188065634962955227308464237590614429708054541342152176248972249011", "iterations": 216 }, "flux_residuals": [ "2E-90", "8.03095663784942982004017861682945972694367560665831452875121952825969055241998227359544253E-90", "0E-91", "0E-182", "-2E-90", "0E-182", "4.11277424337188873998001164748217208257916960880726216879189800574493447435176596005285769E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.05", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.00938330109294341, 0.0 ], "rh_scaled_inf": 2.1892995976308813e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7832765512719234e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1892995976308813e-16 }, "characteristics": { "left": { "slow": 0.01725228618870648, "alfven_n": 0.04543496108361235, "fast": 0.8697898141746797 }, "right": { "slow": 0.021235292963220978, "alfven_n": 0.056748618959468, "fast": 0.6948169236476449 } }, "front_relative_normal_velocity": { "left": -0.6410170209727059, "right": -0.9999996192282494 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600203840310018, "pressure_ratio": 2.5172433309219793, "entropy_over_cv": 0.1819995733550276, "tangential_field_ratio": 1.5628480778665208 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.075, "theta_Bn_degrees": 84.92500000000001, "compression": 1.5600301717847573, "u2x_km_s": -384.5921249768702, "u2y_km_s": -12.08633108988057, "speed2_km_s": 384.78199281338357, "signed_deflection_degrees": 1.8000054549823403, "p2_over_p1": 2.517297262692833, "B2_over_B1": 1.5592704259011194, "entropy_over_cv": 0.18201054122653632, "upstream_fast_Mach": 1.4392334685715777, "downstream_fast_Mach": 0.7369759274852731, "downstream_alfven_margin": 0.5953535377621099, "state_global_normalized": { "rho": "1.56003017178475725400811965597773804617842613577298873618719820413701004078374772695791990", "p": "0.102101576974821307969238640271254544671198199490517290144755598395666030985427480176077592", "u": [ "-0.640986874961450377661523367762138987452816053383056615933754412730553481757963416090122888", "-0.0201438851498009512254439946246684272512640039356809253875138330882509952297038632131084255", "-0E-91" ], "B": [ "0.0557150320456939226345892598827135117021725935206408376678902385797667172024897379537495818", "1.00369639810072812334889613960066226743703272688014846706419688501330075905534131250406570", "0E-91" ] }, "root_record": { "r": "1.56003017178475725400811965597773804617842613577298873618719820413701004078374772695791990", "b": "0.0405600694985437135754574152251260108704386049608202083392254615606370249284268323277124041", "h": "0.00325229182059346716481286076607544117121271995215409739598958252747688151954225345293932571", "A": "0.412369915390835356563418163378493375591093369929761011806833004815266483554492040894606138", "denominator": "0.994926326632425412499032110202780002173201639068279048237505074954648947984518321492987345", "polynomial_residual": "-2.39091255373134267711007E-66", "bracket_initial_signs": [ "1.46653239195224473188803193325187453491376499390884623648527340211533496151617376000676350", "-1.99872793345902076492924330912871843304382937445858845572747579235343454914644959033609169" ], "bracket_derivative_max": "-5.53657776664023613052062541899496077538608689934086043152448777676800672110249801908151825", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.03106201411582447994260588132906701007762084489078551962547471743293868393678305293647857E-90", "-3E-91", "0E-182", "-3E-90", "0E-182", "1.37058794819422687166528080431607995424231937730473522932826480922172172657726393598417735E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.075", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.0089979108544909, 0.0 ], "rh_scaled_inf": 2.1893613754542473e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7833235744042308e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1893613754542473e-16 }, "characteristics": { "left": { "slow": 0.01733758708633211, "alfven_n": 0.04565915631904189, "fast": 0.8697878318338438 }, "right": { "slow": 0.021340242545680486, "alfven_n": 0.0570288194501909, "fast": 0.6948137081999048 } }, "front_relative_normal_velocity": { "left": -0.6410126940811517, "right": -0.9999991432636292 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600301717847573, "pressure_ratio": 2.517297262692833, "entropy_over_cv": 0.18201054122653615, "tangential_field_ratio": 1.5628860718565145 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.1, "theta_Bn_degrees": 84.9, "compression": 1.560039690019253, "u2x_km_s": -384.5845620701089, "u2y_km_s": -12.053465066762934, "speed2_km_s": 384.7734026706798, "signed_deflection_degrees": 1.7951492352568015, "p2_over_p1": 2.517349984882156, "B2_over_B1": 1.5592724228470607, "entropy_over_cv": 0.18202131614737588, "upstream_fast_Mach": 1.4392392027261882, "downstream_fast_Mach": 0.736972712372255, "downstream_alfven_margin": 0.5951250105292907, "state_global_normalized": { "rho": "1.56003969001925312756198520798165680829282566026409183058926246077190298979189448147405264", "p": "0.102103715386820250497543090018451444286899799443023615051432948793636928679172266894233163", "u": [ "-0.640974270116848160881212749274699019374782482487226528808252591304862701106295460792872552", "-0.0200891084446048886761771504054282064667944319908005041962679262816167414751610231409224009", "-0E-91" ], "B": [ "0.0555572963970822442769119134070405355084700312441260505032736029932270287367249697172654705", "1.00370643092574120198555947478435510341272877681400539586641957289322085680495259903292576", "0E-91" ] }, "root_record": { "r": "1.56003969001925312756198520798165680829282566026409183058926246077190298979189448147405264", "b": "0.0405601235530763748747899617877111514750895028485281604982334138043549905676352092272750586", "h": "0.00328433252676368474994044485115325729874859523282864311664974195495768011978375346401854352", "A": "0.412338428585692731599572586967419921880961805272625240775266319291145004518344616794585070", "denominator": "0.994876310903027430866351422476331999914141080025837370309457101401171237245550186043568663", "polynomial_residual": "-1.036835164342299192427849E-65", "bracket_initial_signs": [ "1.46650500557946720453751105906906402313278581335120065956197378786618792129539524826178439", "-1.99853234149791470881797621209125655563823811932616681340662988849613699466236744363867481" ], "bracket_derivative_max": "-5.53630930230640989074453102898949449934233140390356844668297237821840245899733613690451489", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "6E-91", "0E-182", "1.0E-89", "0E-182", "5.94435650686673300625471152806702473519201687771012022314278914163116513762961745714210367E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.1", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.008612519452903273, 0.0 ], "rh_scaled_inf": 6.938893903907228e-18, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.017422886843752733, "alfven_n": 0.0458833454189777, "fast": 0.8697857399426836 }, "right": { "slow": 0.02144518952387235, "alfven_n": 0.057309009083431575, "fast": 0.694810476965263 } }, "front_relative_normal_velocity": { "left": -0.6410083559482684, "right": -0.9999984769132877 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560039690019253, "pressure_ratio": 2.517349984882156, "entropy_over_cv": 0.18202131614737604, "tangential_field_ratio": 1.5629239372590118 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.125, "theta_Bn_degrees": 84.875, "compression": 1.5600489387257246, "u2x_km_s": -384.57709432528657, "u2y_km_s": -12.020593218634634, "speed2_km_s": 384.7649102257225, "signed_deflection_degrees": 1.7902914890317092, "p2_over_p1": 2.5174014973514374, "B2_over_B1": 1.559274113601273, "entropy_over_cv": 0.18203189809682646, "upstream_fast_Mach": 1.4392446956206788, "downstream_fast_Mach": 0.7369695771419094, "downstream_alfven_margin": 0.5948964781767315, "state_global_normalized": { "rho": "1.56004893872572463897669576996328395836753092914103930790246817722784176690340062501163327", "p": "0.102105804732574293691122887752523829277700397238702812735270663431235541500739057477821019", "u": [ "-0.640961823875477659285383406317370371206368162426499233256498340991961374200946031966804394", "-0.0200343220310577230391814279548270823084449021268282716522027016445320520066383732391535624", "-0E-91" ], "B": [ "0.0553995522375081241789453685509789945966556137922343149616976227383336031049409439135094182", "1.00371624163515132846506458944035856664695378974763822883196380165732268996615768815316402", "0E-91" ] }, "root_record": { "r": "1.56004893872572463897669576996328395836753092914103930790246817722784176690340062501163327", "b": "0.0405601930519023621639958026020383063884415533157825895029257466978059874714019519492353436", "h": "0.00331653033762622612663936397066355207635738133385334715147680755933425150616495706708143363", "A": "0.412306942934740480249805630598702119032624197449899650668827351820349841774807474741392968", "denominator": "0.994826050366534536708259354841794930820810403507869934515157622983137601369845621258739030", "polynomial_residual": "5.13104999359754974483652E-66", "bracket_initial_signs": [ "1.46647601870284920754613743174413904099692873162406619662255017604583275146142366646988708", "-1.99833811158446417075881912900154839940038408095708138170780713268915145445572045421562617" ], "bracket_derivative_max": "-5.53604085111795884763813877754579774755192623351083341120309677595435928281901467252281595", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-3E-91", "0E-182", "-6E-90", "0E-182", "-2.94207189610608518669283261540476570111880267729269925487365575873479102307025708731534754E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.125", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.008227126926047637, 0.0 ], "rh_scaled_inf": 4.3789766023053104e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7834199337491628e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -4.3789766023053104e-16 }, "characteristics": { "left": { "slow": 0.017508185459410987, "alfven_n": 0.04610752839896445, "fast": 0.8697835385031986 }, "right": { "slow": 0.02155013388491005, "alfven_n": 0.05758918780584588, "fast": 0.6948072299450787 } }, "front_relative_normal_velocity": { "left": -0.6410040065756959, "right": -0.9999976201773518 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600489387257246, "pressure_ratio": 2.517401497351437, "entropy_over_cv": 0.1820318980968264, "tangential_field_ratio": 1.5629616740729493 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.15, "theta_Bn_degrees": 84.85000000000001, "compression": 1.5600579178952523, "u2x_km_s": -384.5697217477551, "u2y_km_s": -11.98771561494135, "speed2_km_s": 384.75651548844564, "signed_deflection_degrees": 1.7854322301831695, "p2_over_p1": 2.5174517999636037, "B2_over_B1": 1.5592754981686596, "entropy_over_cv": 0.18204228705436307, "upstream_fast_Mach": 1.439249947249446, "downstream_fast_Mach": 0.7369665217939171, "downstream_alfven_margin": 0.594667940690599, "state_global_normalized": { "rho": "1.56005791789525238715015419584920090458032919836931254756314329829409000184631619438275086", "p": "0.102107845006523758830223346116782810360240627343739062160549442863854818184641273548081236", "u": [ "-0.640949536246258501401275754901371633027302763920341024410683559430949379927935162683326768", "-0.0199795260249022498853177641671860533924168131178494661768696864799392004549771410752590158", "-0E-91" ], "B": [ "0.0552417997976615597401978774746656926943879972299467263264766761411861594323246580021904596", "1.00372583022128500332772051145169897000523520024468282430149293218718603874111837926883109", "0E-91" ] }, "root_record": { "r": "1.56005791789525238715015419584920090458032919836931254756314329829409000184631619438275086", "b": "0.0405602779951275288565800304749850645767945372882211090655436534232574423330792952718075250", "h": "0.00334888526624858789845498168789933132280152085074437467779456354910194002147409222654311415", "A": "0.412275458425995794125009787073194347802375127666430235257555093253509766867267522235973317", "denominator": "0.994775545024266140030043885724086695319510952441543193050434162961689353812526767140220259", "polynomial_residual": "-6.53640180748139715725815E-66", "bracket_initial_signs": [ "1.46644543146995746262461073365121100020584059025458011024036130120488280450307804862015018", "-1.99814524338990551047023336688022643751740031263833592433475450599559043466155421068686221" ], "bracket_derivative_max": "-5.53577241278984794853653857592970879435970534105007676339882205910816895929608533066531231", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-4E-91", "0E-182", "-6E-90", "0E-182", "3.74832874763826160970987982458459256247794579732701240296412337429696226221430123236638064E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.15", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.007841733311789811, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": -2.220446049250313e-16, "normal_momentum": 1.7834692701379637e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1895534492640346e-16 }, "characteristics": { "left": { "slow": 0.017593482931747912, "alfven_n": 0.046331705274550224, "fast": 0.86978122751741 }, "right": { "slow": 0.021655075615906186, "alfven_n": 0.057869355564091736, "fast": 0.6948039671407183 } }, "front_relative_normal_velocity": { "left": -0.6409996459651492, "right": -0.9999965730559848 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600579178952523, "pressure_ratio": 2.5174517999636037, "entropy_over_cv": 0.18204228705436332, "tangential_field_ratio": 1.5629992822969834 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.175, "theta_Bn_degrees": 84.825, "compression": 1.5600666275187625, "u2x_km_s": -384.5624443428738, "u2y_km_s": -11.954832325132019, "speed2_km_s": 384.74821846876426, "signed_deflection_degrees": 1.7805714725917003, "p2_over_p1": 2.5175008925830205, "B2_over_B1": 1.5592765765541288, "entropy_over_cv": 0.1820524829996554, "upstream_fast_Mach": 1.4392549576068916, "downstream_fast_Mach": 0.736963546328087, "downstream_alfven_margin": 0.5944393980571318, "state_global_normalized": { "rho": "1.56006662751876243950630303882554803595177982688657249273285924347558859477255558674009621", "p": "0.102109836203167307160972490289856228745542990683260471702482496828896144510009468038175081", "u": [ "-0.640937407238122991578528519309043114232192696842207700386978904823038195103776874016593022", "-0.0199247205418866975365960072597813221710073246712229468532543708868960778967642119578388743", "-0E-91" ], "B": [ "0.0550840393082397860487954325764089693551310686993353501538501928654985870171962712327148196", "1.00373519667658616123229153317362316242442673567431080544588101218968385052871821398677592", "0E-91" ] }, "root_record": { "r": "1.56006662751876243950630303882554803595177982688657249273285924347558859477255558674009621", "b": "0.0405603783828812520447198046610121707280023574929290309345355794333882038756882219571498701", "h": "0.00338139732593757592483955507478990002243564282806936569360207484191198991127566984795131834", "A": "0.412243975047477604556967100922418715759880677377827059467427453930803721449953148584175040", "denominator": "0.994724794877423604388635683208175562853756473924567583814205777670776085018846927459820452", "polynomial_residual": "1.0057447647312194998195E-67", "bracket_initial_signs": [ "1.46641324402763752253493193313598135410388033020552054851937325181563784463379547274637371", "-1.99795373658466645742592069503082404325992717299271799247932985172605097710513003874777593" ], "bracket_derivative_max": "-5.53550398703503258376307146925845762976508912784172946176379471427611610956671577614934042", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.03149883827390078537731598353834080644029647998689947757087192409834926130563037421001190E-90", "3E-91", "0E-182", "7E-90", "0E-182", "-5.76817730731411059689509435018761918832809063213766580338595919915064263323467269829182862E-69", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.175", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.007456338647994208, 0.0 ], "rh_scaled_inf": 2.189619721044598e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7835193777907956e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.189619721044598e-16 }, "characteristics": { "left": { "slow": 0.017678779259203033, "alfven_n": 0.046555876061286694, "fast": 0.8697788069873611 }, "right": { "slow": 0.021760014703972513, "alfven_n": 0.058149512304829155, "fast": 0.6948006885535549 } }, "front_relative_normal_velocity": { "left": -0.6409952741184184, "right": -0.9999953355493857 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600666275187625, "pressure_ratio": 2.5175008925830205, "entropy_over_cv": 0.18205248299965537, "tangential_field_ratio": 1.5630367619294916 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.2, "theta_Bn_degrees": 84.80000000000001, "compression": 1.5600750675870263, "u2x_km_s": -384.55526211600966, "u2y_km_s": -11.921943418658785, "speed2_km_s": 384.7400191765741, "signed_deflection_degrees": 1.775709230142189, "p2_over_p1": 2.517548775075492, "B2_over_B1": 1.5592773487625948, "entropy_over_cv": 0.18206248591256785, "upstream_fast_Mach": 1.4392597266874225, "downstream_fast_Mach": 0.736960650744356, "downstream_alfven_margin": 0.594210850262639, "state_global_normalized": { "rho": "1.56007506758702631540770158803568633625117969085170573169303390308023098746740969779731892", "p": "0.102111778317061952196128427920272519417350003323100267976914871026576620926677982238346029", "u": [ "-0.640925436860016114668478625768743075884888862562811808671311597981146541407692880917377141", "-0.0198699056977646425108735192616662706384456177091228196295417765378382871269693066187316124", "-0E-91" ], "B": [ "0.0549262709999472973037548965107168188671342688216719303185924399060326838915576689177681352", "1.00374434099361615816627325488187534900890213027534377885495054019153881986673991871424273", "0E-91" ] }, "root_record": { "r": "1.56007506758702631540770158803568633625117969085170573169303390308023098746740969779731892", "b": "0.0405604942153164329180062926258528772433580371432735496677928839195006418719396788324447012", "h": "0.00341406653023932784347109842739000816146660868945378975406633737262962964824507820786151125", "A": "0.412212492787206564366911761246618294917010391805378010853860497110200078402570843258309224", "denominator": "0.994673799927090276192758711570258143155518580821291784388254576227227301630078284154109516", "polynomial_residual": "-4.59494575211443401933470E-66", "bracket_initial_signs": [ "1.46637945652201428793664378014367460786820047473168418450968046039227757934498094396583833", "-1.99776359083836529067000502122050587099178859182288629875192696866262598322336621108160829" ], "bracket_derivative_max": "-5.53523557356445792661776254711826340089693668024068584113738458247083456504391068844894265", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "1E-91", "0E-182", "-3E-90", "0E-182", "2.63562179370909334953752595135264312342938067359036335288009850676191453065870007652703380E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.2", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.007070942972523711, 0.0 ], "rh_scaled_inf": 1.7835702567992828e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7835702567992828e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.017764074440214363, "alfven_n": 0.04678004077472915, "fast": 0.8697762769151175 }, "right": { "slow": 0.021864951136219935, "alfven_n": 0.058429657974720245, "fast": 0.6947973941849679 } }, "front_relative_normal_velocity": { "left": -0.6409908910373682, "right": -0.9999939076577904 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600750675870263, "pressure_ratio": 2.517548775075492, "entropy_over_cv": 0.1820624859125678, "tangential_field_ratio": 1.5630741129685732 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.225, "theta_Bn_degrees": 84.775, "compression": 1.560083238090661, "u2x_km_s": -384.54817507253733, "u2y_km_s": -11.889048964976956, "speed2_km_s": 384.73191762175185, "signed_deflection_degrees": 1.7708455167238506, "p2_over_p1": 2.517595447308261, "B2_over_B1": 1.5592778147989785, "entropy_over_cv": 0.18207229577315948, "upstream_fast_Mach": 1.439264254485451, "downstream_fast_Mach": 0.7369578350427882, "downstream_alfven_margin": 0.5939822972935017, "state_global_normalized": { "rho": "1.56008323809066096970658117801799991357557535114918631488169857172927595151780113645676595", "p": "0.102113671342823071974954730493084685009260798618458780733999812251141571961532943594046946", "u": [ "-0.640913625120895541192875654152239859913514094122130871148187050704056643466917942211359869", "-0.0198150816082949249364269474228107127781945106186034719346862278330929659028945441936445020", "-0E-91" ], "B": [ "0.0547684951034958682835475979203400408760104871420854384170854071609929483774182055780518278", "1.00375326316505375846333708223599674979319575409726914127016261585838109237236861164542087", "0E-91" ] }, "root_record": { "r": "1.56008323809066096970658117801799991357557535114918631488169857172927595151780113645676595", "b": "0.0405606254926094972583270082033434704507591428039315741152122677288640122496229784586842957", "h": "0.00344689289293933636721689798691186753994208517572738356870818786229834594258472879720701587", "A": "0.412181011633205029639664645691074657792421339575805396729021303043012399025214256798945877", "denominator": "0.994622560174231514130512501606199080315928948880595779426745757868083626729490064734842950", "polynomial_residual": "-6.519018946687076600362E-68", "bracket_initial_signs": [ "1.46634406909849252866124008695486939537870314991984901875501426689811638220329778532972305", "-1.99757480581981000575007237967998042014507731684347960624706421280358998034202251846908829" ], "bracket_derivative_max": "-5.53496717208705825971906941786404724949674234478567057614068431619821160963233269758301699", "iterations": 216 }, "flux_residuals": [ "0E-90", "1.60634528865412958551916028223699444531426357557658534668228637811895254176841153743836040E-89", "-4E-91", "0E-182", "-6E-90", "0E-182", "3.73970045446412519455557364261523888817460113441914097971083544288991917906720706738750785E-69", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.225", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.006685546323239566, 0.0 ], "rh_scaled_inf": 2.189755636109116e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.189755636109116e-16 }, "characteristics": { "left": { "slow": 0.017849368473218524, "alfven_n": 0.047004199430436655, "fast": 0.8697736373027668 }, "right": { "slow": 0.02196988489975848, "alfven_n": 0.05870979252042923, "fast": 0.6947940840363441 } }, "front_relative_normal_velocity": { "left": -0.6409864967239384, "right": -0.9999922893814706 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560083238090661, "pressure_ratio": 2.5175954473082616, "entropy_over_cv": 0.18207229577315942, "tangential_field_ratio": 1.5631113354120472 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.25, "theta_Bn_degrees": 84.75000000000001, "compression": 1.5600911390201289, "u2x_km_s": -384.541183217839, "u2y_km_s": -11.856149033544938, "speed2_km_s": 384.72391381415486, "signed_deflection_degrees": 1.7659803462301837, "p2_over_p1": 2.5176409091500105, "B2_over_B1": 1.5592779746682053, "entropy_over_cv": 0.18208191256168385, "upstream_fast_Mach": 1.4392685409953945, "downstream_fast_Mach": 0.7369550992235762, "downstream_alfven_margin": 0.5937537391361716, "state_global_normalized": { "rho": "1.56009113902012877643442567374297560082758599845415898290265946962616284893907237197270754", "p": "0.102115515275124421282242852488651235387326634451510982509404757944920211067830251012261797", "u": [ "-0.640901972029731633002150597637264198047618679654670895585839054734637003684592967901314368", "-0.0197602483892415639362077998076238780988528721437198596247613601021896711190617716985884122", "-0E-91" ], "B": [ "0.0546107118496045758617447171294311494418606720792042514848473180145174088726295168039895864", "1.00376196318369512162786221962765771818679130085025352811029997073660911523649718010678961", "0E-91" ] }, "root_record": { "r": "1.56009113902012877643442567374297560082758599845415898290265946962616284893907237197270754", "b": "0.0405607722149603960108912951723827369849545859112165044319662153960105672976896060002203784", "h": "0.00347987642806247335582874991605456364825423234004823281015732907772252236001974007354536211", "A": "0.412149531573497041503280912805673851690249962766333253474420880354488027407590933656175931", "denominator": "0.994571075619694718724508075952527496856830835049313314284967188124807648203386579066050405", "polynomial_residual": "1.185899600177707212529754E-65", "bracket_initial_signs": [ "1.46630708190175740941733915440957099552947250155489564462736138630645645788736150758115021", "-1.99738738119699746876552655962070389269228364417540641146092777591918427325256032640984673" ], "bracket_derivative_max": "-5.53469878230975628769693947028055858079749151665057752450356794180663577855228866673611978", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.03184254437424765239162692293522095784773416637016919685488482779474276076447623379498165E-90", "6E-91", "0E-182", "4E-90", "0E-182", "-6.80384420679799116137139159616165987591657803279466829754413780673614631147420318061892767E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.25", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.0063001487380012515, 0.0 ], "rh_scaled_inf": 1.7836743292567957e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7836743292567957e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.017934661356650786, "alfven_n": 0.04722835204397212, "fast": 0.8697708881524188 }, "right": { "slow": 0.022074815981697322, "alfven_n": 0.05898991588862245, "fast": 0.6947907581090764 } }, "front_relative_normal_velocity": { "left": -0.6409820911801437, "right": -0.9999904807207345 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600911390201289, "pressure_ratio": 2.5176409091500105, "entropy_over_cv": 0.1820819125616837, "tangential_field_ratio": 1.5631484292574553 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.275, "theta_Bn_degrees": 84.725, "compression": 1.5600987703657374, "u2x_km_s": -384.5342865573045, "u2y_km_s": -11.823243693824203, "speed2_km_s": 384.71600776362123, "signed_deflection_degrees": 1.7611137325589308, "p2_over_p1": 2.5176851604708617, "B2_over_B1": 1.559277828375207, "entropy_over_cv": 0.18209133625858923, "upstream_fast_Mach": 1.439272586211675, "downstream_fast_Mach": 0.7369524432870399, "downstream_alfven_margin": 0.5935251757771717, "state_global_normalized": { "rho": "1.56009877036573751263012625126321941315673075347435284960681663768424016957974742686757360", "p": "0.102117310108698143826500450506033729605671994377905204038013955865658174239838572755350083", "u": [ "-0.640890477595507449423381655445831526516035222560630578423615521074637703322775037291421835", "-0.0197054061563736729815921722941490747609487197441866421209822669982726578599407007995479577", "-0E-91" ], "B": [ "0.0544529214689998205705362521634192621104690146763091442231043394220921872489345835520013715", "1.00377044104245378896647378095636302990286565926620635055437001388696870980338789414515021", "0E-91" ] }, "root_record": { "r": "1.56009877036573751263012625126321941315673075347435284960681663768424016957974742686757360", "b": "0.0405609343825926059314021282710551580829781445346099320667590669072625992805641082471141248", "h": "0.00351301714987301466246129756633825420322250395157861851497507637601401679594670189249748675", "A": "0.412118052596108307914151770658875760414914649505854300976406576355597170079596606683783562", "denominator": "0.994519346264209362014680632668290699277477159869178391781048670243102858031287807071677781", "polynomial_residual": "5.96053841796909546774709E-66", "bracket_initial_signs": [ "1.46626849507577501992928221552255668486207306504847480371264851655429472282459183412282590", "-1.99720131663711255752859468090818993061655052329180227117822743271828217570842587278375957" ], "bracket_derivative_max": "-5.53443040393746243623505842889677694940021680340574967487174270762304697216959081383971841", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.03196017802839751864657417058456176918544865152372864291410418962522994372770734904681234E-90", "0E-91", "0E-182", "-3E-90", "0E-182", "-3.42013922621730449622149718566531084917082904820985877876460308338283154752537442486017392E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.275", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.0059147502546663695, 0.0 ], "rh_scaled_inf": 2.189896047358952e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.189896047358952e-16 }, "characteristics": { "left": { "slow": 0.018019953088945113, "alfven_n": 0.0474524986309024, "fast": 0.8697680294662054 }, "right": { "slow": 0.022179744369144747, "alfven_n": 0.05927002802596837, "fast": 0.694787416404565 } }, "front_relative_normal_velocity": { "left": -0.6409776744080741, "right": -0.9999884816759264 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600987703657374, "pressure_ratio": 2.5176851604708617, "entropy_over_cv": 0.1820913362585893, "tangential_field_ratio": 1.5631853945020577 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.3, "theta_Bn_degrees": 84.7, "compression": 1.5601061321176404, "u2x_km_s": -384.52748509633125, "u2y_km_s": -11.790333015279225, "speed2_km_s": 384.70819947997006, "signed_deflection_degrees": 1.756245689612033, "p2_over_p1": 2.5177282011423765, "B2_over_B1": 1.5592773759249208, "entropy_over_cv": 0.1821005668445183, "upstream_fast_Mach": 1.439276390128721, "downstream_fast_Mach": 0.7369498672336273, "downstream_alfven_margin": 0.5932966072030955, "state_global_normalized": { "rho": "1.56010613211764034230676181221513796745819200852504994650850294542578926175457059275576192", "p": "0.102119055838334784377324300317580571675688737834947923214743671472321590638642956506833928", "u": [ "-0.640879141827218753898102760776406898914214653184984287095726086041511498108759448526645235", "-0.0196505550254653752154346825608857785988337615461115460538553206696257747936912755757539573", "-0E-91" ], "B": [ "0.0542951241924153482129158270969397602380325996291923009219586966003353888376656424765875178", "1.00377869673436067002650521833178234687047618913630571682380836405482723775906143451400967", "0E-91" ] }, "root_record": { "r": "1.56010613211764034230676181221513796745819200852504994650850294542578926175457059275576192", "b": "0.0405611119957531303093778266819231681773978719523325961387647171396334062564616532954307938", "h": "0.00354631507287466575510914846031653033860768404962162047598536873624198204015258127343072523", "A": "0.412086574689066185447501579877086982229291592226986866524764367271706652429359802808324155", "denominator": "0.994467372108387017368903202516754202352897469412654020883157651887536079645766163421504284", "polynomial_residual": "8.28718338979152996825579E-66", "bracket_initial_signs": [ "1.46622830876379290951188329769617541692902947488291470166958457340514383031180679039479795", "-1.99701661180652728983519400238362499118279374320253282460815425436729219602829990224355851" ], "bracket_derivative_max": "-5.53416203667307413746006199223713990918448964958327830481422602743955818076627872287786303", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-3E-91", "0E-182", "-1E-90", "0E-182", "-4.75572892069633097836443151635178663736204227550311137840739430591416071129703220400703304E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_0.3", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.005529350911090522, 0.0 ], "rh_scaled_inf": 2.1899679393790674e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1899679393790674e-16 }, "characteristics": { "left": { "slow": 0.018105243668534252, "alfven_n": 0.04767663920679842, "fast": 0.8697650612462802 }, "right": { "slow": 0.022284670049208175, "alfven_n": 0.05955012887913758, "fast": 0.6947840589242164 } }, "front_relative_normal_velocity": { "left": -0.640973246409894, "right": -0.9999862922474267 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601061321176404, "pressure_ratio": 2.5177282011423765, "entropy_over_cv": 0.18210056684451836, "tangential_field_ratio": 1.5632222311428376 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.325, "theta_Bn_degrees": 84.675, "compression": 1.5601132242658358, "u2x_km_s": -384.5207788403244, "u2y_km_s": -11.75741706737743, "speed2_km_s": 384.7004889730008, "signed_deflection_degrees": 1.75137623129559, "p2_over_p1": 2.5177700310375566, "B2_over_B1": 1.5592766173222896, "entropy_over_cv": 0.18210960430030837, "upstream_fast_Mach": 1.4392799527409652, "downstream_fast_Mach": 0.7369473710639142, "downstream_alfven_margin": 0.5930680334006078, "state_global_normalized": { "rho": "1.56011322426583580055705858972054270910705413655565133212219782358799994008475186015185950", "p": "0.102120752458883300861976345594970972449797030747823422587246717238465634445573522654032367", "u": [ "-0.640867964733874021110103524928613437231892778274088829002202405733042225538208311458117914", "-0.0195956951122957187442363714024730944137138618801301091154433471644823268261423280733648181", "-0E-91" ], "B": [ "0.0541373202505922715243240818902738732388723975475880228315151220972446180260233449634426324", "1.00378673025256402884130284743583270785291268432120869985037708854772236530673032291053648", "0E-91" ] }, "root_record": { "r": "1.56011322426583580055705858972054270910705413655565133212219782358799994008475186015185950", "b": "0.0405613050547124997676276980699786726459489815989846011727408467879826524737328136232887305", "h": "0.00357977021181058811306275643945725015019323052894453359567478117308675894028366287638725751", "A": "0.412055097840399661093221479254214104761689286402775990439957166039568653917661501906424082", "denominator": "0.994415153152721389421526607651690245673797639503459200683268991605851952877365330036329677", "polynomial_residual": "-1.156040806451408791344763E-65", "bracket_initial_signs": [ "1.46618652310834062608412245271519676608345246097642981158445817214262998250284374948915437", "-1.99683326637079993884274822677433594607787256724778288756828431271927978682528556609984997" ], "bracket_derivative_max": "-5.53389368021747510167537162555418341139787425511384237888808318013756062129026210583058933", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "-1E-91", "0E-182", "-1E-90", "0E-182", "6.63491168089778477441288199560268616128456663900375860950701887390305050823680575992140940E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.325", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.005143950745127189, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.018190533093849787, "alfven_n": 0.047900773787235264, "fast": 0.8697619834948199 }, "right": { "slow": 0.02238959300899415, "alfven_n": 0.05983021839480285, "fast": 0.694780685669444 } }, "front_relative_normal_velocity": { "left": -0.6409688071878431, "right": -0.9999839124356527 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601132242658358, "pressure_ratio": 2.517770031037557, "entropy_over_cv": 0.18210960430030854, "tangential_field_ratio": 1.5632589391764973 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.35, "theta_Bn_degrees": 84.65, "compression": 1.5601200468001677, "u2x_km_s": -384.5141677946967, "u2y_km_s": -11.724495919589156, "speed2_km_s": 384.69287625249393, "signed_deflection_degrees": 1.7465053715198164, "p2_over_p1": 2.517810650030845, "B2_over_B1": 1.5592755525722624, "entropy_over_cv": 0.1821184486069911, "upstream_fast_Mach": 1.4392832740428456, "downstream_fast_Mach": 0.7369449547786043, "downstream_alfven_margin": 0.5928394543564438, "state_global_normalized": { "rho": "1.56012004680016777779758472364435327935266311044151507057475971740018887292358000944698566", "p": "0.102122399965251076421181247798116752283045249108447677634767571001832987606588065664195408", "u": [ "-0.640856946324494444603372259406661367410214810891123499921198222231165558264457649467712777", "-0.0195408265326485918992360328684553242054145048143652311863168879730749964857961071610930508", "-0E-91" ], "B": [ "0.0539795098742790918845438655634670481006197416487207678499882362989558585500327652959987707", "1.00379454159032946998228982578084818917722366349083108381402108636178547609136613857990982", "0E-91" ] }, "root_record": { "r": "1.56012004680016777779758472364435327935266311044151507057475971740018887292358000944698566", "b": "0.0405615135597647731378860543363343382234264436069647730472947432695003113665735545508559106", "h": "0.00361338258166342639848736013069439312880301512690705814548429994095432889993017236221031495", "A": "0.412023622038139334056980751724137024503522106860505209114826205769701071722628110398239373", "denominator": "0.994362689397588344139972161771184406522254544535486443049288121887296030589339447596883068", "polynomial_residual": "-1.186231660005336501506371E-65", "bracket_initial_signs": [ "1.46614313825123025962463987125692494977872481771167679920589610970052429826182247776424652", "-1.99665127999467413555191854285961004523151555130874230049948465221308587013986367474811731" ], "bracket_derivative_max": "-5.53362533426953457543720486000806156683581427834034844072810564542567148472701727174021062", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.03232227542277672322872359689758446609308035367569282548148363108513153491334443627553693E-90", "1E-91", "0E-182", "0E-90", "0E-182", "6.80899985396957501657021366655499570208242153898184116882023028766746537748498550381513147E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.35", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.004758549794627621, 0.0 ], "rh_scaled_inf": 3.567783469256541e-16, "rh_components": { "mass": -2.220446049250313e-16, "normal_momentum": 3.567783469256541e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": -0.0, "energy": -2.1901150968795444e-16 }, "characteristics": { "left": { "slow": 0.018275821363322186, "alfven_n": 0.048124902387792275, "fast": 0.8697587962140223 }, "right": { "slow": 0.02249451323560831, "alfven_n": 0.060110296519639075, "fast": 0.6947772966416679 } }, "front_relative_normal_velocity": { "left": -0.640964356744236, "right": -0.9999813422410571 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601200468001677, "pressure_ratio": 2.517810650030845, "entropy_over_cv": 0.1821184486069911, "tangential_field_ratio": 1.5632955185994595 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.375, "theta_Bn_degrees": 84.625, "compression": 1.5601265997103255, "u2x_km_s": -384.50765196486833, "u2y_km_s": -11.691569641387582, "speed2_km_s": 384.6853613282104, "signed_deflection_degrees": 1.7416331241989986, "p2_over_p1": 2.5178500579981247, "B2_over_B1": 1.559274181679793, "entropy_over_cv": 0.1821270997457927, "upstream_fast_Mach": 1.4392863540288057, "downstream_fast_Mach": 0.7369426183785293, "downstream_alfven_margin": 0.5926108700574094, "state_global_normalized": { "rho": "1.56012659971032550415173780468482154954563543117133338484382904108673962574361195009931818", "p": "0.102123998352403931424163642444686398014429215474832606971210773211327283692276328419314111", "u": [ "-0.640846086608113944890336720515715116738783860726335049571101249866023467102056035611061855", "-0.0194859494023126384662341322610779123528846472524693402894253845841600285333586141572841000", "-0E-91" ], "B": [ "0.0538216932942317210806409427819065455906317691394721719925916929027272110200714462664880755", "1.00380213074103992441770651686506987227321668780170533886691856847807346738046156036273450", "0E-91" ] }, "root_record": { "r": "1.56012659971032550415173780468482154954563543117133338484382904108673962574361195009931818", "b": "0.0405617375112275384126094633700225092852717094229413896618489595795027382725777074880918329", "h": "0.00364715219765533640323357529871234716929148204406748894764204354010666827452016611473884533", "A": "0.411992147270317397566557177811242426857189759905105760281960871928562495386114201422351490", "denominator": "0.994309980843245939019504664249869417013551186004280568204866466985389849498389204907097706", "polynomial_residual": "5.75384228313016096245546E-66", "bracket_initial_signs": [ "1.46609815433355699007195398666372312639483164213369870209822997449833133977023066073660481", "-1.99647065234207795838909161924492033291094669678726028026744759820485605996730359178566813" ], "bracket_derivative_max": "-5.53335699852610658597019972772989194261497216762114640292719352476057730780720975844290341", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.03244604041508186077125428769644971576963010272687385944443840170952284631126497135505659E-90", "2E-91", "0E-182", "-2E-90", "0E-182", "-3.30311421714351454656594094132084701022237697172255854597116465366154684943181557064379092E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.375", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.004373148097440709, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.01836110847538088, "alfven_n": 0.04834902502405315, "fast": 0.8697554994061081 }, "right": { "slow": 0.022599430716155437, "alfven_n": 0.06039036320032334, "fast": 0.694773891842315 } }, "front_relative_normal_velocity": { "left": -0.6409598950814626, "right": -0.9999785816641292 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601265997103255, "pressure_ratio": 2.5178500579981247, "entropy_over_cv": 0.18212709974579266, "tangential_field_ratio": 1.5633319694078682 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.4, "theta_Bn_degrees": 84.60000000000001, "compression": 1.5601328829858436, "u2x_km_s": -384.5012313562675, "u2y_km_s": -11.658638302248704, "speed2_km_s": 384.6779442098918, "signed_deflection_degrees": 1.7367595032514536, "p2_over_p1": 2.5178882548167194, "B2_over_B1": 1.5592725046498417, "entropy_over_cv": 0.18213555769813372, "upstream_fast_Mach": 1.4392891926932938, "downstream_fast_Mach": 0.7369403618646482, "downstream_alfven_margin": 0.5923822804903811, "state_global_normalized": { "rho": "1.56013288298584353397158560941921836625815807494417863203575715107894751475107841478712236", "p": "0.102125547615366135442943142677447174854556580564967442499263689548928747605134479907309023", "u": [ "-0.640835385593779178050560205667772229185390550724616389849725204016861361341392991906799549", "-0.0194310638370811728839581649534963357412815337990021097476442868460896490587673540046217703", "-0E-91" ], "B": [ "0.0536638707412135031217444176940297809742759455476028163216588821423144551042375239584631049", "1.00380949769819563517794374924561939748897345175167886442472503847608027312945138911822444", "0E-91" ] }, "root_record": { "r": "1.56013288298584353397158560941921836625815807494417863203575715107894751475107841478712236", "b": "0.0405619769094419137729425242408459786527149366814289799471866396821867465752464206539267185", "h": "0.00368107907524801377099254581348824994594877976887575100055637768073442829687835560638740701", "A": "0.411960673524967620683327652671244645382875544322477499951343685785369529934751885374700863", "denominator": "0.994257027489834453406314353295612423615534227789836677101882621604761285958995474490658359", "polynomial_residual": "2.66541807063383848617220E-66", "bracket_initial_signs": [ "1.46605157149569963967239228209960334650184642756758255497973440261855349623403114278076455", "-1.99629138307612300988634373342808670562886032410662750350629889876764036411913120478662154" ], "bracket_derivative_max": "-5.53308867268202917191998223561895274350826206614724319498609612768758482605578191055694020", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.03257133853324137821332758440707920247844587787866840233095935075556940263441496694056507E-90", "-3E-91", "0E-182", "-2E-90", "0E-182", "-1.53032189406908032475437132008997570517556885394456440068873472795761679856891917091573648E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.4", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.003987745691412874, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.018446394428454325, "alfven_n": 0.048573141711606094, "fast": 0.8697520930733194 }, "right": { "slow": 0.022704345437739398, "alfven_n": 0.060670418383534895, "fast": 0.6947704712728188 } }, "front_relative_normal_velocity": { "left": -0.6409554222019872, "right": -0.9999756307053947 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601328829858436, "pressure_ratio": 2.5178882548167194, "entropy_over_cv": 0.18213555769813372, "tangential_field_ratio": 1.5633682915975875 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.425, "theta_Bn_degrees": 84.575, "compression": 1.5601388966161018, "u2x_km_s": -384.49490597432975, "u2y_km_s": -11.625701971651257, "speed2_km_s": 384.67062490726056, "signed_deflection_degrees": 1.7318845225994857, "p2_over_p1": 2.517925240365395, "B2_over_B1": 1.5592705214873739, "entropy_over_cv": 0.18214382244562913, "upstream_fast_Mach": 1.439291790030764, "downstream_fast_Mach": 0.7369381852380484, "downstream_alfven_margin": 0.5921536856423056, "state_global_normalized": { "rho": "1.56013889661610173049862247221468021447589532826090224091688832498249835561066564425049639", "p": "0.102127047749220419185904966716936974271135789448325888211171158993208988681893638527235953", "u": [ "-0.640824843290549544820053617324087032397718868664939939188730886905341157423413020952555361", "-0.0193761699527520954107779992938213220309649724656642048653269086660963312654310317812319056", "-0E-91" ], "B": [ "0.0535060424459952361064615781774683594146371689162781029744066972623721822670682112979110430", "1.00381664245541414282738505481441013855500811888504159732861358154223355317380635318238748", "0E-91" ] }, "root_record": { "r": "1.56013889661610173049862247221468021447589532826090224091688832498249835561066564425049639", "b": "0.0405622317547725486928578764816827644711590648053755605564398625137057034873841583435459228", "h": "0.00371516323014272349491286591005412972418349662930661428298674146835175385737791083146787992", "A": "0.411929200790125330118860371506541038589137177049088742346424010364433071192001172524688822", "denominator": "0.994203829337376418949037595796269810124523268770561935357932354706726675446107119166891353", "polynomial_residual": "9.06647272928669745367311E-66", "bracket_initial_signs": [ "1.46600338987732122977878914684308623260116579331402819723422627863097444749205236272873861", "-1.99611347185910348045547718349894543394021717914221415856229721702124865344320245356241990" ], "bracket_derivative_max": "-5.53282035643012360043989504896967488269014995997858142975209506946899298414312185929564403", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.03269816989671320158981290965230126941411284920863788640334477841487837887316126532638663E-90", "4E-91", "0E-182", "8E-90", "0E-182", "-5.20604145097448646219724811529846767151978800684062525533969611606788578968213015890865014E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_0.425", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.003602342614387945, 0.0 ], "rh_scaled_inf": 4.3806885377074216e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -4.3806885377074216e-16 }, "characteristics": { "left": { "slow": 0.01853167922097006, "alfven_n": 0.048797252466043835, "fast": 0.869748577217921 }, "right": { "slow": 0.022809257387463158, "alfven_n": 0.0609504620159552, "fast": 0.6947670349346199 } }, "front_relative_normal_velocity": { "left": -0.6409509381083495, "right": -0.9999724893654156 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601388966161018, "pressure_ratio": 2.517925240365395, "entropy_over_cv": 0.1821438224456291, "tangential_field_ratio": 1.563404485164201 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.45, "theta_Bn_degrees": 84.55000000000001, "compression": 1.5601446405903252, "u2x_km_s": -384.48867582449833, "u2y_km_s": -11.592760719076683, "speed2_km_s": 384.66340343001946, "signed_deflection_degrees": 1.727008196169344, "p2_over_p1": 2.5179610145243587, "B2_over_B1": 1.5592682321973605, "entropy_over_cv": 0.1821518939700883, "upstream_fast_Mach": 1.4392941460356752, "downstream_fast_Mach": 0.7369360884999453, "downstream_alfven_margin": 0.5919250855002002, "state_global_normalized": { "rho": "1.56014464059032525066350596485487286915836693226342735524274996544147783651892114899734075", "p": "0.102128498749107986390663901425995948849042039023118300787887656395612640025685435540354703", "u": [ "-0.640814459707497200171367099253557216530169922369390657886324202528002186822477774830237481", "-0.0193212678651278072595794335379044857308482148396554590046495133875827330732193567168980615", "-0E-91" ], "B": [ "0.0533482086393551941437223685208527747470970641790380344152854701399648867244196563461366726", "1.00382356500643027074267354506641570023652576650209327008882449954178014286054155061438254", "0E-91" ] }, "root_record": { "r": "1.56014464059032525066350596485487286915836693226342735524274996544147783651892114899734075", "b": "0.0405625020476076251194765773625795671013792652055549153097770709850701435443703830712824436", "h": "0.00374940467828033019080079518642347725266151448998097841120942795534818845983173722182985561", "A": "0.411897729053827392056549916487545194559803543165974356071226505380580101117642593124296806", "denominator": "0.994150386385776650178847204223502819395031081503802060261462496153239553447519421492647835", "polynomial_residual": "-1.045324869473076200007658E-65", "bracket_initial_signs": [ "1.46595360961736954210307078225077903505436519669760793752175785618862769921084236488253961", "-1.99593691835249519925260208648365064882629734351323651768031037848074510684788643448982666" ], "bracket_derivative_max": "-5.53255204946119357060899481799458206047254216266455125531281588041716705957050290617013325", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.03282653462642159059075488996181096448314579167581630377865837288691846920354825280667192E-90", "1E-91", "0E-182", "1E-90", "0E-182", "6.00305531686882707429251574737665149862845555276120435502290560452821112117456080224814366E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.45", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.003216938904207039, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.018616962851354762, "alfven_n": 0.0490213573029638, "fast": 0.8697449518421998 }, "right": { "slow": 0.022914166552428793, "alfven_n": 0.06123049404426789, "fast": 0.6947635828291654 } }, "front_relative_normal_velocity": { "left": -0.6409464428031639, "right": -0.9999691576447897 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601446405903252, "pressure_ratio": 2.5179610145243587, "entropy_over_cv": 0.18215189397008835, "tangential_field_ratio": 1.563440550103013 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.475, "theta_Bn_degrees": 84.525, "compression": 1.5601501148975845, "u2x_km_s": -384.48254091222424, "u2y_km_s": -11.559814614009076, "speed2_km_s": 384.6562797878522, "signed_deflection_degrees": 1.7221305378911795, "p2_over_p1": 2.5179955771752596, "B2_over_B1": 1.559265636784779, "entropy_over_cv": 0.18215977225351485, "upstream_fast_Mach": 1.4392962607024915, "downstream_fast_Mach": 0.7369340716516816, "downstream_alfven_margin": 0.5916964800511522, "state_global_normalized": { "rho": "1.56015011489758453002484078084227449335062905953774943487040178051121374910681226691749835", "p": "0.102129900610228525676239149818224967869206391317793368716530143831511649485813461021398935", "u": [ "-0.640804234853707063384627840614662581061525440120011582665190592928782557171323426551618809", "-0.0192663576900151257006038797994559418733531165148331474011145229014869563770112066601725579", "-0E-91" ], "B": [ "0.0531903695520791493278492090013350836053968808212100982796679503471338822602755431733705488", "1.00383026534509611019731865788465598598156812633742727571233473991703556639464462847107150", "0E-91" ] }, "root_record": { "r": "1.56015011489758453002484078084227449335062905953774943487040178051121374910681226691749835", "b": "0.0405627877883588587295754043649693374268406572624970993444517601500709659253540072921899678", "h": "0.00378380343584132914602959741274010466405121737517430990243148889775769390120413672457207701", "A": "0.411866258304112193978236606334054388693879044415283082260947916664930882909295886561439925", "denominator": "0.994096698634822275218244383741125163402119284575328401260214072864171970869062978743788410", "polynomial_residual": "-1.071634112029320218609787E-65", "bracket_initial_signs": [ "1.46590223085407768442591283675593237616806275018168244851158675834176281364035622042028071", "-1.99576172221695467212961361571001821432200406738846238881283068116601379311642267064441925" ], "bracket_derivative_max": "-5.53228375146402440317831483489550125259367524439927782484109633450181713264676481443119662", "iterations": 216 }, "flux_residuals": [ "-2E-90", "-8.03295643284475742007715542460101114245517529367364753735856754038485451944343809677988771E-90", "1E-91", "0E-182", "-2E-90", "0E-182", "6.15487708696341001227793081598315220984579710155296945381285571831957689352205986474523397E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.475", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.002831534598708446, 0.0 ], "rh_scaled_inf": 2.1905026756469017e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.784180862987679e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1905026756469017e-16 }, "characteristics": { "left": { "slow": 0.018702245318034313, "alfven_n": 0.04924545623796818, "fast": 0.8697412169484643 }, "right": { "slow": 0.02301907291973747, "alfven_n": 0.06151051441515882, "fast": 0.694760114957909 } }, "front_relative_normal_velocity": { "left": -0.6409419362891203, "right": -0.9999656355441514 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601501148975845, "pressure_ratio": 2.5179955771752596, "entropy_over_cv": 0.18215977225351498, "tangential_field_ratio": 1.5634764864090485 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.5, "theta_Bn_degrees": 84.5, "compression": 1.5601553195267952, "u2x_km_s": -384.47650124296615, "u2y_km_s": -11.526863725935119, "speed2_km_s": 384.64925399042284, "signed_deflection_degrees": 1.717251561699002, "p2_over_p1": 2.518028928201189, "B2_over_B1": 1.5592627352546111, "entropy_over_cv": 0.18216745727810676, "upstream_fast_Mach": 1.4392981340256823, "downstream_fast_Mach": 0.7369321346947285, "downstream_alfven_margin": 0.5914678692823191, "state_global_normalized": { "rho": "1.56015531952679526784707894862720318383937705965595189567723770805060774532977400349570573", "p": "0.102131253327840222354557445912307751011352552114750393834566220092312132775244340184135382", "u": [ "-0.640794168738276828609693636306399236117355343797756185396584266122720844817154533851745397", "-0.0192114395432251991320617674146799387812705781774469590213942341709281535933304434737955104", "-0E-91" ], "B": [ "0.0530325254149603937686483968193389215462065312064857422098132926367517933693231119701472209", "1.00383674346538100525255758032446195011567316013768775271730765733022709234870289725873743", "0E-91" ] }, "root_record": { "r": "1.56015531952679526784707894862720318383937705965595189567723770805060774532977400349570573", "b": "0.0405630889774615002622880634260116429493427951505722161092245104062152679812048037829209587", "h": "0.00381835951924587814428814474654344855582863427840241688800329148704296790026403418034549957", "A": "0.411834788529019626495751497408975727080028086373555593455921860658447967213563688335693670", "denominator": "0.994042766084182766618685425522325122675016882690500904715978145609251028766905795985994812", "polynomial_residual": "1.7381412456983105051914E-67", "bracket_initial_signs": [ "1.46584925372496466076672215303971404058137107312296368900111242473126833125826003715294441", "-1.99558788311231810666879166831584400174968003472931019236163251837039377578265554279571575" ], "bracket_derivative_max": "-5.53201546212538221664227895522935630282586683770022061391102168496475582603441734507619919", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.03308786467557846502691583915421853047698211852707210524165320243537921076507802652179156E-90", "3E-91", "0E-182", "1E-90", "0E-182", "-9.98411799844464327410528040391817809342735259427943343785428141878070467694486392809958250E-69", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.5", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.002446129735727505, 0.0 ], "rh_scaled_inf": 1.7842410059261955e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7842410059261955e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.01878752661943387, "alfven_n": 0.049469549286664055, "fast": 0.8697373725390456 }, "right": { "slow": 0.023123976476489456, "alfven_n": 0.06179052307531607, "fast": 0.6947566313223111 } }, "front_relative_normal_velocity": { "left": -0.6409374185689832, "right": -0.9999619230641713 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601553195267952, "pressure_ratio": 2.518028928201189, "entropy_over_cv": 0.1821674572781068, "tangential_field_ratio": 1.563512294077051 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.525, "theta_Bn_degrees": 84.475, "compression": 1.5601602544667184, "u2x_km_s": -384.4705568221902, "u2y_km_s": -11.493908124344054, "speed2_km_s": 384.6423260473759, "signed_deflection_degrees": 1.7123712815306404, "p2_over_p1": 2.5180610674866806, "B2_over_B1": 1.5592595276118448, "entropy_over_cv": 0.18217494902625633, "upstream_fast_Mach": 1.4392997659997222, "downstream_fast_Mach": 0.7369302776306847, "downstream_alfven_margin": 0.5912392531809286, "state_global_normalized": { "rho": "1.56016025446671841231760772650221613410570479192833306269999709184078419376778074441930818", "p": "0.102132556897259770201301655866148511560037652868124907425575872100311675778226380888839686", "u": [ "-0.640784261370316975919594787115124392057024888110929121347952075519172713611491843065036077", "-0.0191565135405734221183269338847495435138342735681900513657331197540291947045305088522660101", "-0E-91" ], "B": [ "0.0528746764587997616773198444289071701450123213316836661170651664366454773581890597116452320", "1.00384299936137153745438572505331209464984058569693412967535505785939702448359245340819270", "0E-91" ] }, "root_record": { "r": "1.56016025446671841231760772650221613410570479192833306269999709184078419376778074441930818", "b": "0.0405634056153743369280077069439752030727664882195562133934972290890877464043375480208751518", "h": "0.00385307294515383006630324040220619738477083218588740653096567617487929904480785371938001962", "A": "0.411803319716591065187328452550893518061669897804045380654067516455369630952611510505147172", "denominator": "0.993988588733409972327177375210650507770338444729375744950589406891605010235163666091495641", "polynomial_residual": "-1.568438969984350138891935E-65", "bracket_initial_signs": [ "1.46579467836683594601725974012642418242471499663424931771109752022392182957792801434656636", "-1.99541540069760042429662688183263807797079899526340956907801999692165265998556246524575620" ], "bracket_derivative_max": "-5.53174718113001308963204195380871400266330419199465086471972431662111026736733510909161419", "iterations": 216 }, "flux_residuals": [ "-3E-90", "0", "3E-91", "0E-182", "1E-90", "0E-182", "9.01039937886870171215897336140805827379129935543379667338362759216833346156391378500468086E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.525", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.002060724353096493, 0.0 ], "rh_scaled_inf": 4.3813311683905034e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7843019215403971e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 2.220446049250313e-16, "t2_induction": -0.0, "energy": 4.3813311683905034e-16 }, "characteristics": { "left": { "slow": 0.01887280675397792, "alfven_n": 0.04969363646466346, "fast": 0.8697334186162968 }, "right": { "slow": 0.023228877209784077, "alfven_n": 0.06207051997142994, "fast": 0.6947531319238394 } }, "front_relative_normal_velocity": { "left": -0.6409328896455921, "right": -0.9999580202055561 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601602544667184, "pressure_ratio": 2.5180610674866806, "entropy_over_cv": 0.1821749490262563, "tangential_field_ratio": 1.563547973101485 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.55, "theta_Bn_degrees": 84.45, "compression": 1.5601649197059602, "u2x_km_s": -384.4647076553705, "u2y_km_s": -11.46094787872761, "speed2_km_s": 384.6354959683368, "signed_deflection_degrees": 1.7074897113276937, "p2_over_p1": 2.5180919949177114, "B2_over_B1": 1.559256013861474, "entropy_over_cv": 0.1821822474805501, "upstream_fast_Mach": 1.439301156619091, "downstream_fast_Mach": 0.7369285004612772, "downstream_alfven_margin": 0.5910106317342781, "state_global_normalized": { "rho": "1.56016491970596014590309876159820272648643081109848211305195200261837792265851505025748648", "p": "0.102133811313862383186121919816747432483174412665137473799501307975472091470297239111339167", "u": [ "-0.640774512758950782855439920443289810493289381773761071744499205534621682919912039349515857", "-0.0191015797978793503955189436776835396477879279678336113331802913906405061856545692327287980", "-0E-91" ], "B": [ "0.0527168229144056515089824384611585234406285390617101852465352647075751125505770622330706080", "1.00384903302727151033667020948405267723612404359846139984186066493173465108559043752308603", "0E-91" ] }, "root_record": { "r": "1.56016491970596014590309876159820272648643081109848211305195200261837792265851505025748648", "b": "0.0405637377025796938934985890193557260340210653482485439218230361565761901658563095006515465", "h": "0.00388794373046476626667442524369965907821870179293865179419500562659647985842164983892034253", "A": "0.411771851854869352438824720922241102039374304313768578751712407479696048465955045954778012", "denominator": "0.993934166581938146781978018461132953311491315715659868611132609656439564552132342901268439", "polynomial_residual": "-1.9047498610954816285374E-67", "bracket_initial_signs": [ "1.46573850491578406504228783950396839826223990453053092624007476351891792008376682409777134", "-1.99524427463099425947285383433770632966895070481614696027497506175177301906993547034060818" ], "bracket_derivative_max": "-5.53147890816064220962742071116319147413031703949586568492345060554345377490259291031131030", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "2E-91", "0E-182", "-1E-90", "0E-182", "1.09437493266210942350533290182054585517891391571355361794921322558518778126986577588258429E-68", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.55", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.0016753184886444984, 0.0 ], "rh_scaled_inf": 0.0, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.018958085720090348, "alfven_n": 0.04991771778758354, "fast": 0.869729355182593 }, "right": { "slow": 0.023333775106719773, "alfven_n": 0.062350505050192975, "fast": 0.6947496167639678 } }, "front_relative_normal_velocity": { "left": -0.6409283495218617, "right": -0.999953926969049 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601649197059602, "pressure_ratio": 2.518091994917712, "entropy_over_cv": 0.18218224748055012, "tangential_field_ratio": 1.563583523476533 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.575, "theta_Bn_degrees": 84.425, "compression": 1.5601693152329719, "u2x_km_s": -384.4589537479886, "u2y_km_s": -11.427983058579969, "speed2_km_s": 384.62876376291103, "signed_deflection_degrees": 1.7026068650354953, "p2_over_p1": 2.5181217103817013, "B2_over_B1": 1.5592521940084973, "entropy_over_cv": 0.18218935262376879, "upstream_fast_Mach": 1.439302305878274, "downstream_fast_Mach": 0.7369268031883606, "downstream_alfven_margin": 0.5907820049297352, "state_global_normalized": { "rho": "1.56016931523297187084519432634040624053732472363013129248376544037103458955327080295405068", "p": "0.102135016573081807162226224301470711583653473032791423808738319917199909879529719060216753", "u": [ "-0.640764922913314336462964311876708265297835567204559703459663590713024990876572070372128682", "-0.0190466384309666158442799436360375774451043248369736414401341030422947597580440586150124685", "-0E-91" ], "B": [ "0.0525589650125940481626128351867383266055970425961908755849239128641135346466811585825717646", "1.00385484445740193373025985722086029779321594057771051592067899819547990815260249317654323", "0E-91" ] }, "root_record": { "r": "1.56016931523297187084519432634040624053732472363013129248376544037103458955327080295405068", "b": "0.0405640852395834358432251089566454197310914236622171177143675539720010455474108390282653169", "h": "0.00392297189231803072696434719550251172939972149075195466266970247875429002794694740965539687", "A": "0.411740384931898779289691498876473376108662186322857279538867778578418384671923388476603491", "denominator": "0.993879499629083982137536638567612245133375998447535862253383786420598686973454717284852802", "polynomial_residual": "1.575888045217815434682281E-65", "bracket_initial_signs": [ "1.46568073350718917625068973835447210009496872614714325668781338716086710870094100851006166", "-1.99507450456986894595054916466319814640025557070419327839174137713652424573165291560993532" ], "bracket_derivative_max": "-5.53121064289797300798396984055823059822116359890160773612055530000341015830986781151864357", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "2E-91", "0E-182", "0E-90", "0E-182", "-9.05535141415973796503692620046619556582524276677868100461905500740977458759821312616703213E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.575", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.0012899121801973083, 0.0 ], "rh_scaled_inf": 1.7844260712431665e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7844260712431665e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.01904336351619448, "alfven_n": 0.050141793271046606, "fast": 0.8697251822403315 }, "right": { "slow": 0.023438670154394044, "alfven_n": 0.06263047825829997, "fast": 0.694746085844177 } }, "front_relative_normal_velocity": { "left": -0.6409237982007817, "right": -0.9999496433554291 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601693152329719, "pressure_ratio": 2.5181217103817017, "entropy_over_cv": 0.1821893526237689, "tangential_field_ratio": 1.5636189451961 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.6, "theta_Bn_degrees": 84.4, "compression": 1.5601734410360502, "u2x_km_s": -384.4532951055339, "u2y_km_s": -11.395013733397704, "speed2_km_s": 384.62212944068506, "signed_deflection_degrees": 1.6977227566030657, "p2_over_p1": 2.518150213767513, "B2_over_B1": 1.5592480680579195, "entropy_over_cv": 0.18219626443888742, "upstream_fast_Mach": 1.439303213771761, "downstream_fast_Mach": 0.7369251858139175, "downstream_alfven_margin": 0.5905533727547366, "state_global_normalized": { "rho": "1.56017344103605019479560867788277367991048770232012196862685779273665026187016284485943329", "p": "0.102136172670410331515367130541676660363816100558747157341071815090198365170714311398773757", "u": [ "-0.640755491842556545820902289563318762708676720039936362530014504716400143985159633855130583", "-0.0189916895556628414295523285427097386890297368909949331548012174083517600173431048581983932", "-0E-91" ], "B": [ "0.0524011029841885452391960468077917832914701175689412013260921220613824626828881974928933586", "1.00386043364620100787800481121110563185773497212581437305399934560859794991230229947955818", "0E-91" ] }, "root_record": { "r": "1.56017344103605019479560867788277367991048770232012196862685779273665026187016284485943329", "b": "0.0405644482269149686169069176719404699660015632180594566363684430429444407781160528728760494", "h": "0.00395815744809276498519208683332330521817490322276352988757538347486825027262852602340890967", "A": "0.411708918935725067283635968250848587053512341415749256280582709292444460029670213069599415", "denominator": "0.993824587874046639618813114317441665435402098525337484036831592512700551028774526694172429", "polynomial_residual": "-1.347101223462893231932029E-65", "bracket_initial_signs": [ "1.46562136427571965964057679549411532305812929229527581138116527934863171019143866384494523", "-1.99490609017076949010302923626704812777671956225487562657030285752263241952001591484787807" ], "bracket_derivative_max": "-5.53094238502068628127164456661512023700966609829968362285424555259477372899173309456478347", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.03362893065222804836420738738995049392687480478513031805164824262974593932478579129373385E-90", "-1E-91", "0E-182", "-1E-90", "0E-182", "7.74162147060760167064394795391421308513146361713425574610489070562396934962159430084556018E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.6", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.000904505465577285, 0.0 ], "rh_scaled_inf": 2.1909183904764404e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": -1.7844893055589407e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1909183904764404e-16 }, "characteristics": { "left": { "slow": 0.019128640140713162, "alfven_n": 0.05036586293068025, "fast": 0.8697208997919319 }, "right": { "slow": 0.02354356233990345, "alfven_n": 0.06291043954244796, "fast": 0.6947425391659547 } }, "front_relative_normal_velocity": { "left": -0.6409192356854169, "right": -0.9999451693655121 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601734410360502, "pressure_ratio": 2.5181502137675134, "entropy_over_cv": 0.1821962644388876, "tangential_field_ratio": 1.563654238253808 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.625, "theta_Bn_degrees": 84.375, "compression": 1.560177297103337, "u2x_km_s": -384.4477317335035, "u2y_km_s": -11.362039972679733, "speed2_km_s": 384.6155930112255, "signed_deflection_degrees": 1.6928373999830708, "p2_over_p1": 2.5181775049654536, "B2_over_B1": 1.5592436360147508, "entropy_over_cv": 0.1822029829090752, "upstream_fast_Mach": 1.4393038802940479, "downstream_fast_Mach": 0.7369236483400589, "downstream_alfven_margin": 0.5903247351967894, "state_global_normalized": { "rho": "1.56017729710333691659072481945149666653310496093148230046546469365175662974844927114309192", "p": "0.102137279601398800772241219228338828780461393889364292813366774998585436292921901465944919", "u": [ "-0.640746219555839155061368307372484707814351767755236267727453983200503587779468680229490711", "-0.0189367332877995561071631515384532658456603668733813264293103762787285897458109013567920751", "-0E-91" ], "B": [ "0.0522432370600203673588867168180167399760030481599815431606362960339633373291277485721207536", "1.00386580058822410735559841695454077588771208064242217242966006280459754781428696475211833", "0E-91" ] }, "root_record": { "r": "1.56017729710333691659072481945149666653310496093148230046546469365175662974844927114309192", "b": "0.0405648266651272409233091853454874284893489108183815330111011596095917062418436067531797041", "h": "0.00399350041540794384188114806100148111931146702335041744834327976390391577318073907993652152", "A": "0.411677453854395350323916334571443917259293330075024667902963268301891560786166856749091658", "denominator": "0.993769431315907781005114039412537394032600165582794854125899419237612405287476229687867957", "polynomial_residual": "-1.199850975898080280897206E-65", "bracket_initial_signs": [ "1.46556039735533270932196298756354452472177500520507330345796635501559269505561708716880432", "-1.99473903108941553131315883929328970253811369374534550443299962043348628770305363098162296" ], "bracket_derivative_max": "-5.53067413420543929892138285359315395534413658565677115265120758160284296304876709579542427", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "0E-91", "0E-182", "-3E-90", "0E-182", "6.89621444003144263708645263187279213023053296516186351942419412816827042818914193558341149E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.625", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.0005190983826032503, 0.0 ], "rh_scaled_inf": 2.1910049114524934e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7845533130048157e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1910049114524934e-16 }, "characteristics": { "left": { "slow": 0.019213915592068836, "alfven_n": 0.05058992678211749, "fast": 0.8697165078398356 }, "right": { "slow": 0.02364845165034366, "alfven_n": 0.0631903888493363, "fast": 0.6947389767307951 } }, "front_relative_normal_velocity": { "left": -0.6409146619789069, "right": -0.9999405050001497 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560177297103337, "pressure_ratio": 2.518177504965454, "entropy_over_cv": 0.18220298290907533, "tangential_field_ratio": 1.5636894026429993 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.65, "theta_Bn_degrees": 84.35000000000001, "compression": 1.560180883422819, "u2x_km_s": -384.4422636374021, "u2y_km_s": -11.329061845927265, "speed2_km_s": 384.60915448407957, "signed_deflection_degrees": 1.687950809131779, "p2_over_p1": 2.518203583867274, "B2_over_B1": 1.5592388978840066, "entropy_over_cv": 0.18220950801769545, "upstream_fast_Mach": 1.4393043054396353, "downstream_fast_Mach": 0.736922190769023, "downstream_alfven_margin": 0.5900960922434698, "state_global_normalized": { "rho": "1.56018088342281901216576917720742563891875951928990385072386086156725074358482000487066394", "p": "0.102138337361656626168317647759163723677176806788691439444977954699497925192447956475380169", "u": [ "-0.640737106062336756882434279113807294933334891038474429301357569082559548377441995267577777", "-0.0188817697432121096970208715556840837863758024355613158625753776263153674149904899257285785", "-0E-91" ], "B": [ "0.0520853674709283925379805322279690715524084040483068847968632313537289118176728010199597499", "1.00387094527814376479815360225615457286604911548112879472026766315672534031940255137885188", "0E-91" ] }, "root_record": { "r": "1.56018088342281901216576917720742563891875951928990385072386086156725074358482000487066394", "b": "0.0405652205547967461302775524294277625507147945660861738588082167539939844372780840501920312", "h": "0.00402900081212241184281813943914274005300090879582412868568129951920198646338771811789512043", "A": "0.411645989675958156533211413414070512166645329581582254855414400210188074084695020469694253", "denominator": "0.993714029953631600243585658053390108145635299243488511083236263523787280446890844103645909", "polynomial_residual": "-9.13856016549313267113479E-66", "bracket_initial_signs": [ "1.46549783287927493052065315527834351638154919961431535124967705030608009919095786970526704", "-1.99457332698070028942055927876380520102215847690603049044842522761079815006604871785033455" ], "bracket_derivative_max": "-5.53040589012686489717582795327422447726525527970808112175570124617899611573773147826241237", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.03390866864363246504516892547704323815893381038426961860074926916079058215150102847621690E-90", "2E-91", "0E-182", "1E-90", "0E-182", "5.25306727693333732830295535724550611344241180473802436520899575535321986950615431376967938E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.65", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.0001336909690903658, 0.0 ], "rh_scaled_inf": 2.1910925588036607e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1910925588036607e-16 }, "characteristics": { "left": { "slow": 0.019299189868683578, "alfven_n": 0.05081398484099678, "fast": 0.869712006386506 }, "right": { "slow": 0.02375333807280936, "alfven_n": 0.06347032612566655, "fast": 0.6947353985401995 } }, "front_relative_normal_velocity": { "left": -0.6409100770844666, "right": -0.9999356502602301 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560180883422819, "pressure_ratio": 2.518203583867274, "entropy_over_cv": 0.18220950801769553, "tangential_field_ratio": 1.5637244383567352 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.675, "theta_Bn_degrees": 84.325, "compression": 1.5601841999823287, "u2x_km_s": -384.4368908227421, "u2y_km_s": -11.296079422643752, "speed2_km_s": 384.602813868775, "signed_deflection_degrees": 1.6830629980090195, "p2_over_p1": 2.5182284503661685, "B2_over_B1": 1.5592338536707082, "entropy_over_cv": 0.18221583974830577, "upstream_fast_Mach": 1.4393044892030291, "downstream_fast_Mach": 0.7369208131031767, "downstream_alfven_margin": 0.5898674438824235, "state_global_normalized": { "rho": "1.56018419998232862060864894219628298693813854680273199077983466281050229546257197284704818", "p": "0.102139345946851797175112051135534703540947196306014264875135036508587890774149190282205557", "u": [ "-0.640728151371236806553093774752438038169882452529684473904087190537393300430567363612202687", "-0.0188267990377395877227296837280982061137721467709612425151612113093972166486814775698680042", "-0E-91" ], "B": [ "0.0519274944477591746264957756292792077503634772953876006275920350960515030716518123755104759", "1.00387586771074965443242554731279923684738769953439025257557454654690115560354125032446678", "0E-91" ] }, "root_record": { "r": "1.56018419998232862060864894219628298693813854680273199077983466281050229546257197284704818", "b": "0.0405656298965235241310277099730016503579987991992579222351087061326784238493738841175482576", "h": "0.00406465865633492053868248954140155025702386983949832143616273975639964099823462484144636243", "A": "0.411614526388463390118006338599038731665734749591176210902393481178853528441797155931490954", "denominator": "0.993658383786064855192504524597381704080045005462930515549359079217538076890384775470240579", "polynomial_residual": "2.14949108823137921686624E-66", "bracket_initial_signs": [ "1.46543367098008294106705703304111352081259135311176781926381672247360459896100956326740421", "-1.99440897749868949922208103143615891137778154491025873148145977050638225324886763077145408" ], "bracket_derivative_max": "-5.53013765245757055934030169802485904450757138734942297709205284086237828179620010290345336", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.03405083935314875197453631338604592938496623060830350774585976334869403884157098837594697E-90", "2E-91", "0E-182", "5E-90", "0E-182", "-1.23572709096454140745643449519498185305016611256835137995393043307755120099783380516144612E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.675", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.00025171673714998854, 0.0 ], "rh_scaled_inf": 1.7846836477569242e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 1.7846836477569242e-16, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.019384462968979155, "alfven_n": 0.05103803712296222, "fast": 0.8697073954344293 }, "right": { "slow": 0.023858221594394335, "alfven_n": 0.06375025131814266, "fast": 0.6947318045956755 } }, "front_relative_normal_velocity": { "left": -0.6409054810053858, "right": -0.9999306051466773 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601841999823287, "pressure_ratio": 2.5182284503661685, "entropy_over_cv": 0.18221583974830569, "tangential_field_ratio": 1.5637593453877972 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.7, "theta_Bn_degrees": 84.3, "compression": 1.560187246769543, "u2x_km_s": -384.4316132950438, "u2y_km_s": -11.263092772334836, "speed2_km_s": 384.59657117481987, "signed_deflection_degrees": 1.6781739805781373, "p2_over_p1": 2.5182521043567774, "B2_over_B1": 1.559228503379882, "entropy_over_cv": 0.1822219780846578, "upstream_fast_Mach": 1.4393044315787404, "downstream_fast_Mach": 0.7369195153450145, "downstream_alfven_margin": 0.5896387901013659, "state_global_normalized": { "rho": "1.56018724676954303035353906420934761573484121214329676955950125014555358171363359114076515", "p": "0.102140305352710892986921852933223296424706941410856750968817137460070413064302931798490283", "u": [ "-0.640719355491739636410806690598145305013893056926839443098116358334120626022922926880596575", "-0.0187718212872247262174263288486367926686609933929034506467230963017459932935653654650565420", "-0E-91" ], "B": [ "0.0517696182213669658071655808731593849636480745915862025814410039550752513665750958102955853", "1.00388056788094857541459200538845048491748228827328511093221080255327941085168525205081058", "0E-91" ] }, "root_record": { "r": "1.56018724676954303035353906420934761573484121214329676955950125014555358171363359114076515", "b": "0.0405660546909311632866999791639182993205928513086115156094364550335529140016447860544731114", "h": "0.00410047396638416652171185871252839384539220483006335828556665272432288364038326020694927879", "A": "0.411583063979962313237435991009469668483822909183216741498800631750027593951508540644015240", "denominator": "0.993602492811936899494507908571726264824231728093668552557944527472931660142269847646607767", "polynomial_residual": "1.566167174884338991922280E-65", "bracket_initial_signs": [ "1.46536791178958397737370708083115849679235030989588026442828088369213260534821092858370712", "-1.99424598229662033202078296831884267950880589147614552057970963082556069052611499952640208" ], "bracket_derivative_max": "-5.52986942086813748233002800289367069950562282151518994377052383314800588943713533285824568", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.03419454471885618485711665089429710415383005392378712849183225009555645028657660255746905E-90", "-1E-91", "0E-182", "-2E-90", "0E-182", "-9.00485575509190318469025228803933878667722327924617516602875832116717021225442907817215183E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_0.7", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.0006371246983103264, 0.0 ], "rh_scaled_inf": 2.1912712332876378e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7847499753017438e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1912712332876378e-16 }, "characteristics": { "left": { "slow": 0.019469734891377103, "alfven_n": 0.05126208364366356, "fast": 0.8697026749861134 }, "right": { "slow": 0.023963102202191416, "alfven_n": 0.06403016437347078, "fast": 0.6947281948987376 } }, "front_relative_normal_velocity": { "left": -0.6409008737450295, "right": -0.999925369660452 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560187246769543, "pressure_ratio": 2.5182521043567774, "entropy_over_cv": 0.1822219780846578, "tangential_field_ratio": 1.563794123728685 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.725, "theta_Bn_degrees": 84.275, "compression": 1.5601900237719846, "u2x_km_s": -384.42643105983507, "u2y_km_s": -11.230101964508297, "speed2_km_s": 384.5904264117028, "signed_deflection_degrees": 1.6732837708059514, "p2_over_p1": 2.518274545735185, "B2_over_B1": 1.5592228470165603, "entropy_over_cv": 0.18222792301069735, "upstream_fast_Mach": 1.4393041325612859, "downstream_fast_Mach": 0.7369182974971593, "downstream_alfven_margin": 0.5894101308880813, "state_global_normalized": { "rho": "1.56019002377198466551430812293962424177798175528260918113471136028549884729132248099491707", "p": "0.102141215575019093967038887910990627059336477760580814491372361579219393152781260150661867", "u": [ "-0.640710718433058470851821018902188174416103065801638232643292208486387551880773312833270328", "-0.0187168366075138264956439243735493288045816221675285966834619631469307824902936278224899170", "-0E-91" ], "B": [ "0.0516117390226137391566420225729866047547634744377466652874996627601502279130891600007361118", "1.00388504578376443497350219995086897662350165695434133706941307537811783875798402942876125", "0E-91" ] }, "root_record": { "r": "1.56019002377198466551430812293962424177798175528260918113471136028549884729132248099491707", "b": "0.0405664949386668024451896840090924694392478105931178159240730630435854525366683146748975383", "h": "0.00413644676084883023957222982504705988934851638414157908755686650183313526196504001399153984", "A": "0.411551602438507527876527771612267764358429078905537048755208048614165781087071530370497002", "denominator": "0.993546357029859714579907079741748653412634223283790138780349724534124220354452383048314667", "polynomial_residual": "7.68241447418536806578026E-66", "bracket_initial_signs": [ "1.46530055543889650490532410592338848695973684599463300627023381223051788692889964082778899", "-1.99408434102690030421853693284228515220347698388728818675535180639888279117084600819927907" ], "bracket_derivative_max": "-5.52960119502711962950949516042650098520292545851834443128349336354021562636390288903656826", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "0E-91", "0E-182", "-1E-90", "0E-182", "-4.41761733774630150771542285576859649032461511849235003307005614837757938052020750341093160E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.725", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.0010225328765871844, 0.0 ], "rh_scaled_inf": 2.1913622607538895e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1913622607538895e-16 }, "characteristics": { "left": { "slow": 0.019555005634298815, "alfven_n": 0.0514861244187564, "fast": 0.869697845044088 }, "right": { "slow": 0.024067979883292467, "alfven_n": 0.06431006523835944, "fast": 0.6947245694509072 } }, "front_relative_normal_velocity": { "left": -0.6408962553068376, "right": -0.9999199438025509 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601900237719846, "pressure_ratio": 2.518274545735185, "entropy_over_cv": 0.18222792301069746, "tangential_field_ratio": 1.5638287733716172 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.75, "theta_Bn_degrees": 84.25, "compression": 1.560192530977021, "u2x_km_s": -384.4213441226517, "u2y_km_s": -11.197107068674002, "speed2_km_s": 384.5843795888927, "signed_deflection_degrees": 1.6683923826627112, "p2_over_p1": 2.51829577439892, "B2_over_B1": 1.5592168845857808, "entropy_over_cv": 0.18223367451056433, "upstream_fast_Mach": 1.4393035921451869, "downstream_fast_Mach": 0.7369171595623615, "downstream_alfven_margin": 0.5891814662304231, "state_global_normalized": { "rho": "1.56019253097702107235787454170354713328043236864626607843916028105253770234808463986773333", "p": "0.102142076609620193053455072913748851203860319326107689592224085278124636272233144097876046", "u": [ "-0.640702240204419441814471358203678143368065239308590786840182619422878700206562246212898821", "-0.0186618451144566698910070022017350025389228602048682083999018892328780034401705900504737226", "-0E-91" ], "B": [ "0.0514538570823692112697137417153680016973436647303738886734551767166947150265334475651053700", "1.00388930141433823135930478890561360466479433646594282342782308386007790510080785578947546", "0E-91" ] }, "root_record": { "r": "1.56019253097702107235787454170354713328043236864626607843916028105253770234808463986773333", "b": "0.0405669506404011330362645351940884162109788476440954419480125078865933318576090291853312811", "h": "0.00417257705854761558660598211542656696335292989856324813663641766685017243264693810711061598", "A": "0.411520141752152957723785366728172355450827342797165407428932584286670702810148014858393259", "denominator": "0.993489976438327941800227721404177724289571147471590277159356597345661467373475821217338840", "polynomial_residual": "6.04407091423867545601064E-66", "bracket_initial_signs": [ "1.46523160205843083314534066454400341877717540235901301756678540613183077674666947468640310", "-1.99392405334110617294725323492768971702408311675751651998935003274313683574676827139926273" ], "bracket_derivative_max": "-5.52933297460104276981973461214029199506252356139908174537889637838423393484468552212945005", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-3E-91", "0E-182", "-1E-90", "0E-182", "-3.47593478866602212222608714022709821945942587673670277091994762272419865017484982030884855E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.75", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.0014079412341812302, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.784884951336056e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 2.220446049250313e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.019640275196165534, "alfven_n": 0.051710159463902186, "fast": 0.8696929056109054 }, "right": { "slow": 0.024172854624788423, "alfven_n": 0.06458995385951946, "fast": 0.6947209282537125 } }, "front_relative_normal_velocity": { "left": -0.6408916256943253, "right": -0.999914327574007 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560192530977021, "pressure_ratio": 2.5182957743989203, "entropy_over_cv": 0.1822336745105645, "tangential_field_ratio": 1.5638632943085318 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.775, "theta_Bn_degrees": 84.22500000000001, "compression": 1.5601947683718649, "u2x_km_s": -384.41635248903697, "u2y_km_s": -11.164108154343861, "speed2_km_s": 384.57843071583903, "signed_deflection_degrees": 1.6634998301220554, "p2_over_p1": 2.518315790246958, "B2_over_B1": 1.5592106160925858, "entropy_over_cv": 0.18223923256859276, "upstream_fast_Mach": 1.4393028103249705, "downstream_fast_Mach": 0.7369161015434998, "downstream_alfven_margin": 0.5889527961163143, "state_global_normalized": { "rho": "1.56019476837186490591758685022011286457675537385234765087849821841166975856029260395172563", "p": "0.102142888452416607124076697759657326814615278031096872079422982968032118716672526557369846", "u": [ "-0.640693920815061604755656824159909996749921352919649612547086156622172091674220688392985645", "-0.0186068469239064324595615774901476463697067279726113961541450912474641845222439923436422131", "-0E-91" ], "B": [ "0.0512959726315108649473393873865486541942828945061299613273649830397121742558463040345548636", "1.00389333476792803659736495046393103280993470743029576461069919110694037205614067043066846", "0E-91" ] }, "root_record": { "r": "1.56019476837186490591758685022011286457675537385234765087849821841166975856029260395172563", "b": "0.0405674217968284012429806673720071431252629466890759036195069028898338134906642519421260081", "h": "0.00420886487853929027263557496258580435393642457101652689159516467222146982576881202732480633", "A": "0.411488681908953830053055177742701166044655151093913761682213756662892861765470126649307978", "denominator": "0.993433351035718914692122833589799854845299322306437137949477748689361730740350390642692557", "polynomial_residual": "-3.67987998840531748513751E-66", "bracket_initial_signs": [ "1.46516105177788973506285827094634976785134500115163812387372154755574916095387955728411504", "-1.99376511888998281873359936736262758553731326967924158585949546510819489257386894651421477" ], "bracket_derivative_max": "-5.52906475925440350318918296018314064031931016958642846652313535977913076128123298595210318", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-4E-91", "0E-182", "-6E-90", "0E-182", "2.11654460849691215132032355509877240604255052594639105388334795746236702471975898603785311E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_0.775", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.0017933497332973912, 0.0 ], "rh_scaled_inf": 2.19154769698441e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.19154769698441e-16 }, "characteristics": { "left": { "slow": 0.019725543575398474, "alfven_n": 0.051934188794768396, "fast": 0.8696878566891396 }, "right": { "slow": 0.024277726413769254, "alfven_n": 0.06486983018366398, "fast": 0.694717271308688 } }, "front_relative_normal_velocity": { "left": -0.6408869849110828, "right": -0.9999085209758897 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601947683718649, "pressure_ratio": 2.518315790246958, "entropy_over_cv": 0.18223923256859276, "tangential_field_ratio": 1.5638976865310847 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.8, "theta_Bn_degrees": 84.2, "compression": 1.560196735943574, "u2x_km_s": -384.4114561645422, "u2y_km_s": -11.13110529103176, "speed2_km_s": 384.57257980197153, "signed_deflection_degrees": 1.6586061271609658, "p2_over_p1": 2.5183345931797185, "B2_over_B1": 1.5592040415420243, "entropy_over_cv": 0.18224459716931077, "upstream_fast_Mach": 1.4393017870951688, "downstream_fast_Mach": 0.7369151234435811, "downstream_alfven_margin": 0.5887241205337466, "state_global_normalized": { "rho": "1.56019673594357391674672394551211404535553910843155575473522819248509863903333803006479393", "p": "0.102143651099369388321462742771180374695025156368508305555698272957253306133240771996586895", "u": [ "-0.640685760274236955120704041507506575466320367521767331964789026328253704066730676112437692", "-0.0185518421517195996485437080917211382019802220963167724397837108389909424470622997731802200", "-0E-91" ], "B": [ "0.0511380859009239719492997379990055722362473287768674104433726854503917927789653777784064514", "1.00389714583990897904738020821110811714582521678038109344936280446403478320747544567698102", "0E-91" ] }, "root_record": { "r": "1.56019673594357391674672394551211404535553910843155575473522819248509863903333803006479393", "b": "0.0405679084086664102494093964428058375490462565181075819482959129802015668588475011457405036", "h": "0.00424531024012272696950479258825385696176948789047101506762125001256094491694150744133579922", "A": "0.411457222896966657609617111273491408771377697035330715813758152626247190287084499161936334", "denominator": "0.993376480820292691371804601417312260326138699514664426767993644965390414010848529136333325", "polynomial_residual": "-8.61351632374128269524989E-66", "bracket_initial_signs": [ "1.46508890472626907108408051448599895086360131106395265331705927583023944025517930210271177", "-1.99360753732344211519196097166886213655206769337594530231716160763514302633175249770256050" ], "bracket_derivative_max": "-5.52879654864966827222368304051529162249325285302494372124298082164009207001044821627258264", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.03478471550711369760135135046393065151225509106381210882173993610578982527663393382011574E-90", "2E-91", "0E-182", "-3E-90", "0E-182", "4.95479791937044378932960538360623953554713778097354881354909267619347123048097106017586343E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.8", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.002178758336144967, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.019810810770418876, "alfven_n": 0.05215821242702864, "fast": 0.8696826982813872 }, "right": { "slow": 0.024382595237323973, "alfven_n": 0.06514969415750853, "fast": 0.6947135986173755 } }, "front_relative_normal_velocity": { "left": -0.6408823329607752, "right": -0.9999025240093042 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560196735943574, "pressure_ratio": 2.518334593179719, "entropy_over_cv": 0.18224459716931074, "tangential_field_ratio": 1.5639319500306517 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.825, "theta_Bn_degrees": 84.17500000000001, "compression": 1.5601984336790509, "u2x_km_s": -384.40665515472625, "u2y_km_s": -11.09809854825353, "speed2_km_s": 384.5668268567004, "signed_deflection_degrees": 1.6537112877597273, "p2_over_p1": 2.518352183099069, "B2_over_B1": 1.55919716093915, "entropy_over_cv": 0.18224976829744047, "upstream_fast_Mach": 1.4393005224503188, "downstream_fast_Mach": 0.7369142252657404, "downstream_alfven_margin": 0.5884954394707803, "state_global_normalized": { "rho": "1.56019843367905093781221354393199126977792924799191934311860086103536853829903765212182603", "p": "0.102144364546498235337102464516520369877944502049406481593772746638474809913400400809007513", "u": [ "-0.640677758591210445306823921267582052707731477795593260316622655786312234765699148266166424", "-0.0184968309137558809303896358158320952750558349592330078157380366281524899822776011307211267", "-0E-91" ], "B": [ "0.0509801971215016158122719544443680653129243541980852358180169259761668830108940482270379602", "1.00390073462577322576760417509350489439517577494037176150746553857252181051401406533773442", "0E-91" ] }, "root_record": { "r": "1.56019843367905093781221354393199126977792924799191934311860086103536853829903765212182603", "b": "0.0405684104766565225646871877967560104310470498747663009292358636667236064629005959928902590", "h": "0.00428191316283694523554382614685726715768685925624746199668030098398345465248888692748569610", "A": "0.411425764704249220500441449311736798237925829255781483248892300118833769303464425824102772", "denominator": "0.993319365790192087060142817437638306149556817131619156410204152976796974171715914241471176", "polynomial_residual": "-1.192453066793456273574895E-65", "bracket_initial_signs": [ "1.46501516103185841757233029498993861222761884278702006637005814817198259297772596702071864", "-1.99345130829056178574027077472072994068174774569792186400367328321035628746651184526483369" ], "bracket_derivative_max": "-5.52852834244727236017106891386728729230323144796375391202114878559949848235161615500527503", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "-1E-91", "0E-182", "-3E-90", "0E-182", "6.86022638738683353083732154670336425518600386718497193196507872091331814366277384124139287E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.825", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.0025641670049377516, 0.0 ], "rh_scaled_inf": 2.1917376427696654e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": -1.7850932196133714e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1917376427696654e-16 }, "characteristics": { "left": { "slow": 0.019896076779648032, "alfven_n": 0.05238223037636268, "fast": 0.8696774303902666 }, "right": { "slow": 0.024487461082540626, "alfven_n": 0.06542954572777093, "fast": 0.6947099101813231 } }, "front_relative_normal_velocity": { "left": -0.640877669847143, "right": -0.9998963366753925 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601984336790509, "pressure_ratio": 2.518352183099069, "entropy_over_cv": 0.18224976829744044, "tangential_field_ratio": 1.563966084798326 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.85, "theta_Bn_degrees": 84.15, "compression": 1.5601998615650439, "u2x_km_s": -384.401949465156, "u2y_km_s": -11.065087995526875, "speed2_km_s": 384.5611718894162, "signed_deflection_degrees": 1.648815325901882, "p2_over_p1": 2.518368559908321, "B2_over_B1": 1.5591899742890218, "entropy_over_cv": 0.18225474593789812, "upstream_fast_Mach": 1.4392990163849635, "downstream_fast_Mach": 0.7369134070132404, "downstream_alfven_margin": 0.5882667529155451, "state_global_normalized": { "rho": "1.56019986156504387152866926263188037605079968838363989765087679820853992704950070500540070", "p": "0.102145028789881504655247326167746811478829740963166617076009213460513314842780782675069020", "u": [ "-0.640669915775260002120373953362963853725947945187264518870092407112854339583142721607852597", "-0.0184418133258781244017902286065186971151523066905676967721319502551597440649634042269892062", "-0E-91" ], "B": [ "0.0508223065241447147341300123112801381526363816277382593230165084038370424261134430677411835", "1.00390410112112996468408695730774905198629736869674575092012778223950684360495836843414191", "0E-91" ] }, "root_record": { "r": "1.56019986156504387152866926263188037605079968838363989765087679820853992704950070500540070", "b": "0.0405689280015636624234017510145367587668800003299360900891858232973716969889767779136380240", "h": "0.00431867366646115421814879656898458060052656696507384380702757764183306323504567861998028159", "A": "0.411394307318860548088553542036311296425209455799554452397705586528858950171927329336072134", "denominator": "0.993262005943442706738578560442406468276003516450893644864045895487025526810174445951980940", "polynomial_residual": "7.40190653243386335744156E-66", "bracket_initial_signs": [ "1.46493982082224169982082553395158292366382490672378327010682439943399291293826967272910963", "-1.99329643143958424733320788342821941952321657994655076563911133075199147094724744935939918" ], "bracket_derivative_max": "-5.52826014030561887515566864166040244056884645234950933786956071836223216275793937914602567", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "-4E-91", "0E-182", "-3E-90", "0E-182", "-4.25885083854513465148523770525720846787643308582257856974011026538115869500486357840682596E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.85", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.00294957570189415, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.0199813416015074, "alfven_n": 0.05260624265845662, "fast": 0.869672053018418 }, "right": { "slow": 0.02459232393650628, "alfven_n": 0.0657093848411714, "fast": 0.6947062060020861 } }, "front_relative_normal_velocity": { "left": -0.6408729955740017, "right": -0.9998899589753325 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601998615650439, "pressure_ratio": 2.518368559908321, "entropy_over_cv": 0.18225474593789814, "tangential_field_ratio": 1.5640000908249199 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.875, "theta_Bn_degrees": 84.12500000000001, "compression": 1.5602010195881457, "u2x_km_s": -384.3973391014059, "u2y_km_s": -11.032073702371338, "speed2_km_s": 384.55561490948975, "signed_deflection_degrees": 1.643918255574189, "p2_over_p1": 2.518383723512234, "B2_over_B1": 1.5591824815967048, "entropy_over_cv": 0.182259530075794, "upstream_fast_Mach": 1.4392972688936507, "downstream_fast_Mach": 0.7369126686894722, "downstream_alfven_margin": 0.5880380608562389, "state_global_normalized": { "rho": "1.56020101958814567693284901550786452883920850397930193065498507485791786163682212512848451", "p": "0.102145643825656221756312183653151950427392246146890488073974173800282382055095736757179406", "u": [ "-0.640662231835676544728140773493349686751560749722014957366056269407862724188033701362539745", "-0.0183867895039522313475920669042035166491589428344952653114465492903127599248684617588156218", "-0E-91" ], "B": [ "0.0506644143397620445252759606984251635611403221938990575082377754713719237648776512764865406", "1.00390724532170538656484051944651435673337847827153139373850506086664651941635754561701952", "0E-91" ] }, "root_record": { "r": "1.56020101958814567693284901550786452883920850397930193065498507485791786163682212512848451", "b": "0.0405694609841763182623276011449305866906584144460654242857707178914202721867237380116738601", "h": "0.00435559177101479613467064986387160874875256349445540183213949501422453711670584683223446576", "A": "0.411362850728860900891448088858959934007114797528999540143537855901960527046993422298406124", "denominator": "0.993204401277952977936002946878821939656225173903374756976427570216207553897830181194465016", "polynomial_residual": "1.000114769896125038495646E-65", "bracket_initial_signs": [ "1.46486288422429782956245390474232418407879095659901609199149357729634702051588881349924466", "-1.99314290641791544120714646152437640656559487273915994060128396699562296371555031617202649" ], "bracket_derivative_max": "-5.52799194188107772067794769990414844812764968688241977325679824653610484682407211034629083", "iterations": 216 }, "flux_residuals": [ "0E-90", "-1.60704869287031355773957560630632394441861898701971571735811517324493002596702254049111302E-89", "2E-91", "0E-182", "6E-90", "0E-182", "-5.75506650857975322025071351196577416920158897223750587456831106702898723582436978885044543E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.875", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.0033349843892373013, 0.0 ], "rh_scaled_inf": 2.19193209952819e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.785235936098651e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.19193209952819e-16 }, "characteristics": { "left": { "slow": 0.02006660523441862, "alfven_n": 0.05283024928900299, "fast": 0.8696665661685041 }, "right": { "slow": 0.02469718378630705, "alfven_n": 0.06598921144443254, "fast": 0.6947024860812263 } }, "front_relative_normal_velocity": { "left": -0.6408683101452419, "right": -0.9998833909103383 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5602010195881457, "pressure_ratio": 2.518383723512234, "entropy_over_cv": 0.18225953007579387, "tangential_field_ratio": 1.5640339681009636 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.9, "theta_Bn_degrees": 84.1, "compression": 1.5602019077347944, "u2x_km_s": -384.39282406905835, "u2y_km_s": -10.999055738308241, "speed2_km_s": 384.5501559262725, "signed_deflection_degrees": 1.6390200907665782, "p2_over_p1": 2.518397673817014, "B2_over_B1": 1.5591746828672688, "entropy_over_cv": 0.1822641206964324, "upstream_fast_Mach": 1.4392952799709333, "downstream_fast_Mach": 0.7369120102979552, "downstream_alfven_margin": 0.5878093632811284, "state_global_normalized": { "rho": "1.56020190773479435699863965676641503293616367593842775424039751637709086229556868306479553", "p": "0.102146209650018092279860473481657249967298207555139323401681279916731146446000419696737322", "u": [ "-0.640654706781764003102860794449684997137816334704606494475761145875961801210159038494948088", "-0.0183317595638470707693471378961404779572681957205326997373197518832061297814585756233070298", "-0E-91" ], "B": [ "0.0505065207992702616278072612317011687827139883185577720699049063483280692813476395951742064", "1.00391016722334266679883687172395414764907431659324870728280052733447264942339176458273933", "0E-91" ] }, "root_record": { "r": "1.56020190773479435699863965676641503293616367593842775424039751637709086229556868306479553", "b": "0.0405700094253065452735248514228515440209674982376518252459037144727875897287072414319182428", "h": "0.00439266749675759053181268640955734188847944423502982067094214060000898434488177295146084889", "A": "0.411331394922311752483494795797818043619056720575604399625599117988420177832407093885106682", "denominator": "0.993146551791514183646751884712829664008519387889091066822525061942762864589532809974881328", "polynomial_residual": "4.43203098324109928806236E-66", "bracket_initial_signs": [ "1.46478435136420134700085335001324996165397751776876837291442765839095559798030900993915184", "-1.99299073287212365063110941857855822572964175997092079378430577474270563089731527259589647" ], "bracket_derivative_max": "-5.52772374682798455237440484370932825207918350292694257798657953028477450861930695224106584", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.03539945202495787390684060816132114326680537028666760411238879920746381839126401297806017E-90", "-1E-91", "0E-182", "-1E-90", "0E-182", "-2.55067402443124731542087441520270593245822835510162420072947358841315438089905773189551032E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.9", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.0037203930291951955, 0.0 ], "rh_scaled_inf": 2.1920310199750016e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1920310199750016e-16 }, "characteristics": { "left": { "slow": 0.020151867676803596, "alfven_n": 0.05305425028370082, "fast": 0.86966096984321 }, "right": { "slow": 0.02480204061902806, "alfven_n": 0.06626902548427929, "fast": 0.6946987504203121 } }, "front_relative_normal_velocity": { "left": -0.6408636135648292, "right": -0.9998766324816606 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5602019077347944, "pressure_ratio": 2.5183976738170144, "entropy_over_cv": 0.1822641206964325, "tangential_field_ratio": 1.5640677166167056 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.925, "theta_Bn_degrees": 84.075, "compression": 1.5602025259912728, "u2x_km_s": -384.3884043737036, "u2y_km_s": -10.966034172860637, "speed2_km_s": 384.54479494909594, "signed_deflection_degrees": 1.6341208454721101, "p2_over_p1": 2.5184104107303136, "B2_over_B1": 1.5591665781057888, "entropy_over_cv": 0.1822685177853117, "upstream_fast_Mach": 1.4392930496113696, "downstream_fast_Mach": 0.7369114318423364, "downstream_alfven_margin": 0.5875806601785489, "state_global_normalized": { "rho": "1.56020252599127294609267505480070197468096135199340224180723519619889870268135620341647205", "p": "0.102146726259221513147187982744250859487853231051628615990559053184727940500923977811301221", "u": [ "-0.640647340622839336963199726076646359573162110249063392728482778923150367523433321124219159", "-0.0182767236214343938783127180627686747280225127237580726111227125552582943232112843361994350", "-0E-91" ], "B": [ "0.0503486261335939262033260726685852923314292576961090505680355697991662748486325590223052416", "1.00391286682200194697974649866222783093172675835005223759571753288817411618089295353715560", "0E-91" ] }, "root_record": { "r": "1.56020252599127294609267505480070197468096135199340224180723519619889870268135620341647205", "b": "0.0405705733257899680338154271491006223472208438886310494018520326842593215395780375521175593", "h": "0.00442990086418957932374031710119646711598545169335866653006674079752749451070334822907347796", "A": "0.411299939887275771402277219494684453624217615315679495826953094393173416029338853458480162", "denominator": "0.993088457481800495379868873310317393313020417596147020429157794254098398136738563291976972", "polynomial_residual": "-8.02893236463446123639692E-66", "bracket_initial_signs": [ "1.46470422236742306736717141966959264135720150117582877695862707138528454032056704562443564", "-1.99283991044793830565785931548209498596315703568025017673127850044554648820681695871005760" ], "bracket_derivative_max": "-5.52745555479863972103272116736613873002830395249343457510342210784639792916650842866748758", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.03555697564114382478778136683977533572418634959692415189063412155774536813134894607665752E-90", "-3E-91", "0E-182", "0E-90", "0E-182", "4.62127305004458171493995442244569234031813135216803139705267711281612106785304307242064610E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_0.925", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.004105801584000794, 0.0 ], "rh_scaled_inf": 2.1921310687124635e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": -2.1921310687124635e-16 }, "characteristics": { "left": { "slow": 0.020237128927084576, "alfven_n": 0.053278245658255764, "fast": 0.8696552640452423 }, "right": { "slow": 0.024906894421753457, "alfven_n": 0.06654882690743903, "fast": 0.694694999020919 } }, "front_relative_normal_velocity": { "left": -0.6408589058368046, "right": -0.9998696836905859 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5602025259912728, "pressure_ratio": 2.5184104107303136, "entropy_over_cv": 0.18226851778531183, "tangential_field_ratio": 1.5641013363621128 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.95, "theta_Bn_degrees": 84.05, "compression": 1.5602028743437095, "u2x_km_s": -384.3840800209395, "u2y_km_s": -10.93300907555325, "speed2_km_s": 384.53953198727197, "signed_deflection_degrees": 1.62922053368693, "p2_over_p1": 2.5184219341612324, "B2_over_B1": 1.5591581673173458, "entropy_over_cv": 0.18227272132812422, "upstream_fast_Mach": 1.4392905778095235, "downstream_fast_Mach": 0.7369109333263917, "downstream_alfven_margin": 0.587351951536904, "state_global_normalized": { "rho": "1.56020287434370949757069703004006804235245680263185011155689738644956916477483544712957521", "p": "0.102147193649579583643519616349230528623413307007955205892983996136160938147964345100502609", "u": [ "-0.640640133368232555208414844846574463068020214848620289545703407077136202394555736318111652", "-0.0182216817925887485527026373850868261114294965412848756099663384257540025973986569970026284", "-0E-91" ], "B": [ "0.0501907305736655252901969639502614642248306907883608902070023645196502072181045097335060525", "1.00391534411376031629432400626063670524561034312955036788232588037877069961539572583377191", "0E-91" ] }, "root_record": { "r": "1.56020287434370949757069703004006804235245680263185011155689738644956916477483544712957521", "b": "0.0405711526864857832106513154324243487518507007372101934238866800667864189026110170587623216", "h": "0.00446729189405117260911097212531321487841984757634279367719317736303498591287614000538821821", "A": "0.411268485611816803058806630089110683669900347920505418113520972735390124962472337349937583", "denominator": "0.993030118346369006339789006659157649633288755095452831361958122317412734318154747498677130", "polynomial_residual": "-4.77236493162101197913286E-66", "bracket_initial_signs": [ "1.46462249735873073200694276913810101256219525129043058887755350106681767178572919639640345", "-1.99269043879024877486913523150783350811554996646279195688174641492931974812016193343706113" ], "bracket_derivative_max": "-5.52718736544330720185705200882839871562210651636714789714891551621921158537176057000899518", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.03571603535044026226114350245641766333219559485141689783393591383077917213864750017264260E-90", "0E-91", "0E-182", "1E-90", "0E-182", "2.74719272452723063329620204534581794785029693977433931716197087880524053929836317966093538E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_0.95", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.004491210015892144, 0.0 ], "rh_scaled_inf": 0.0, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.020322388983684183, "alfven_n": 0.05350223542838019, "fast": 0.8696494487773299 }, "right": { "slow": 0.025011745181566392, "alfven_n": 0.06682861566064151, "fast": 0.6946912318846291 } }, "front_relative_normal_velocity": { "left": -0.6408541869652842, "right": -0.9998625445384374 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5602028743437095, "pressure_ratio": 2.5184219341612324, "entropy_over_cv": 0.18227272132812422, "tangential_field_ratio": 1.5641348273268694 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 0.975, "theta_Bn_degrees": 84.025, "compression": 1.560202952778077, "u2x_km_s": -384.3798510163721, "u2y_km_s": -10.899980515912436, "speed2_km_s": 384.53436705009295, "signed_deflection_degrees": 1.6243191694102261, "p2_over_p1": 2.5184322440203184, "B2_over_B1": 1.5591494505070256, "entropy_over_cv": 0.18227673131075633, "upstream_fast_Mach": 1.4392878645599634, "downstream_fast_Mach": 0.7369105147540245, "downstream_alfven_margin": 0.5871232373446656, "state_global_normalized": { "rho": "1.56020295277807707151477084286168996658336236393837096568057866092451663703818955136396834", "p": "0.102147611817464116459833411022232766595840787848562158659153316633042874717588188659716992", "u": [ "-0.640633085027286735847926913524231325287711045578267014249312314227004060939865286778658791", "-0.0181666341931873937589907277854703821917641364343762845826583249568871576811551423694264405", "-0E-91" ], "B": [ "0.0500328343504254960310601617513939472414505624029803035166983459909200578375185190082834612", "1.00391759909481179271534752138265077677099810311640664733749500203963587482813007920027821", "0E-91" ] }, "root_record": { "r": "1.56020295277807707151477084286168996658336236393837096568057866092451663703818955136396834", "b": "0.0405717475082767623443898905977637482653704428212886809121001716422390295196707715265546016", "h": "0.00450484060732319526723642261739357364895757694155569581883093612924406672990471048597395206", "A": "0.411237032083999851651552746739663323208726520271789185718758461800025722301965070400950257", "denominator": "0.992971534382659764738598451030141273326173825063500504642560311309714030085048910800001179", "polynomial_residual": "-7.96596394614785773872257E-66", "bracket_initial_signs": [ "1.46453917646218966400159050601696484183663405373250316195707445235380109164059767972179475", "-1.99254231754310314410892084431654952472463158670930841086329297434016408097993474083638128" ], "bracket_derivative_max": "-5.52691917841021350997824022181033574051527777684480764052968683856146661054479113841689772", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.03587663130463477480061883366206916618537560609915471416719335922870930915374267611919626E-90", "3E-91", "0E-182", "1E-90", "0E-182", "4.58612051407494990203379040504930123336482306114711338806531665849368492117261967915980248E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_0.975", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.004876618287112508, 0.0 ], "rh_scaled_inf": 2.1923345518089306e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1923345518089306e-16 }, "characteristics": { "left": { "slow": 0.020407647845025485, "alfven_n": 0.053726219609793284, "fast": 0.8696435240422236 }, "right": { "slow": 0.025116592885549044, "alfven_n": 0.06710839169061888, "fast": 0.694687449013031 } }, "front_relative_normal_velocity": { "left": -0.6408494569544589, "right": -0.9998552150265739 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560202952778077, "pressure_ratio": 2.5184322440203184, "entropy_over_cv": 0.1822767313107564, "tangential_field_ratio": 1.5641681895003776 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.0, "theta_Bn_degrees": 84.0, "compression": 1.5602027612801936, "u2x_km_s": -384.37571736561483, "u2y_km_s": -10.86694856346613, "speed2_km_s": 384.52930014683153, "signed_deflection_degrees": 1.6194167666441868, "p2_over_p1": 2.5184413402195673, "B2_over_B1": 1.55914042767992, "entropy_over_cv": 0.18228054771928842, "upstream_fast_Mach": 1.4392849098572638, "downstream_fast_Mach": 0.7369101761292667, "downstream_alfven_margin": 0.586894517590374, "state_global_normalized": { "rho": "1.56020276128019372261146917154351724605856611232569575380258091128127896231606837082986472", "p": "0.102147980759305648694325879996418989224258230298114040231417331890273718676215767750206365", "u": [ "-0.640626195609358046426031693714124022258796643256826375092074187203661175176303461555817415", "-0.0181115809391102139370668638243780430901243385515570188279085089990316548625306799092157314", "-0E-91" ], "B": [ "0.0498749376948222489714080674868837135194498817904055833464165841831568385006310477072852675", "1.00391963176146730399901793287551772305700235424938558082627559320578344954610721830176279", "0E-91" ] }, "root_record": { "r": "1.56020276128019372261146917154351724605856611232569575380258091128127896231606837082986472", "b": "0.0405723577920692547069917802956382157825883259503130315765447280801549215647049951622159378", "h": "0.00454254702522693433359411157900758721802180654244607067855007780915489029312666163148785941", "A": "0.411205579291891062084233220839854237670145610790444878056361522636970849025749477152083228", "denominator": "0.992912705587995807240024781969297986748811531494371238476117328067434969791687230846544107", "polynomial_residual": "-2.02743785789677287718841E-66", "bracket_initial_signs": [ "1.46445425980116342832912346450283482895090707179706019802019757663590733582001949342930756", "-1.99239554634970698219850544465799514232977383662873437675719795550064554442660742495630880" ], "bracket_derivative_max": "-5.52665099334554660220361818243464557165328075361420484972148892487440954500890436714003134", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "-2E-91", "0E-182", "0E-90", "0E-182", "1.16736405281174838999787855230866734816378046705365684737203633142829628253467101685365093E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.005262026359910472, 0.0 ], "rh_scaled_inf": 4.384875973096087e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7856062833621709e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": -0.0, "energy": -4.384875973096087e-16 }, "characteristics": { "left": { "slow": 0.020492905509532082, "alfven_n": 0.053950198218221196, "fast": 0.8696374898426968 }, "right": { "slow": 0.025221437520782587, "alfven_n": 0.06738815494410577, "fast": 0.6946836504077207 } }, "front_relative_normal_velocity": { "left": -0.6408447158085951, "right": -0.9998476951563913 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5602027612801936, "pressure_ratio": 2.5184413402195673, "entropy_over_cv": 0.18228054771928848, "tangential_field_ratio": 1.5642014228717573 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.025, "theta_Bn_degrees": 83.97500000000001, "compression": 1.5602022998357226, "u2x_km_s": -384.37167907428943, "u2y_km_s": -10.83391328774378, "speed2_km_s": 384.5243312867404, "signed_deflection_degrees": 1.6145133393939552, "p2_over_p1": 2.518449222672422, "B2_over_B1": 1.5591310988411249, "entropy_over_cv": 0.18228417053999488, "upstream_fast_Mach": 1.4392817136960039, "downstream_fast_Mach": 0.7369099174562785, "downstream_alfven_margin": 0.5866657922626375, "state_global_normalized": { "rho": "1.56020229983572248817114077560620404975363195352552453559167989836204663083592575719325683", "p": "0.102148300471593452813532606630531933668486062594348582559944124215452560015620687188439625", "u": [ "-0.640619465123815764941984039225654878624760816996941935934198230799041027056942137105670028", "-0.0180565221462396333490456053614054453389103962714070410839617903934071078714223524105247782", "-0E-91" ], "B": [ "0.0497170408378121914300334133730024137892988195415062399503996544461976724834045597361477394", "1.00392144211015466848672361877413771518741246620498712144612252471412798712866310133602515", "0E-91" ] }, "root_record": { "r": "1.56020229983572248817114077560620404975363195352552453559167989836204663083592575719325683", "b": "0.0405729835387931902371571627100297930988552733984780626660510717043415291628502506964273510", "h": "0.00458041116922418715490842821551775383358866991617375618097937758353700450223444639032308950", "A": "0.411174127223557701887303762913394022393495977721212212311452790827110150064314786884364598", "denominator": "0.992853631959583192535314679324698672614320452216167896193286102288103027082121117309087008", "polynomial_residual": "6.86783103633993167540953E-66", "bracket_initial_signs": [ "1.46436774749831449656866792213404107545683482310563546010992042038034632444270594965935347", "-1.99225012485242209362697604067902718050905104177911833867889155305187501293799910720580651" ], "bracket_derivative_max": "-5.52638280989345476500095470936283209485068739871109229990621882784410830016066588500364440", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.03620243256223534316959918678069100912881968324980130601173640237002241507583712584517527E-90", "-2E-91", "0E-182", "-7E-90", "0E-182", "-3.95484982221902790679239135758565751621012647174023522001867566016291308997569255020688410E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.025", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.005647434196540074, 0.0 ], "rh_scaled_inf": 1.7856826777919188e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7856826777919188e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02057816197562812, "alfven_n": 0.05417417126939705, "fast": 0.8696313461815449 }, "right": { "slow": 0.025326279074347195, "alfven_n": 0.06766790536783918, "fast": 0.6946798360703003 } }, "front_relative_normal_velocity": { "left": -0.6408399635320345, "right": -0.9998399849293209 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5602022998357226, "pressure_ratio": 2.5184492226724227, "entropy_over_cv": 0.1822841705399949, "tangential_field_ratio": 1.5642345274298468 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.05, "theta_Bn_degrees": 83.95, "compression": 1.5602015684301713, "u2x_km_s": -384.36773614802536, "u2y_km_s": -10.800874758276318, "speed2_km_s": 384.519460479053, "signed_deflection_degrees": 1.6096089016675885, "p2_over_p1": 2.518455891293776, "B2_over_B1": 1.5591214639957427, "entropy_over_cv": 0.18228759975934405, "upstream_fast_Mach": 1.4392782760707683, "downstream_fast_Mach": 0.7369097387393482, "downstream_alfven_margin": 0.5864370613501325, "state_global_normalized": { "rho": "1.56020156843017137628838229675317588744975898632951109838483514995733499425040647420658418", "p": "0.102148570950875547573117839420597388869786072958320992684524666099680524308078783745594324", "u": [ "-0.640612893580042301265690606200889188173453671203736496566497824500447559237313480931525519", "-0.0180014579304605303915270498043409553415047017951492415310772262775856371164278270523993792", "-0E-91" ], "B": [ "0.0495591440103597509421580675155028339710873093794785690681646649242158018491509071009392744", "1.00392303013741857571107585782738375977128587764015182634465923764952815157253386770969358", "0E-91" ] }, "root_record": { "r": "1.56020156843017137628838229675317588744975898632951109838483514995733499425040647420658418", "b": "0.0405736247494020825519168107595369163176097122765073189897719713269997372426230679430798549", "h": "0.00461843306101731032402719934326965592746226207330953159705516790122521175597749864449358707", "A": "0.411142675867068143143090829790786514044064070854437290288839463357703754897770695406496671", "denominator": "0.992794313494511035051156592834539353905885792912363455017261836689048261526464990901460319", "polynomial_residual": "8.91273910596310066715899E-66", "bracket_initial_signs": [ "1.46427963967560491615353875327804419711291995666369487527570766357208509397892249605658392", "-1.99210605269276525821065510139239738207334799341030561005015215265260712904351616395661290" ], "bracket_derivative_max": "-5.52611462769604548871099185548414868010001567239403176157250473685451974249004195349350659", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-2E-91", "0E-182", "-1E-90", "0E-182", "-5.13302302456407539817781586742715390136287150898427834942530038621407053797071530007128849E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.05", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.006032841759260917, 0.0 ], "rh_scaled_inf": 2.1926482433742395e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7857598475373103e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1926482433742395e-16 }, "characteristics": { "left": { "slow": 0.020663417241738414, "alfven_n": 0.05439813877906117, "fast": 0.8696250930615848 }, "right": { "slow": 0.025431117533322042, "alfven_n": 0.06794764290855858, "fast": 0.694676006002379 } }, "front_relative_normal_velocity": { "left": -0.6408352001291937, "right": -0.9998320843468308 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5602015684301713, "pressure_ratio": 2.518455891293776, "entropy_over_cv": 0.18228759975934417, "tangential_field_ratio": 1.5642675031632007 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.075, "theta_Bn_degrees": 83.92500000000001, "compression": 1.5602005670488934, "u2x_km_s": -384.36388859245994, "u2y_km_s": -10.767833044596092, "speed2_km_s": 384.51468773298274, "signed_deflection_degrees": 1.6047034674760123, "p2_over_p1": 2.518461345999968, "B2_over_B1": 1.5591115231488804, "entropy_over_cv": 0.18229083536399832, "upstream_fast_Mach": 1.4392745969761467, "downstream_fast_Mach": 0.7369096399828924, "downstream_alfven_margin": 0.5862083248416033, "state_global_normalized": { "rho": "1.56020056704889335414383390798644793062434269712518944730020207398730336745898724555026566", "p": "0.102148792193758708898346675012591483345068560638434366105895982013695382409174260016052597", "u": [ "-0.640606480987433219049250266860190291956012538834331496364042421784356002177288421364298464", "-0.0179463884076601518711090957073919253564906831293211596627396924828659690362199819863675789", "-0E-91" ], "B": [ "0.0494012474434373987760521441182835328247730797407280513870517539060426387968655878318304899", "1.00392439583992056680611967651294820579774301893549915438879593778453685723131896725590767", "0E-91" ] }, "root_record": { "r": "1.56020056704889335414383390798644793062434269712518944730020207398730336745898724555026566", "b": "0.0405742814248730320346946248225735388759261843938915749391446097317570948048823125169068650", "h": "0.00465661272254926939482301274290238782138224104813054460033105145019770078766633256185688215", "A": "0.411111225210491844414508808967021791435072032470491469067667485957266069845734471994020934", "denominator": "0.992734750189751538789807104637049347565109662597258086404716428979084571669460911073540640", "polynomial_residual": "-7.49578469481349589107901E-66", "bracket_initial_signs": [ "1.46418993645429698417762153932973166554563855308571487757668246590003307883211439456271406", "-1.99196332951140695771487484366385523910342019688809103966599616023725132636518970082685076" ], "bracket_derivative_max": "-5.52584644639338432798290527443071221221491383705974403188430374555654213484525876736413371", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "0E-91", "0E-182", "1E-90", "0E-182", "4.31748401871800479398224344080232942549767549568053373120033654209970322283888579807258851E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.075", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.006418249010338292, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.020748671306288467, "alfven_n": 0.054622100762961034, "fast": 0.8696187304856555 }, "right": { "slow": 0.0255359528847853, "alfven_n": 0.0682273675130059, "fast": 0.6946721602055728 } }, "front_relative_normal_velocity": { "left": -0.6408304256045644, "right": -0.999823993410425 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5602005670488934, "pressure_ratio": 2.518461345999968, "entropy_over_cv": 0.18229083536399815, "tangential_field_ratio": 1.5643003500600905 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.1, "theta_Bn_degrees": 83.89999999999999, "compression": 1.5601992956770863, "u2x_km_s": -384.36013641323837, "u2y_km_s": -10.734788216236817, "speed2_km_s": 384.5100130577234, "signed_deflection_degrees": 1.5997970508329793, "p2_over_p1": 2.518465586708789, "B2_over_B1": 1.5591012763056504, "entropy_over_cv": 0.18229387734081404, "upstream_fast_Mach": 1.4392706764067347, "downstream_fast_Mach": 0.7369096211914559, "downstream_alfven_margin": 0.5859795827258623, "state_global_normalized": { "rho": "1.56019929567708633644742178136559854158521292962207742027264621283650246798739674218343028", "p": "0.102148964196908480724253249876184128661339640605389620238234220554759243614271461407786865", "u": [ "-0.640600227355397258134584367567323711195950378328235555458730500767003268380411609908827358", "-0.0178913136937280272429499098326393549692048458652377877595851914481347160359009334460260819", "-0E-91" ], "B": [ "0.0492433513680256735239537267816527077543408750757142681401241199591471455944322418854222063", "1.00392553921443901472162443466798479680904001422778424923004598870497021157394174829238983", "0E-91" ] }, "root_record": { "r": "1.56019929567708633644742178136559854158521292962207742027264621283650246798739674218343028", "b": "0.0405749535662067289998588212956219716659940304709112357568368984821310467827533958807663997", "h": "0.00469495017600368937735333034000443631483018287645332316752197524139452449237210390359251949", "A": "0.411079775241899332677303657018414889138400810238968901145460660864238487132726703048647129", "denominator": "0.992674942042160031301580828903458379246469916902370238580794162988012254485908121802592575", "polynomial_residual": "6.3275727295625008255924E-67", "bracket_initial_signs": [ "1.46409863795495392575990372768124558240795327002449584076263546649927894037518156907684496", "-1.99182195494817008943135528072859886297704940893981520743557241131035374155281191662139226" ], "bracket_derivative_max": "-5.52557826562349374842691057531636020729744576419843094219752238986973688011390930203519013", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.03670266016479666183010670276577990812602886070824047197362929698403207228067550530045721E-90", "-6E-91", "0E-182", "-8E-90", "0E-182", "-3.64504077342393732017268101120562835316704946690249690416758764749097606317603744693669664E-68", "1E-91" ], "diagnosis": { "case_id": "R95_phi_1.1", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.006803655912043297, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": -0.0, "energy": -2.1928630179774888e-16 }, "characteristics": { "left": { "slow": 0.02083392416770453, "alfven_n": 0.054846057236851535, "fast": 0.8696122584566194 }, "right": { "slow": 0.02564078511581412, "alfven_n": 0.06850707912792552, "fast": 0.6946682986815043 } }, "front_relative_normal_velocity": { "left": -0.6408256399627138, "right": -0.9998157121216442 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601992956770863, "pressure_ratio": 2.518465586708789, "entropy_over_cv": 0.18229387734081415, "tangential_field_ratio": 1.5643330681085068 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.125, "theta_Bn_degrees": 83.875, "compression": 1.5601977542997931, "u2x_km_s": -384.35647961601387, "u2y_km_s": -10.70174034273353, "speed2_km_s": 384.50543646244915, "signed_deflection_degrees": 1.5948896657550238, "p2_over_p1": 2.518468613339477, "B2_over_B1": 1.5590907234711704, "entropy_over_cv": 0.18229672567684155, "upstream_fast_Mach": 1.4392665143571322, "downstream_fast_Mach": 0.7369096823697119, "downstream_alfven_margin": 0.5857508349917893, "state_global_normalized": { "rho": "1.56019775429979317402317260630267314307410279447686492256514602262044952726451898018075403", "p": "0.102149086957049185795518195261463991519228199953296615579783538743439828815383748494605371", "u": [ "-0.640594132693356357457402028732894406083159050240582857050598545074867140525346382791359708", "-0.0178362339045558828121789763500343459030169995087804271641595231305461499957990770030940417", "-0E-91" ], "B": [ "0.0490854560151132047681001704979919115882708647538253288806597341109425312671623190438221772", "1.00392646025786910424135800384915575726278789448540371236049746557308593356512335089558701", "0E-91" ] }, "root_record": { "r": "1.56019775429979317402317260630267314307410279447686492256514602262044952726451898018075403", "b": "0.0405756411744274569337793702176298538612323128267349468892438532250262290579553640851615302", "h": "0.00473344544380490601351769391274096652328435003084415326832303320343721188604485799023927650", "A": "0.411048325949362185255764968615647665003473061927505463926472267509980770432109305140638134", "denominator": "0.992614889048474997789864802639793442645356976472794687824936910847604129799847190096914257", "polynomial_residual": "-3.47433880440058239226456E-66", "bracket_initial_signs": [ "1.46400574429744057697205955108002946176949637648428615852537677026250869088733146872270683", "-1.99168192864202866670432952143707727879657441140533267612088713504612801041092075262460495" ], "bracket_derivative_max": "-5.52531008502235195947812675305826655272223599333209063673908393619676796690584739044885593", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "0E-91", "0E-182", "2E-90", "0E-182", "2.00165402913840912168266666408818578753619557053269160007038233127266785818432919297145147E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.125", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.007189062426652957, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.020919175824413695, "alfven_n": 0.05507000821649496, "fast": 0.8696056769773595 }, "right": { "slow": 0.02574561421348465, "alfven_n": 0.06878677770006429, "fast": 0.6946644214318028 } }, "front_relative_normal_velocity": { "left": -0.6408208432082841, "right": -0.9998072404820648 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601977542997931, "pressure_ratio": 2.5184686133394774, "entropy_over_cv": 0.18229672567684174, "tangential_field_ratio": 1.5643656572961555 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.15, "theta_Bn_degrees": 83.85, "compression": 1.5601959429019017, "u2x_km_s": -384.3529182064474, "u2y_km_s": -10.668689493622534, "speed2_km_s": 384.50095795631427, "signed_deflection_degrees": 1.589981326261421, "p2_over_p1": 2.5184704258127204, "B2_over_B1": 1.5590798646505635, "entropy_over_cv": 0.18229938035932516, "upstream_fast_Mach": 1.4392621108219452, "downstream_fast_Mach": 0.7369098235224619, "downstream_alfven_margin": 0.5855220816283319, "state_global_normalized": { "rho": "1.56019594290190164253572765326103530197378948365578413811807281715452304516970035150916952", "p": "0.102149160470963936426068443929106308723206725016099141140210672815535256010219708691485434", "u": [ "-0.640588197010745678447748743898224015939053206507065797693075219703667557768841493944853889", "-0.0177811491560375558979546896137903004618477177252831725460445987149219485034608016394060658", "-0E-91" ], "B": [ "0.0489275616156967368226826113635496750504284093181466469181827415284228052301609401606181668", "1.00392715896722281180524794253902921506812004963944823601096967477843041996590109237167748", "0E-91" ] }, "root_record": { "r": "1.56019594290190164253572765326103530197378948365578413811807281715452304516970035150916952", "b": "0.0405763442505830958124097012671991733483950089524440104484556252500112185850539288417114842", "h": "0.00477209854861801783345467269527722170854703249970865747439818053784785821375790760727239507", "A": "0.411016877320953011761848472009969486145817347146095856947879582280043203362038482476122576", "denominator": "0.992554591205318115348819435548530701015731517787959307369068085663149888671926146374583444", "polynomial_residual": "9.40503112503623316768076E-66", "bracket_initial_signs": [ "1.46391125560092407233406008691674255164170940521920759375411676338261160603320639245402878", "-1.99154325023110650639843603684083968619762272050456974678895608625677045234223891441844539" ], "bracket_derivative_max": "-5.52504190422389173346569641832579067341741655175656805970696599062398131521741148916602870", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-1E-91", "0E-182", "-2E-90", "0E-182", "-5.41911892189191349790009410496759601209631203082448145720160844963109153349273656925782839E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.15", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.007574468516450345, 0.0 ], "rh_scaled_inf": 2.193082311963295e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.193082311963295e-16 }, "characteristics": { "left": { "slow": 0.02100442627484394, "alfven_n": 0.05529395371766114, "fast": 0.8695989860507811 }, "right": { "slow": 0.02585044016487201, "alfven_n": 0.06906646317617156, "fast": 0.6946605284581047 } }, "front_relative_normal_velocity": { "left": -0.640816035345993, "right": -0.9997985784932998 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601959429019017, "pressure_ratio": 2.5184704258127204, "entropy_over_cv": 0.18229938035932514, "tangential_field_ratio": 1.5643981176104604 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.175, "theta_Bn_degrees": 83.825, "compression": 1.5601938614681445, "u2x_km_s": -384.3494521902082, "u2y_km_s": -10.635635738441344, "speed2_km_s": 384.4965775484535, "signed_deflection_degrees": 1.58507204637414, "p2_over_p1": 2.518471024050657, "B2_over_B1": 1.5590686998489574, "entropy_over_cv": 0.18230184137570324, "upstream_fast_Mach": 1.4392574657957846, "downstream_fast_Mach": 0.7369100446546358, "downstream_alfven_margin": 0.5852933226245053, "state_global_normalized": { "rho": "1.56019386146814443135868614226559087066805858336960799193789604343379279293094059019715190", "p": "0.102149184735494645218412310917516186143076835806839210570241493662247997854227080713002468", "u": [ "-0.640582420317013628927389598206121155913153561037716095721206324069277240449887515204855680", "-0.0177260595640689089599660309096991586532047758247488760001371563911093991627982798804035503", "-0E-91" ], "B": [ "0.0487696684007811525525359822171701707086131381888288782832128044683359094188216781790091344", "1.00392763533962888513533262132792863161544760020054018613600724315621562961977648187150712", "0E-91" ] }, "root_record": { "r": "1.56019386146814443135868614226559087066805858336960799193789604343379279293094059019715190", "b": "0.0405770627957451254954111236658757927783356373596700756976137134546165151927640012138611802", "h": "0.00481090951334893899292555080282734466133377066347412217376551607310743829252402223531078021", "A": "0.410985429344745436037650965890463530980932679370650220363216700692416862928214957359286251", "denominator": "0.992494048509194287333929200683956348336983304655538365679369148944115114475912633059684903", "polynomial_residual": "2.39036742468947130467390E-66", "bracket_initial_signs": [ "1.46381517198387453688284655318625619572946518148056956783183440295483585314276167142636722", "-1.99140591935267590330127379304754198611334854793154570009700021979076182843991062687569887" ], "bracket_derivative_max": "-5.52477372285999921088105114946293579943797453244286358877468654050527377950093104704580409", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.03721672245539491673353769518182754858058599223349855957998275102369711999272885510602674E-90", "-3E-91", "0E-182", "2E-90", "0E-182", "-1.37747807765626629556203285047221832839892742883209069905547010875911301379743761960929240E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.175", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.007959874143724694, 0.0 ], "rh_scaled_inf": 2.1931936542356925e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1931936542356925e-16 }, "characteristics": { "left": { "slow": 0.021089675517424182, "alfven_n": 0.05551789375612758, "fast": 0.8695921856798123 }, "right": { "slow": 0.02595526295705029, "alfven_n": 0.06934613550299916, "fast": 0.694656619762053 } }, "front_relative_normal_velocity": { "left": -0.6408112163806329, "right": -0.9997897261569982 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601938614681445, "pressure_ratio": 2.518471024050657, "entropy_over_cv": 0.18230184137570316, "tangential_field_ratio": 1.5644304490385614 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.2, "theta_Bn_degrees": 83.8, "compression": 1.5601915099830992, "u2x_km_s": -384.3460815729731, "u2y_km_s": -10.602579146728646, "speed2_km_s": 384.49229524798176, "signed_deflection_degrees": 1.580161840117803, "p2_over_p1": 2.5184704079768747, "B2_over_B1": 1.5590572290714855, "entropy_over_cv": 0.18230410871360805, "upstream_fast_Mach": 1.4392525792732667, "downstream_fast_Mach": 0.7369103457712917, "downstream_alfven_margin": 0.5850645579693924, "state_global_normalized": { "rho": "1.56019150998309913258490994174969612027164535592126124114657322158645261931120931443907007", "p": "0.102149159747542035742722604285818399741002944813148619289235742349935958995074069401265541", "u": [ "-0.640576802621621887504281492405624248332669688005322482323546309468997980811072317892455639", "-0.0176709652445477436871754447114859935207746063571012660274653336564298225258582643379857008", "-0E-91" ], "B": [ "0.0486117766013794972693775073990409318044065980968165370851033491443779536817191036939902901", "1.00392788937233282266540479921311801619481011378951599123553095833253182746583068127801550", "0E-91" ] }, "root_record": { "r": "1.56019150998309913258490994174969612027164535592126124114657322158645261931120931443907007", "b": "0.0405777968110086291968388319042409500545713613475216251912626130077185696529588700743600217", "h": "0.00484987836114445289193610288599733467744071092173636227330559997831109351033228435134309723", "A": "0.410953982008814078101179731212451777765119448501331772175867049990652291858927837890816488", "denominator": "0.992433260956491677865567361472329177268300046952264086711618017020744810732503994953697756", "polynomial_residual": "7.13057671648752014142404E-66", "bracket_initial_signs": [ "1.46371749356406578281917170525139113450521272919846099413241896108884085798950111867681538", "-1.99126993564315629145339228518619890956011247249005152224369075878115262286018567126387373" ], "bracket_derivative_max": "-5.52450554056051269183909884754140876202432516575625992244541741276396145379960753878892431", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.03739115168733111879374593869195084159648562305096208245319505297419388054426090927393782E-90", "6E-91", "0E-182", "6E-90", "0E-182", "-4.10956897251421401900426207967087277663809134512928299683103886735085715627002629507045062E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_1.2", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.008345279270771529, 0.0 ], "rh_scaled_inf": 2.193306126971235e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.193306126971235e-16 }, "characteristics": { "left": { "slow": 0.021174923550584365, "alfven_n": 0.05574182834767951, "fast": 0.8695852758674028 }, "right": { "slow": 0.02606008257709257, "alfven_n": 0.06962579462730142, "fast": 0.6946526953452972 } }, "front_relative_normal_velocity": { "left": -0.6408063863170719, "right": -0.9997806834748455 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601915099830992, "pressure_ratio": 2.5184704079768747, "entropy_over_cv": 0.18230410871360803, "tangential_field_ratio": 1.5644626515673157 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.225, "theta_Bn_degrees": 83.775, "compression": 1.5601888884311883, "u2x_km_s": -384.3428063604273, "u2y_km_s": -10.56951978802423, "speed2_km_s": 384.48811106399415, "signed_deflection_degrees": 1.575250721519642, "p2_over_p1": 2.5184685775164115, "B2_over_B1": 1.5590454523232864, "entropy_over_cv": 0.18230618236086593, "upstream_fast_Mach": 1.4392474512490128, "downstream_fast_Mach": 0.7369107268776163, "downstream_alfven_margin": 0.5848357876521431, "state_global_normalized": { "rho": "1.56018888843118823017892389097474277230131209591068075920549865486890955944931468617759688", "p": "0.102149085504065653175680355346919230427662589013623764383504276184573047969336399516750398", "u": [ "-0.640571343934045428464391827589934030563834594476950973416321566293976085731890647104379007", "-0.0176158663133737150485996013075209446747616731703236348741437586484741706830579561511835802", "-0E-91" ], "B": [ "0.0484538864485130027064073306041710125070010545214276457096404999412112820993003149271408050", "1.00392792106269685277424969916239986010837953258506309471049381232447811107347111274483151", "0E-91" ] }, "root_record": { "r": "1.56018888843118823017892389097474277230131209591068075920549865486890955944931468617759688", "b": "0.0405785462974922970324087957512630235317311941077615126356079929022306949350505696762783103", "h": "0.00488900511539226657485215886581606262965117410131061987949259260383416110876434005494294205", "A": "0.410922535301234536095358469980652721560257979705116156703204660148172819347906824964552727", "denominator": "0.992372228543481746465740144496403025528813864694192329097514874547011301488225901130097975", "polynomial_residual": "6.58492234005835236245983E-66", "bracket_initial_signs": [ "1.46361822045857601073778101601929324956752984460579727101926617243159051263046429367488373", "-1.99113529873811289239836459551497923739740079930064933243475432516276230652993655890581595" ], "bracket_derivative_max": "-5.52423735695322141372599849391271509202014840898390906456045142951619855508061396468114152", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.03756711876313405194887161501659866395698749896965572778573730551371564980057987422052839E-90", "-1E-91", "0E-182", "0E-90", "0E-182", "-3.79554243010202763498176951011906880878077248226317828562209119956681253438584745757580868E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_1.225", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.008730683859892775, 0.0 ], "rh_scaled_inf": 6.938893903907228e-18, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.021260170372755488, "alfven_n": 0.05596575750811002, "fast": 0.8695782566165242 }, "right": { "slow": 0.026164899012070888, "alfven_n": 0.0699054404958352, "fast": 0.6946487552094938 } }, "front_relative_normal_velocity": { "left": -0.6408015451602531, "right": -0.9997714504485632 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601888884311883, "pressure_ratio": 2.5184685775164115, "entropy_over_cv": 0.18230618236086582, "tangential_field_ratio": 1.5644947251832966 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.25, "theta_Bn_degrees": 83.75, "compression": 1.5601859967966791, "u2x_km_s": -384.3396265582635, "u2y_km_s": -10.536457731868946, "speed2_km_s": 384.48402500556625, "signed_deflection_degrees": 1.5703387046094528, "p2_over_p1": 2.5184655325957563, "B2_over_B1": 1.5590333696095036, "entropy_over_cv": 0.18230806230549712, "upstream_fast_Mach": 1.4392420817176497, "downstream_fast_Mach": 0.7369111879789244, "downstream_alfven_margin": 0.5846070116619749, "state_global_normalized": { "rho": "1.56018599679667908927154830857622435700046236014093762086987531133086469412214209797529620", "p": "0.102148962002083874899091591377982999350007813630094814565226032073552475280190204815496027", "u": [ "-0.640566044263772547161124178065687820370076439846271365483417179289585223163358888449956165", "-0.0175607628864482453059243001546666059439219031236886437521988201531392226379829128408040587", "-0E-91" ], "B": [ "0.0482959981732111110720856163955182947310039622864992225586077036146924575940063123654147486", "1.00392773040819991282237917707857219768348041599856530570918211921021803122855762085769344", "0E-91" ] }, "root_record": { "r": "1.56018599679667908927154830857622435700046236014093762086987531133086469412214209797529620", "b": "0.0405793112563384296433652597151217482073350606882856161989736608002673571337359066094829570", "h": "0.00492828979972106591226901304353274826447184761036810252311695189231378527745083880224328576", "A": "0.410891089210083368240211841035778420591054833987542955264981861874997745259763334445573425", "denominator": "0.992310951266319282828176881260355721614537596230832400360759082886993241346727055596331186", "polynomial_residual": "2.4521103473514119565109E-67", "bracket_initial_signs": [ "1.46351735278378851544617219262395060784103459057811845978341282350701932399369832724046806", "-1.99100200827225535034546763785976172825258941772011863865982039819198057868933485278223148" ], "bracket_derivative_max": "-5.52396917166386431502707618613191992587747901699649146478839576547314131201958865238033734", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.03774462385081806226182527284981095476736542957307032400133910794949003338886636880720231E-90", "6E-91", "0E-182", "3E-90", "0E-182", "-1.41356171076470579092736100730698091158409697664004843912724092310292525704992234495157750E-68", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_1.25", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.009116087873396888, 0.0 ], "rh_scaled_inf": 2.1935344646749795e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1935344646749795e-16 }, "characteristics": { "left": { "slow": 0.02134541598236971, "alfven_n": 0.056189681253220145, "fast": 0.8695711279301703 }, "right": { "slow": 0.02626971224905624, "alfven_n": 0.07018507305535988, "fast": 0.6946447993563062 } }, "front_relative_normal_velocity": { "left": -0.640796692915195, "right": -0.9997620270799091 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601859967966791, "pressure_ratio": 2.5184655325957563, "entropy_over_cv": 0.18230806230549712, "tangential_field_ratio": 1.5645266698727933 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.275, "theta_Bn_degrees": 83.72500000000001, "compression": 1.560182835063684, "u2x_km_s": -384.336542172183, "u2y_km_s": -10.503393047804664, "speed2_km_s": 384.4800370817539, "signed_deflection_degrees": 1.5654258034195534, "p2_over_p1": 2.518461273142848, "B2_over_B1": 1.559020980935286, "entropy_over_cv": 0.18230974853571594, "upstream_fast_Mach": 1.4392364706738097, "downstream_fast_Mach": 0.7369117290806596, "downstream_alfven_margin": 0.5843782299881725, "state_global_normalized": { "rho": "1.56018283506368394559690252072937400980266683381695206513372202598371324887651782420324123", "p": "0.102148789238673921058289407164289584387529721623483014966070795215052360917111360973736818", "u": [ "-0.640560903620304885902614555132801395034679962354858080968445093656686950417913954909321294", "-0.0175056550796744379877493319763171397681471602275396009409647994548872845870226710858563452", "-0E-91" ], "B": [ "0.0481381120065114991839011583497903130228940251183188794308357554710906900833474659257933038", "1.00392731740643762799216312326648199838473898503635249813328103240573535248120352647604825", "0E-91" ] }, "root_record": { "r": "1.56018283506368394559690252072937400980266683381695206513372202598371324887651782420324123", "b": "0.0405800916887129418969690039991032825498670667811175556786160161882835602478728285143213782", "h": "0.00496773243800057156489908935799945482340641828062474171484564240075083511895664485872678172", "A": "0.410859643723438074788170680640015840868253893872595256059285976951954734265101867277456874", "denominator": "0.992249429121042441721933755952458863251478562501398669713104566117703152736321020213240710", "polynomial_residual": "-8.74352802308320270525751E-66", "bracket_initial_signs": [ "1.46341489065539239637723850610557047083156828815234760956761544367223376212129629778684460", "-1.99087006387943635423736973937757723087816814555227247528102676789613704095840586503516754" ], "bracket_derivative_max": "-5.52370098431612878532832476181439784630026600030683286326693443823954791513610965913215334", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "1E-91", "0E-182", "2E-90", "0E-182", "5.04095745741249027851384236878899806981048278950682066945031115252505204318081770586884228E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_1.275", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.009501491273598967, 0.0 ], "rh_scaled_inf": 1.7864892882562994e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7864892882562994e-16, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.021430660377860365, "alfven_n": 0.056413599598818996, "fast": 0.8695638898113572 }, "right": { "slow": 0.02637452227511859, "alfven_n": 0.07046469225263735, "fast": 0.6946408277874043 } }, "front_relative_normal_velocity": { "left": -0.6407918295869914, "right": -0.9997524133706773 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560182835063684, "pressure_ratio": 2.518461273142848, "entropy_over_cv": 0.1823097485357159, "tangential_field_ratio": 1.5645584856218124 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.3, "theta_Bn_degrees": 83.7, "compression": 1.56017940321616, "u2x_km_s": -384.3335532078945, "u2y_km_s": -10.470325805374195, "speed2_km_s": 384.47614730159285, "signed_deflection_degrees": 1.560512031984741, "p2_over_p1": 2.5184557990870777, "B2_over_B1": 1.5590082863057875, "entropy_over_cv": 0.18231124103993068, "upstream_fast_Mach": 1.43923061811213, "downstream_fast_Mach": 0.7369123501883936, "downstream_alfven_margin": 0.5841494426200874, "state_global_normalized": { "rho": "1.56017940321615989507192051500258025757855036873776661950329093601544766525780221577120143", "p": "0.102148567210971865080333424994310499949027500746270151256598864722248357285574612259978814", "u": [ "-0.640555922013157460337164943152714669309430830303319939032643325304226294714654768342902105", "-0.0174505430089569918252586774392756401720712917434344559765832185621220535332317541685655561", "-0E-91" ], "B": [ "0.0479802281794601026829472250443525413376313582595160577570639077889220882536765195616367470", "1.00392668205512228993125877943734878513504124010645842159771566505084998160571829548850896", "0E-91" ] }, "root_record": { "r": "1.56017940321615989507192051500258025757855036873776661950329093601544766525780221577120143", "b": "0.0405808875958053666636269460428203199305601481872636093517725769256402697183503250120411762", "h": "0.00500733305434159572974663311537274605404384058961913383568067404216098473835598711892891513", "A": "0.410828198829377079982440013085433200066208640712131351690081894982376863398124165674169756", "denominator": "0.992187662103572778028679910005665547588241810039228422308747561802832943378917389442409615", "polynomial_residual": "-1.580749447422647459496382E-65", "bracket_initial_signs": [ "1.46331083418838327260116838779929049064400811453326318831634969885674089512784900974926668", "-1.99073946519265024671510164778001658232024749612595472102028351297737408215249701768736901" ], "bracket_derivative_max": "-5.52343279453164940148481770975162116396870292464355323111964740906722805119575964551664915", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.03810424874127430483995476558363342535536304305883133692052133686999751918041263273266712E-90", "0E-91", "0E-182", "-1E-90", "0E-182", "9.11466940523285414276578722968257343711087553333507855203760422192128212430485313875203225E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_1.3", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.009886894022820874, 0.0 ], "rh_scaled_inf": 2.1937673267823235e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": -0.0, "energy": 2.1937673267823235e-16 }, "characteristics": { "left": { "slow": 0.02151590355766206, "alfven_n": 0.05663751256072382, "fast": 0.869556542263123 }, "right": { "slow": 0.026479329077326863, "alfven_n": 0.07074429803443208, "fast": 0.694636840504465 } }, "front_relative_normal_velocity": { "left": -0.6407869551808113, "right": -0.9997426093226983 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.56017940321616, "pressure_ratio": 2.5184557990870773, "entropy_over_cv": 0.18231124103993057, "tangential_field_ratio": 1.5645901724160765 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.325, "theta_Bn_degrees": 83.675, "compression": 1.560175701237909, "u2x_km_s": -384.33065967111526, "u2y_km_s": -10.437256074121269, "speed2_km_s": 384.4723556740996, "signed_deflection_degrees": 1.555597404342247, "p2_over_p1": 2.518449110359286, "B2_over_B1": 1.5589952857261669, "entropy_over_cv": 0.1823125398067436, "upstream_fast_Mach": 1.4392245240272532, "downstream_fast_Mach": 0.736913051307827, "downstream_alfven_margin": 0.5839206495471385, "state_global_normalized": { "rho": "1.56017570123790888351852210019210315977878008914360100297968983198245571357894332167755161", "p": "0.102148295916172644152018565876698643866761419019144432260245380542606165736737695130151340", "u": [ "-0.640551099451858686337083871134478725353151040093747108887668140980569111843413198202932786", "-0.0173954267902021146491109762114400250086896985896841631664295818161473218743486788732174846", "-0E-91" ], "B": [ "0.0478223469231111403301210791658844834501339555804605907801904744825304312998749854361353273", "1.00392582435208283519923819717731889050690244033115946622110034237222375989308940492489725", "0E-91" ] }, "root_record": { "r": "1.56017570123790888351852210019210315977878008914360100297968983198245571357894332167755161", "b": "0.0405816989788288586706840889605761423415831683036111814600436853283429645472962952132313668", "h": "0.00504709167309609966884256017810327161180776216747436773134480568024735910135770767845995393", "A": "0.410796754515979714018371973659933999261216666174545972947695410499299896572624101759192076", "denominator": "0.992125650209715281913835768017426174607629114942328905688296545336328803466705900428560230", "polynomial_residual": "1.277234077549464845224075E-65", "bracket_initial_signs": [ "1.46320518349706400244204077810362292059691752697135403957038526819379863365044904585032100", "-1.99061021184403161997246293631250949046240102967254415244977905943918639373437686956103646" ], "bracket_derivative_max": "-5.52316460193000664994925641234411916350207545463115454413009539420851111778498341353688339", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.03828636888746402527338883036466668101942432894450903064723066155074099894768588702209621E-90", "4E-91", "0E-182", "4E-90", "0E-182", "-7.36546092368993613879247227551176903036652117756496372564932684683453274394715377005374290E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_1.325", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.010272296083391362, 0.0 ], "rh_scaled_inf": 2.1938854550303675e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7866599270387608e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1938854550303675e-16 }, "characteristics": { "left": { "slow": 0.02160114552021073, "alfven_n": 0.05686142015476015, "fast": 0.8695490852885273 }, "right": { "slow": 0.026584132642748903, "alfven_n": 0.07102389034751105, "fast": 0.694632837509172 } }, "front_relative_normal_velocity": { "left": -0.6407820697018987, "right": -0.9997326149378384 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560175701237909, "pressure_ratio": 2.518449110359286, "entropy_over_cv": 0.18231253980674356, "tangential_field_ratio": 1.5646217302410224 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.35, "theta_Bn_degrees": 83.65, "compression": 1.5601717291125776, "u2x_km_s": -384.32786156757027, "u2y_km_s": -10.404183923590463, "speed2_km_s": 384.4686622082707, "signed_deflection_degrees": 1.550681934531693, "p2_over_p1": 2.518441206891767, "B2_over_B1": 1.5589819792015884, "entropy_over_cv": 0.1823136448249511, "upstream_fast_Mach": 1.4392181884138275, "downstream_fast_Mach": 0.7369138324447887, "downstream_alfven_margin": 0.5836918507588116, "state_global_normalized": { "rho": "1.56017172911257769652858522832150903230680841043834746160693978376843055813733786432270737", "p": "0.102147975351530069657704887791466391757195622298982297588176196061933148785634421789120351", "u": [ "-0.640546435945950407381206868208226022764803594604456001703481813890889891131172638253977278", "-0.0173403065393174372473447523116745860599882657996363102242428920793213922957312218114694730", "-0E-91" ], "B": [ "0.0476644684685271383847643149400076210916706843178117366101233319110908369503976859537517763", "1.00392474429526482351731360565053020430622529455140126643397777939362823432445967926150164", "0E-91" ] }, "root_record": { "r": "1.56017172911257769652858522832150903230680841043834746160693978376843055813733786432270737", "b": "0.0405825258390201984328992505888065644399704282378295004751551310373423667671434887938556477", "h": "0.00508700831885725202081695740990356228275015098760261516653665472532024713309283581399094892", "A": "0.410765310771326195007785783098095903293885607059666296295226819774771358711295009665173545", "denominator": "0.992063393435158414131734563326179904026315967876308146342362846748794781595170572937617029", "polynomial_residual": "1.145659972400969455623041E-65", "bracket_initial_signs": [ "1.46309793869504540770462280090546807329969692391727968518617030185234658561605664959560980", "-1.99048230346485389849189160865065344461907769577502291851483554822344401735068791150997767" ], "bracket_derivative_max": "-5.52289640612872563525375806200027604017875164505397653252301051864651097996699406316936502", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.03847002773237060053053670258733449027973291254358263349440896030097096013861599640139500E-90", "-4E-91", "0E-182", "-4E-90", "0E-182", "-6.60749306120454451247537567829766258603920108218696114543302906091504678534172315357215139E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_1.35", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.01065769741764618, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7867464120123102e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": -0.0, "energy": -2.1940047150352075e-16 }, "characteristics": { "left": { "slow": 0.021686386263943685, "alfven_n": 0.057085322396761874, "fast": 0.8695415188906526 }, "right": { "slow": 0.026688932958451546, "alfven_n": 0.07130346913864385, "fast": 0.6946288188032155 } }, "front_relative_normal_velocity": { "left": -0.6407771731555734, "right": -0.9997224302180006 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601717291125776, "pressure_ratio": 2.518441206891767, "entropy_over_cv": 0.18231364482495116, "tangential_field_ratio": 1.5646531590818047 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.375, "theta_Bn_degrees": 83.625, "compression": 1.560167486823658, "u2x_km_s": -384.32515890299277, "u2y_km_s": -10.371109423327157, "speed2_km_s": 384.4650669130828, "signed_deflection_degrees": 1.5457656365950485, "p2_over_p1": 2.5184320886182654, "B2_over_B1": 1.5589683667372214, "entropy_over_cv": 0.18231455608354344, "upstream_fast_Mach": 1.4392116112665059, "downstream_fast_Mach": 0.7369146936052358, "downstream_alfven_margin": 0.5834630462446588, "state_global_normalized": { "rho": "1.56016748682365794947186741255811066783689775192524356290536691100985472180018032993353107", "p": "0.102147605514356837576980079715661462108438670383340265284375217744633681809982732040063057", "u": [ "-0.640541931504987922436372739819742662599056703390025675591442309798908837730549276435841192", "-0.0172851823722119271840924299070118193996587650610295735315697768710863595394209016883346743", "-0E-91" ], "B": [ "0.0475065930467789550665618748557385684429851821221711259952210675098006566255339671537781902", "1.00392344188273041582105999709298170527973226210080351435891661867979517106978352328618228", "0E-91" ] }, "root_record": { "r": "1.56016748682365794947186741255811066783689775192524356290536691100985472180018032993353107", "b": "0.0405833681776397962596264344368427030796914208348799141551677180164728027209553608448816767", "h": "0.00512708301645948789559109316778531106162777931052633937809917977783249256063277772259031111", "A": "0.410733867583497610946176929119222155767219525009038092813903132062894554992582691270644224", "denominator": "0.992000891775474141464979155249804357429496917942356408618065883614674575175473973347638677", "polynomial_residual": "-2.13104221270610633970086E-66", "bracket_initial_signs": [ "1.46298909989524700251694348110655610833135102683014716076413866457197509728310044478288115", "-1.99035573968552790865370048012880704320914108308064103322026028762027230089888246481095504" ], "bracket_derivative_max": "-5.52262820674327477463787984548947852517097656657191405003988514295153685053755652621616567", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.03865522545139957670833894956225921639902352580575171833515099396227942994764039063698990E-90", "-2E-91", "0E-182", "-6E-90", "0E-182", "1.22920570017318309434860678118843229077802701285496349208754550017487854249234070814696855E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_1.375", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.011043097987928215, 0.0 ], "rh_scaled_inf": 1.7868336742517771e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7868336742517771e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.021771625787299697, "alfven_n": 0.05730921930257134, "fast": 0.8695338430726027 }, "right": { "slow": 0.026793730011500542, "alfven_n": 0.07158303435460263, "fast": 0.6946247843882924 } }, "front_relative_normal_velocity": { "left": -0.6407722655472302, "right": -0.9997120551651237 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560167486823658, "pressure_ratio": 2.5184320886182654, "entropy_over_cv": 0.18231455608354352, "tangential_field_ratio": 1.564684458923293 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.4, "theta_Bn_degrees": 83.60000000000001, "compression": 1.560162974354486, "u2x_km_s": -384.32255168312406, "u2y_km_s": -10.338032642877481, "speed2_km_s": 384.4615697974932, "signed_deflection_degrees": 1.5408485245765875, "p2_over_p1": 2.5184217554739776, "B2_over_B1": 1.55895444833824, "entropy_over_cv": 0.182315273571705, "upstream_fast_Mach": 1.439204792579947, "downstream_fast_Mach": 0.7369156347952545, "downstream_alfven_margin": 0.5832342359942998, "state_global_normalized": { "rho": "1.56016297435448607764702645406094638574719047505838199190411935671415079329995659825428268", "p": "0.102147186402024538842166032976070248693021570519299440273702862484851997606011290936300232", "u": [ "-0.640537586138540014338134693303739872565430317137245497800998046776024561572934475869132245", "-0.0172300544047958025788967180826626457351878364855127932333144487265805104127199874045622844", "-0E-91" ], "B": [ "0.0473487208889458051015183282990519169958645530588054466933410496975800172227491531188515277", "1.00392191711265835211603377837385235444666221817081406007971909867807034360720124299633355", "0E-91" ] }, "root_record": { "r": "1.56016297435448607764702645406094638574719047505838199190411935671415079329995659825428268", "b": "0.0405842259959716963387241316033862184679981768801967611060297758665917066176565294101600318", "h": "0.00516731579097856875247516384855564573153367019943061366081564042753628859720306733946187873", "A": "0.410702424940575901682757726812340702844565625332959852227663626022901891682492403439482787", "denominator": "0.991938145226117972298167343667510435527009573042372765534025242592431062910171832404247528", "polynomial_residual": "-9.03348028807281061230429E-66", "bracket_initial_signs": [ "1.46287866720989772679428442433960052657954186334972329852578412310545771155225271902075115", "-1.99023052013560043521045962904299361615143675019028116718421526501419378800973656137019204" ], "bracket_derivative_max": "-5.52236000338706447881576319321787941699121626575996502082440637754210328692842669651172938", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "1E-91", "0E-182", "-1E-90", "0E-182", "5.21121684317995754922774865250098502788805333457911005700506684464851781022538688809366065E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_1.4", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.011428497756587589, 0.0 ], "rh_scaled_inf": 1.7869217139172424e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7869217139172424e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02185686408871904, "alfven_n": 0.05753311088803948, "fast": 0.8695260578375037 }, "right": { "slow": 0.026898523788960585, "alfven_n": 0.0718625859421621, "fast": 0.694620734266107 } }, "front_relative_normal_velocity": { "left": -0.6407673468823393, "right": -0.9997014897811831 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560162974354486, "pressure_ratio": 2.518421755473978, "entropy_over_cv": 0.18231527357170507, "tangential_field_ratio": 1.5647156297500724 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.425, "theta_Bn_degrees": 83.575, "compression": 1.5601581916882434, "u2x_km_s": -384.3200399137134, "u2y_km_s": -10.304953651788269, "speed2_km_s": 384.4581708704391, "signed_deflection_degrees": 1.5359306125228431, "p2_over_p1": 2.518410207395554, "B2_over_B1": 1.5589402240098233, "entropy_over_cv": 0.1823157972788142, "upstream_fast_Mach": 1.4391977323488148, "downstream_fast_Mach": 0.7369166560210592, "downstream_alfven_margin": 0.5830054199974202, "state_global_normalized": { "rho": "1.56015819168824332657589297174487248341073968753342680056396752854523343854061688363187518", "p": "0.102146718011963669655680744175611713161551406673352932803229109867392799614888385174379802", "u": [ "-0.640533399856188978670988436712689128518824091881508449809792648636757397287712251650742674", "-0.0171749227529804458464224835993455609094523671624012847613541444929638443010078777519303024", "-0E-91" ], "B": [ "0.0471908522261152843528307222259146945495802123412917304270486432315634278322420775736944937", "1.00392016998334392913618587554721948542830209387211652528218527964343406837178534188875644", "0E-91" ] }, "root_record": { "r": "1.56015819168824332657589297174487248341073968753342680056396752854523343854061688363187518", "b": "0.0405850992953235808972152706787251360705511100427577300451897563914905012251434067638739143", "h": "0.00520770666773164306196237197260074059304623433874232379931344974716125667336331722846763198", "A": "0.410670982830643840893271445467848903851710106559565906186098910293955859233135123581924732", "denominator": "0.991875153782428992326160000267892756865687821038672697755015156819131724383447601886075881", "polynomial_residual": "3.17516857812740335430494E-66", "bracket_initial_signs": [ "1.46276664075053668433029563799584631801295429074875235013152736011858852999890544307825359", "-1.99010664444375276461817987085352960682879135740883149039132618485010021326776874145991706" ], "bracket_derivative_max": "-5.52209179567144581887517004390504995879540454639509760606733774553434431063680810806031266", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-1E-91", "0E-182", "-2E-90", "0E-182", "-1.83190250308142030485293705425606329026211953960165044083068688406469290929026636460194322E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.425", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.011813896685981796, 0.0 ], "rh_scaled_inf": 2.1943692878320257e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": -2.1943692878320257e-16 }, "characteristics": { "left": { "slow": 0.021942101166643562, "alfven_n": 0.057756997169025895, "fast": 0.869518163188504 }, "right": { "slow": 0.0270033142778953, "alfven_n": 0.0721421238480996, "fast": 0.6946166684383698 } }, "front_relative_normal_velocity": { "left": -0.6407624171664461, "right": -0.9996907340681903 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601581916882434, "pressure_ratio": 2.518410207395554, "entropy_over_cv": 0.18231579727881397, "tangential_field_ratio": 1.564746671546443 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.45, "theta_Bn_degrees": 83.55000000000001, "compression": 1.5601531388079557, "u2x_km_s": -384.3176236005184, "u2y_km_s": -10.271872519606992, "speed2_km_s": 384.45487014083824, "signed_deflection_degrees": 1.531011914482565, "p2_over_p1": 2.5183974443210957, "B2_over_B1": 1.558925693757156, "entropy_over_cv": 0.18231612719444348, "upstream_fast_Mach": 1.439190430567778, "downstream_fast_Mach": 0.7369177572889932, "downstream_alfven_margin": 0.5827765982437726, "state_global_normalized": { "rho": "1.56015313880795574244114951163760901768762897361208204057771865716044516679420649002704817", "p": "0.102146200341663641767266636513856246283124639600904704513733769795357449130433176571410485", "u": [ "-0.640529372667530653148402473428489086479990002582845190344954665642959538334612469123708871", "-0.0171197875326783173963567672522369915906732142414014204096356649355827987624812901378181762", "-0E-91" ], "B": [ "0.0470329872893833945374780474068109908230176527774221746914156490791073999659721647868723784", "1.00391820049319897780496721588098546752215179244506474050151468317704204180856876671225682", "0E-91" ] }, "root_record": { "r": "1.56015313880795574244114951163760901768762897361208204057771865716044516679420649002704817", "b": "0.0405859880770267744387209608034928867932455891579223959310229430209106587065357001125090367", "h": "0.00524825567227730775151430305963401910975462078314222881886188151353762828318765749559867009", "A": "0.410639541241785018055522204978155223650073144922300403689547651505878098507554957661523680", "denominator": "0.991811917439629900397067449388717447887453582504621960988900255197004932878763050638703183", "polynomial_residual": "-1.16796307811981682083970E-66", "bracket_initial_signs": [ "1.46265302062801388552101199202441669468679393647434384931407996085136637795401001779186039", "-1.98998411223779921521582780763613006086406884141567131354681467648608384108422400327096492" ], "bracket_derivative_max": "-5.52182358320570917930107117807011512895384115836875962362051213917920140386737890607437512", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-1E-91", "0E-182", "0E-90", "0E-182", "6.73932188811823517839186650212714313198981682792807027579512814892393962015070985398937432E-68", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.45", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.012199294738475813, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.022027337019516747, "alfven_n": 0.05798087816139897, "fast": 0.8695101591287739 }, "right": { "slow": 0.02710810146536725, "alfven_n": 0.07242164801919505, "fast": 0.6946125869067983 } }, "front_relative_normal_velocity": { "left": -0.6407574764051716, "right": -0.9996797880281931 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601531388079557, "pressure_ratio": 2.518397444321096, "entropy_over_cv": 0.18231612719444368, "tangential_field_ratio": 1.5647775842964213 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.475, "theta_Bn_degrees": 83.525, "compression": 1.560147815696494, "u2x_km_s": -384.3153027493047, "u2y_km_s": -10.238789315881721, "speed2_km_s": 384.45166761758844, "signed_deflection_degrees": 1.526092444506675, "p2_over_p1": 2.5183834661901576, "B2_over_B1": 1.5589108575854274, "entropy_over_cv": 0.1823162633083594, "upstream_fast_Mach": 1.4391828872315113, "downstream_fast_Mach": 0.7369189386055282, "downstream_alfven_margin": 0.582547770723176, "state_global_normalized": { "rho": "1.56014781569649416266757329693550987317957734430557257832846873172793769916053310999958356", "p": "0.102145633388672792711096218773235117242795338096662499791472907292330470045538955818825698", "u": [ "-0.640525504582174447492938917201580796683540854520897104553526437179958480586102482643391694", "-0.0170646488598028692932891321483837508353376257980053691400411144217504344413083398225929399", "-0E-91" ], "B": [ "0.0468751263098545680293481030720326437563228452628629371181761415147307813355545904324352845", "1.00391600864075184049902404832280913326288057377118850813734864101595819426506988305619379", "0E-91" ] }, "root_record": { "r": "1.56014781569649416266757329693550987317957734430557257832846873172793769916053310999958356", "b": "0.0405868923424362480576916014023384396179979345688434866795361835479221225493754868732153217", "h": "0.00528896283041567043563694265664113875687012294223099535241136996371000017956300635580699764", "A": "0.410608100162083820427562860135146575567638559572818745301256208043428055266958298397283256", "denominator": "0.991748436192827044490130644935153949707976365825378540644649772459833530169159708644567557", "polynomial_residual": "1.296036999877343482675174E-65", "bracket_initial_signs": [ "1.46253780695249099472761319752403768884694477354337856680601541437467062797177157212120008", "-1.98986292314468565424457854377665912049262685606817630613655364672585729595787329021869259" ], "bracket_derivative_max": "-5.52155536559708289711633472497637538320098976591388797675876555104377619644031356210310800", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.03941140862864000363865145558953994627269188792179744354843113908768670590793058607688492E-90", "1E-91", "0E-182", "4E-90", "0E-182", "-7.47921465562235254248893807060227903244828856124715330601584619678904593169447477395351195E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_1.475", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.01258469187644223, 0.0 ], "rh_scaled_inf": 2.1946179992940877e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7871904990920102e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": -0.0, "t1_induction": 0.0, "t2_induction": -0.0, "energy": 2.1946179992940877e-16 }, "characteristics": { "left": { "slow": 0.022112571645783792, "alfven_n": 0.05820475388103597, "fast": 0.8695020456615052 }, "right": { "slow": 0.027212885338437926, "alfven_n": 0.07270115840223101, "fast": 0.6946084896731165 } }, "front_relative_normal_velocity": { "left": -0.640752524604212, "right": -0.9996686516632753 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560147815696494, "pressure_ratio": 2.5183834661901576, "entropy_over_cv": 0.18231626330835948, "tangential_field_ratio": 1.5648083679837372 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.5, "theta_Bn_degrees": 83.50000000000001, "compression": 1.5601422223365742, "u2x_km_s": -384.3130773658461, "u2y_km_s": -10.205704110161076, "speed2_km_s": 384.448563309568, "signed_deflection_degrees": 1.5211722166482256, "p2_over_p1": 2.5183682729437473, "B2_over_B1": 1.5588957154998315, "entropy_over_cv": 0.1823162056105225, "upstream_fast_Mach": 1.4391751023346946, "downstream_fast_Mach": 0.7369201999772647, "downstream_alfven_margin": 0.5823189374255154, "state_global_normalized": { "rho": "1.56014222233657420664700196604387861583511139949914910693648376419316274815029972664674360", "p": "0.102145017150598396002765833568716367750371557176449769645802945722669136635261668096985328", "u": [ "-0.640521795609743373816756257882289625953295064099192887374911660121543979992618910456243311", "-0.0170095068502684588763640610166185979902927307785024726706113564286894279451601694823078942", "-0E-91" ], "B": [ "0.0467172695186416927497232879899803187262425774211305719191084580099519724698554454954681856", "1.00391359442464734811438009873650923189535383727779157772160183008960055804581352675212876", "0E-91" ] }, "root_record": { "r": "1.56014222233657420664700196604387861583511139949914910693648376419316274815029972664674360", "b": "0.0405878120929306238304593606588863622580460890900243234711547044288419972828245325109919532", "h": "0.00532982816818841243055105135483787274957197506967730454454851485976981133784365344599332158", "A": "0.410576659579625415028483106040741306002341488192690834574150234817118084493032526565473220", "denominator": "0.991684710037010457828674803379119933522865284439374578444751255564619257487184561393312967", "polynomial_residual": "1.06307095683782871360781E-66", "bracket_initial_signs": [ "1.46242099983344208228383762184628387036322510986679518341860325109843971277180376571191807", "-1.98974307679048800169808763535695613841673443932752194112492836539308514741367159110318801" ], "bracket_derivative_max": "-5.52128714245073188713195094612338885944847764168618725897691710562684057881163081986328430", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-5E-91", "0E-182", "-5E-90", "0E-182", "-6.13553384905699348154122648757972978829053910926127993474451843047227579244320052407943792E-68", "2E-91" ], "diagnosis": { "case_id": "R95_phi_1.5", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.012970088062261357, 0.0 ], "rh_scaled_inf": 1.787281650091061e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.787281650091061e-16, "t1_momentum": 0.0, "t2_momentum": -0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": -0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02219780504389164, "alfven_n": 0.058428624343823135, "fast": 0.8694938227899124 }, "right": { "slow": 0.027317665884167723, "alfven_n": 0.07298065494399263, "fast": 0.6946043767390556 } }, "front_relative_normal_velocity": { "left": -0.6407475617693386, "right": -0.9996573249755573 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601422223365742, "pressure_ratio": 2.5183682729437478, "entropy_over_cv": 0.18231620561052264, "tangential_field_ratio": 1.564839022591837 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.525, "theta_Bn_degrees": 83.475, "compression": 1.5601363587107562, "u2x_km_s": -384.3109474559244, "u2y_km_s": -10.172616971994158, "speed2_km_s": 384.4455572256353, "signed_deflection_degrees": 1.5162512449623529, "p2_over_p1": 2.5183518645243264, "B2_over_B1": 1.5588802675055682, "entropy_over_cv": 0.18231595409108753, "upstream_fast_Mach": 1.439167075872013, "downstream_fast_Mach": 0.7369215414109317, "downstream_alfven_margin": 0.5820900983407428, "state_global_normalized": { "rho": "1.56013635871075626660718393383328786113044680562821836228436552286393893913549888862441252", "p": "0.102144351625106671296188078657728533105870189564943993881663350153612410119837891796756675", "u": [ "-0.640518245759874077502788617268078762759931701185704019225590211341516376295642004316482057", "-0.0169543616199902623384966445477229413337781749147491906956272069265675278071305873132137255", "0E-91" ], "B": [ "0.0465594171468661371459475971295983136181642261530958127054601535693272663877424121561047407", "1.00391095784364679693500209050829275712354891776323594095393277147622086297935826863646548", "0E-91" ] }, "root_record": { "r": "1.56013635871075626660718393383328786113044680562821836228436552286393893913549888862441252", "b": "0.0405887473299121792831364535504797659511264745895219323953592817427144282282690981138460218", "h": "0.00537085171187885255376499451742028629786711912876866734697561610249316798901689795401468499", "A": "0.410545219482495730621740052418300823803183697158588622717906038032785361232913723891623549", "denominator": "0.991620738967053895128314266309769525186653723838978370188998856281896179015884412368033692", "polynomial_residual": "-3.60178967280764230433943E-66", "bracket_initial_signs": [ "1.46230259937965438115402776168419113826001747289976626625662467707115818489517350386820988", "-1.98962457280041072099493925361969346858084675874209871595050577404268860757555971362289420" ], "bracket_derivative_max": "-5.52101891336975625329911734290417860384281562248287338501302160317888478021522049801267400", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.03979873813131797555398439865858125670008972065824503911312963852726167270359229666390342E-90", "-3E-91", "0E-182", "-2E-90", "0E-182", "2.07902614443164654001919191274368207673932356466562263436878326107851675048004021279111887E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_1.525", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.013355483258321353, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.022283037212289056, "alfven_n": 0.058652489565655795, "fast": 0.8694854905172319 }, "right": { "slow": 0.02742244308961596, "alfven_n": 0.0732601375912677, "fast": 0.6946002481063535 } }, "front_relative_normal_velocity": { "left": -0.6407425879063986, "right": -0.9996458079671954 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601363587107562, "pressure_ratio": 2.5183518645243264, "entropy_over_cv": 0.1823159540910877, "tangential_field_ratio": 1.564869548103881 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.55, "theta_Bn_degrees": 83.45, "compression": 1.5601302248014455, "u2x_km_s": -384.3089130253301, "u2y_km_s": -10.139527970930514, "speed2_km_s": 384.4426493746291, "signed_deflection_degrees": 1.5113295435062344, "p2_over_p1": 2.5183342408758085, "B2_over_B1": 1.5588645136078414, "entropy_over_cv": 0.18231550874040325, "upstream_fast_Mach": 1.4391588078381563, "downstream_fast_Mach": 0.7369229629133872, "downstream_alfven_margin": 0.5818612534588757, "state_global_normalized": { "rho": "1.56013022480144549862467730106906034932061290254780837464491372717089453718631762903683433", "p": "0.102143636809922794500393317176627753489149211967456065563320541648741201891671224664121048", "u": [ "-0.640514855042216868586899147224043297975830626628853681260640930608322923377787052150836065", "-0.0168992132848841882649423237245547445753726751630518866041669566227914826695937801770621364", "0E-91" ], "B": [ "0.0464015694256577752590978601031447590555926657482947208789154227808328964929896974165775424", "1.00390809889662792530364469427177075065478379096960160587662445910087523490030375168026006", "0E-91" ] }, "root_record": { "r": "1.56013022480144549862467730106906034932061290254780837464491372717089453718631762903683433", "b": "0.0405896980548068519363840792210762668938516337296670949441768358946030825037996613377426838", "h": "0.00541203348801201170886250477060750302553044980827799402220432721936249200442608059531749440", "A": "0.410513779858781439700973528867392571398568335217809316757952460321210308011657093005148220", "denominator": "0.991556522977714868980588479420453190286202003726671417424870235890885605362444548939911429", "polynomial_residual": "1.414502458494875309309222E-65", "bracket_initial_signs": [ "1.46218260569922904824785276134950443841459138422891180626184127561320476804637457045956753", "-1.98950741079878529646430289101105675544882040010222022167391463420716955093863887167583198" ], "bracket_derivative_max": "-5.52075067795518988615539602555147318321107164845383275871011175661314466204558067442499778", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.03999471300488566049623974517128436141820462412481031250925148820328684706479093597636857E-90", "2E-91", "0E-182", "3E-90", "0E-182", "-8.16576358132890938817534075523329105098440577432004635524772425939553136275794813618083657E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.55", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.013740877427018348, 0.0 ], "rh_scaled_inf": 2.194999565537641e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -2.194999565537641e-16 }, "characteristics": { "left": { "slow": 0.0223682681494267, "alfven_n": 0.058876349562438465, "fast": 0.8694770488467218 }, "right": { "slow": 0.027527216941840883, "alfven_n": 0.0735396062908467, "fast": 0.6945961037767544 } }, "front_relative_normal_velocity": { "left": -0.6407376030213142, "right": -0.9996341006403823 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601302248014455, "pressure_ratio": 2.5183342408758085, "entropy_over_cv": 0.18231550874040325, "tangential_field_ratio": 1.5648999445027445 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.575, "theta_Bn_degrees": 83.425, "compression": 1.5601238205908918, "u2x_km_s": -384.30697407986145, "u2y_km_s": -10.106437176520076, "speed2_km_s": 384.4398397653685, "signed_deflection_degrees": 1.506407126339046, "p2_over_p1": 2.5183154019435627, "B2_over_B1": 1.5588484538118603, "entropy_over_cv": 0.18231486954901255, "upstream_fast_Mach": 1.4391502982278208, "downstream_fast_Mach": 0.7369244644916179, "downstream_alfven_margin": 0.5816324027699981, "state_global_normalized": { "rho": "1.56012382059089181378196352849132556910408523987323735916493976215312712670394676577815210", "p": "0.102142872702830907856250524607737124726702088725287634562287124155603919587309417803342963", "u": [ "-0.640511623466435753641308338578411809526570952957831228255553897807720297803162315025747540", "-0.0168440619608667911310109661337992050708974945200550599785004298717668029363207653634314530", "0E-91" ], "B": [ "0.0462437265861550118814830205671548621025450268389967712391398011132581094655713654642630579", "1.00390501758258489009487050252554483600641398421654381083110251536031566250058806992632090", "0E-91" ] }, "root_record": { "r": "1.56012382059089181378196352849132556910408523987323735916493976215312712670394676577815210", "b": "0.0405906642690642439270773066419697322970696057767145326042286296885611558274319381439590397", "h": "0.00545337352335467825582223912436245830351535232981274767574196026143950719813175291278583773", "A": "0.410482340696569940478248397042445755170801089075240108084970896063089675262916737614790417", "denominator": "0.991492062063634686372210088177228109350887811217768924291427693806749606223349289920448375", "polynomial_residual": "6.32857247380131048412028E-66", "bracket_initial_signs": [ "1.46206101889958193039782099306539474226724167997089388455941639349821301457016734840146881", "-1.98939159040906869763570622026284521087897925443742223219950973244472482030552252197118662" ], "bracket_derivative_max": "-5.52048243580599904635704311386918111244012126969484134820419582502847527446031348429980772", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.04019222820911558568238474652005017442587845835670200942835953892460381878791308450508427E-90", "-8E-91", "0E-182", "-2E-90", "0E-182", "-3.65384685011338208198836263856770053881813888306989880722687417333404577780061053644269490E-67", "4E-91" ], "diagnosis": { "case_id": "R95_phi_1.575", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.014126270530756558, 0.0 ], "rh_scaled_inf": 4.3902580432981244e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7875597732525947e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 4.3902580432981244e-16 }, "characteristics": { "left": { "slow": 0.02245349785375719, "alfven_n": 0.05910020435008497, "fast": 0.8694684977816627 }, "right": { "slow": 0.02763198742789963, "alfven_n": 0.07381906098952272, "fast": 0.69459194375201 } }, "front_relative_normal_velocity": { "left": -0.6407326071200831, "right": -0.9996222029973468 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601238205908918, "pressure_ratio": 2.518315401943563, "entropy_over_cv": 0.18231486954901266, "tangential_field_ratio": 1.5649302117710173 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.6, "theta_Bn_degrees": 83.4, "compression": 1.5601171460611898, "u2x_km_s": -384.3051306253251, "u2y_km_s": -10.073344658313111, "speed2_km_s": 384.4371284066529, "signed_deflection_degrees": 1.5014840075219162, "p2_over_p1": 2.5182953476744117, "B2_over_B1": 1.5588320881228395, "entropy_over_cv": 0.1823140365076525, "upstream_fast_Mach": 1.4391415470357072, "downstream_fast_Mach": 0.7369260461527389, "downstream_alfven_margin": 0.5814035462642598, "state_global_normalized": { "rho": "1.56011714606118986946894438535238000664649172641972536144510817205682084025442462140149482", "p": "0.102142059301674129973117552084647034585780392133997405040999938438551803335037566909294834", "u": [ "-0.640508551042208468159601129286173873857561196925427005267809578669880782460576314894441914", "-0.0167889077638551847587150693445254862482069050430436550051214362258020615137856959450600046", "0E-91" ], "B": [ "0.0460858888595048078047960246881565334492108499976133882220600669501733229594296805481975879", "1.00390171390062824299014015580864320651114320422958335190901653227228246315914936002055046", "0E-91" ] }, "root_record": { "r": "1.56011714606118986946894438535238000664649172641972536144510817205682084025442462140149482", "b": "0.0405916459741576267068916268964036278512762785936080059131173643968118961221897839994993689", "h": "0.00549487184491547416719037892366071462451512741377002605804820088603258189341781092858518736", "A": "0.410450901983949338874666159357338698634189021108625284714443409269591063554881387490939670", "denominator": "0.991427356219338485340107263714692645255732423192807308224832708890193256297300955762126824", "polynomial_residual": "4.70033966121310701514528E-66", "bracket_initial_signs": [ "1.46193783908744433500576341053947555742034855041340078996619181925994490901547179767225373", "-1.98927711125384183032370693147163148191449608288460240551408809533824301842777625769261347" ], "bracket_derivative_max": "-5.52021418651908093428949771637178436320329534872938768766934030355001918660517851742272963", "iterations": 216 }, "flux_residuals": [ "-2E-90", "1.60807825678654870819711842849684583566600232700524316244304092188632982986086390790328390E-89", "-8E-91", "0E-182", "-5E-90", "0E-182", "-2.71409662787610521797511052028638803900713273466962705655737918988855032210122227430744312E-67", "3E-91" ], "diagnosis": { "case_id": "R95_phi_1.6", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.014511662531948412, 0.0 ], "rh_scaled_inf": 2.1952596118444021e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7876540382618107e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.1952596118444021e-16 }, "characteristics": { "left": { "slow": 0.022538726323735145, "alfven_n": 0.059324053944518534, "fast": 0.8694598373253561 }, "right": { "slow": 0.02773675453484826, "alfven_n": 0.07409850163409154, "fast": 0.6945877680338782 } }, "front_relative_normal_velocity": { "left": -0.6407276002087784, "right": -0.9996101150403544 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601171460611898, "pressure_ratio": 2.518295347674411, "entropy_over_cv": 0.18231403650765243, "tangential_field_ratio": 1.5649603498910034 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.625, "theta_Bn_degrees": 83.375, "compression": 1.5601102011942791, "u2x_km_s": -384.3033826675359, "u2y_km_s": -10.040250485860174, "speed2_km_s": 384.43451530726185, "signed_deflection_degrees": 1.4965602011178842, "p2_over_p1": 2.5182740780166313, "B2_over_B1": 1.5588154165459978, "entropy_over_cv": 0.18231300960725427, "upstream_fast_Mach": 1.4391325542565219, "downstream_fast_Mach": 0.7369277079039948, "downstream_alfven_margin": 0.5811746839318768, "state_global_normalized": { "rho": "1.56011020119427906082899297737096780806606140597029522799686677097183414779464477277513680", "p": "0.102141196604354565825430717310756276344102873788547892059314705193866831754690487182216927", "u": [ "-0.640505637779226509443619824028400951620177644037693400240389194056148946621636789896114602", "-0.0167337508097669557321413935853914579657820729265812939859131265722085559563814206058689497", "0E-91" ], "B": [ "0.0459280564768627051597436616660032067280586272057355438962344744032851826572969417791562852", "1.00389818784998490655486727684869597518617898251323697957169409869895813003736502105178405", "0E-91" ] }, "root_record": { "r": "1.56011020119427906082899297737096780806606140597029522799686677097183414779464477277513680", "b": "0.0405926431715839458178373200292927951883841916102051710664607699603120082735378036143807493", "h": "0.00553652847994492197043190972372628380170505237302296190693943547494527720530569182480730473", "A": "0.410419463709008430513288167123019907958362032439217509219570148054654598735847387844300685", "denominator": "0.991362405439235271762443485743025974199206939147970127012339324799926613635879525168660405", "polynomial_residual": "2.85670818948112992088816E-66", "bracket_initial_signs": [ "1.46181306636886380536453614725553355196193166778196615822461544593986164065856660380915694", "-1.98916397295480797449812151784274775389427637389447202937907283370449548269768449478527409" ], "bracket_derivative_max": "-5.51994592968926224574790575222279558102932544085917576564717750213290590821839427665090556", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.04059188036598861189781512044964541198255404262747434067786633028014791102409338375943869E-90", "-4E-91", "0E-182", "2E-90", "0E-182", "-1.64973207167775583017013908286154129081147200025205652340069142752792227061650317309054890E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_1.625", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.014897053393014663, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.022623953557817246, "alfven_n": 0.059547898361671826, "fast": 0.8694510674811273 }, "right": { "slow": 0.027841518249741702, "alfven_n": 0.07437792817135158, "fast": 0.694583576624124 } }, "front_relative_normal_velocity": { "left": -0.6407225822935486, "right": -0.9995978367717061 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601102011942791, "pressure_ratio": 2.5182740780166313, "entropy_over_cv": 0.18231300960725416, "tangential_field_ratio": 1.5649903588447207 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.65, "theta_Bn_degrees": 83.35000000000001, "compression": 1.5601029859719435, "u2x_km_s": -384.3017302123171, "u2y_km_s": -10.007154728712047, "speed2_km_s": 384.43200047595536, "signed_deflection_degrees": 1.4916357211918554, "p2_over_p1": 2.5182515929199534, "B2_over_B1": 1.558798439086559, "entropy_over_cv": 0.18231178883894322, "upstream_fast_Mach": 1.4391233198849764, "downstream_fast_Mach": 0.7369294497527582, "downstream_alfven_margin": 0.5809458157631304, "state_global_normalized": { "rho": "1.56010298597194351234973195605409024612150255929846771879854376085247417851894333526254703", "p": "0.102140284608833316709243465894657471492714696996971264502982807439265546134628876423156523", "u": [ "-0.640502883687195169992552964808623478450787894138005764602120949063131968892023758848765782", "-0.0166785912145200767713348311436025940149008490326465378006049417069467806905285912623391250", "0E-91" ], "B": [ "0.0457702296693928528479804801622461961046090514749886087225910768470723248122724541142270471", "1.00389443942999815011733239769688436803350627927904335850216462235178964900864091765090441", "0E-91" ] }, "root_record": { "r": "1.56010298597194351234973195605409024612150255929846771879854376085247417851894333526254703", "b": "0.0405936558628638257447682142308496522541377978719928758302298091928006967677170675703913389", "h": "0.00557834345593551247679060967076076990135323232374227781991544339263182637055548611041347589", "A": "0.410388025859836682714312744014008356647323283165694236192467764706960918251696543287317710", "denominator": "0.991297209717617956285799122422078711445128070743450654441038667280864502490158353381512158", "polynomial_residual": "-1.72067086686204913138962E-66", "bracket_initial_signs": [ "1.46168670084920490066125865775360812468362401659420335284237510868145079728714308715395716", "-1.98905217513279120893034405637149710074610127529216907812770798843563212861413067288148256" ], "bracket_derivative_max": "-5.51967766490929771367944153866126421489866022063307746076747486446548191137195601054825867", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.04079401770055362384316274750152236184237413935607663991641763362989425784387836576114625E-90", "-1E-91", "0E-182", "0E-90", "0E-182", "9.93795010252956986431057163569070270163141735119787966399218627087783055291742327506308605E-68", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.65", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.01528244307638452, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 6.938893903907228e-18, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.022709179554462347, "alfven_n": 0.0597717376174872, "fast": 0.8694421882523219 }, "right": { "slow": 0.02794627855963382, "alfven_n": 0.07465734054810401, "fast": 0.694579369524519 } }, "front_relative_normal_velocity": { "left": -0.6407175533806176, "right": -0.9995853681937397 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5601029859719435, "pressure_ratio": 2.518251592919954, "entropy_over_cv": 0.1823117888389434, "tangential_field_ratio": 1.5650202386139018 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.675, "theta_Bn_degrees": 83.325, "compression": 1.5600955003758121, "u2x_km_s": -384.3001732655001, "u2y_km_s": -9.974057456419693, "speed2_km_s": 384.42958392147375, "signed_deflection_degrees": 1.4867105818105564, "p2_over_p1": 2.5182278923355645, "B2_over_B1": 1.5587811557497524, "entropy_over_cv": 0.18231037419403892, "upstream_fast_Mach": 1.439113843915788, "downstream_fast_Mach": 0.7369312717065313, "downstream_alfven_margin": 0.5807169417483683, "state_global_normalized": { "rho": "1.56009550037581206959871431018058785860939559382529782019237721465050712527807061023125292", "p": "0.102139323313130490158723677293625296117341850637386265477948460298634874020133266913802645", "u": [ "-0.640500288775833571394533423257083055773103473073036827049996962984401578748959629080206607", "-0.0166234290940328200644828211359990746569983784506954484621664479149009207392925719251751935", "0E-91" ], "B": [ "0.0456124086682680320671736913145172998282050553955986687656206811625155392236501775422949109", "1.00389046864012756544934959230377045696712769720597414209145322998687247060757030396634867", "0E-91" ] }, "root_record": { "r": "1.56009550037581206959871431018058785860939559382529782019237721465050712527807061023125292", "b": "0.0405946840495415748448918451765910003115605524714307856783550896687354979042321526032814892", "h": "0.00562031680062177329699216909088247254918139544334645650024248460005326792712586016938809370", "A": "0.410356588424524216492448553432153874457787839992031502785104925634932006824458948142038665", "denominator": "0.991231769048663391388700260260602951458090398245853479781505540442768672856366604991322652", "polynomial_residual": "-1.002870626649886922559872E-65", "bracket_initial_signs": [ "1.46155874263314998066847159457986175359018412033949786372185297555777224197891546770859987", "-1.98894171740773482260616303391310309562752069248280068710178251627356471663159781672745869" ], "bracket_derivative_max": "-5.51940939176986863597907766431955791607297560565209124398446099823147803772825735670261741", "iterations": 216 }, "flux_residuals": [ "-2E-90", "-8.04099769612962558999584870381131236284370083413890321967254923543870740799809157001565915E-90", "2E-91", "0E-182", "-1E-90", "0E-182", "5.79289131240186923880057916204472985846398488378113680686596540973106873529835548874224001E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_1.675", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.01566783154449576, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02279440431213146, "alfven_n": 0.05999557172791665, "fast": 0.8694331996423086 }, "right": { "slow": 0.02805103545157734, "alfven_n": 0.07493673871115263, "fast": 0.6945751467368418 } }, "front_relative_normal_velocity": { "left": -0.640712513476285, "right": -0.999572709308829 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600955003758121, "pressure_ratio": 2.518227892335564, "entropy_over_cv": 0.18231037419403873, "tangential_field_ratio": 1.5650499891799925 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.7, "theta_Bn_degrees": 83.30000000000001, "compression": 1.5600877443873582, "u2x_km_s": -384.2987118329248, "u2y_km_s": -9.940958738534203, "speed2_km_s": 384.4272656525375, "signed_deflection_degrees": 1.4817847970424927, "p2_over_p1": 2.518202976216105, "B2_over_B1": 1.5587635665408117, "entropy_over_cv": 0.1823087656640551, "upstream_fast_Mach": 1.4391041263436788, "downstream_fast_Mach": 0.7369331737729449, "downstream_alfven_margin": 0.5804880618780033, "state_global_normalized": { "rho": "1.56008774438735829110418444095157206593736833506842592712029268795639508394796313046129923", "p": "0.102138312715325209822619020800847676785039320917497368758252812450655573123303756374741140", "u": [ "-0.640497853054874698721062120295175830258861747112236465574501294202990059501378286869317845", "-0.0165682645642236705581881155572403244507120610808908798350786402362799238929858046252259052", "0E-91" ], "B": [ "0.0454545937046696819300267618412609992712640877310253927417714357937784217228560268050765707", "1.00388627547994904224857905326248460487525455983406936954687943150398232824457218087800869", "0E-91" ] }, "root_record": { "r": "1.56008774438735829110418444095157206593736833506842592712029268795639508394796313046129923", "b": "0.0405957277331851903543084536296584414923862720814746609260661756385124161591726026513601047", "h": "0.00566244854198033814412926078182043390784634551288266073328480370561277309844834208175632189", "A": "0.410325151391161788556426550692474994364605816954493819794725669919891068937149589120770254", "denominator": "0.991166083426432408581681350127626795034154587941158537134944821653407252999796211743346034", "polynomial_residual": "4.59596257907596632459196E-66", "bracket_initial_signs": [ "1.46142919182469999512966657650394537973215422221890383113136707593138323845979527107568894", "-1.98883259939869971289535920052602354030395173854657795247075912679469041255492784600507991" ], "bracket_derivative_max": "-5.51914110985958138933034120485290703748208037623368834649838802274919456035904128917504158", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "0E-91", "0E-182", "0E-90", "0E-182", "-2.65508488011819903137701094316024019826981498220377869288522367901613608233574023570105029E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.7", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.016053218759794857, 0.0 ], "rh_scaled_inf": 2.1957933183871144e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -6.938893903907228e-18, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.1957933183871144e-16 }, "characteristics": { "left": { "slow": 0.0228796278292879, "alfven_n": 0.060219400708922, "fast": 0.8694241016544773 }, "right": { "slow": 0.028155788912623887, "alfven_n": 0.07521612260730397, "fast": 0.6945709082628776 } }, "front_relative_normal_velocity": { "left": -0.6407074625869253, "right": -0.999559860119384 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600877443873582, "pressure_ratio": 2.518202976216105, "entropy_over_cv": 0.1823087656640553, "tangential_field_ratio": 1.5650796105241527 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.725, "theta_Bn_degrees": 83.27499999999999, "compression": 1.5600797179879005, "u2x_km_s": -384.2973459204392, "u2y_km_s": -9.907858644606744, "speed2_km_s": 384.4250456778476, "signed_deflection_degrees": 1.4768583809579046, "p2_over_p1": 2.518176844515671, "B2_over_B1": 1.5587456714649752, "entropy_over_cv": 0.18230696324069975, "upstream_fast_Mach": 1.4390941671633766, "downstream_fast_Mach": 0.7369351559597584, "downstream_alfven_margin": 0.580259176142514, "state_global_normalized": { "rho": "1.56007971798790044038109952490537971376782613062183395712527011472345688461949330039778206", "p": "0.102137252813555625300699598110840920646898437402497058016753142746857365285174306101302076", "u": [ "-0.640495576534065435424576917582388687190505619551478671549312784937988633738296496556699654", "-0.0165130977410112392056171957832274520712912774190739557347871281638464702432354053955222346", "0E-91" ], "B": [ "0.0452967850097879251780901995652649224782963897039098994362103348918363486964374534297978215", "1.00388185994915474342237837654176331973400005731546829274209631459401571065675389514192782", "0E-91" ] }, "root_record": { "r": "1.56007971798790044038109952490537971376782613062183395712527011472345688461949330039778206", "b": "0.0405967869153863634716066899282972368826604498825761530398315812958741172745665489240827809", "h": "0.00570473870823001692407178000196089545525052862079892850089836859005624205227158395950370194", "A": "0.410293714747840773310592872996335661066890334391485003048955437156116730710941138710997728", "denominator": "0.991100152844869855744069348414940839686532569252297489191562237700427884331293150596215034", "polynomial_residual": "6.95376772521622743837829E-66", "bracket_initial_signs": [ "1.46129804852717527784570803594708210379801628704334469492705397778041926645683505956656110", "-1.98872482072386277046824228933940897394411740932300035297467940476370885124624142646390319" ], "bracket_derivative_max": "-5.51887281876496592908248181050768972368114154416188622004411448759185449922101766297110334", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "0E-91", "0E-182", "1E-90", "0E-182", "-4.01766347043330454444981374456066716780177574145245240845889559591138894272038728585640219E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.725", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.016438604684737092, 0.0 ], "rh_scaled_inf": 1.7881370507935794e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7881370507935794e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02296485010439727, "alfven_n": 0.060443224576474996, "fast": 0.8694148942922404 }, "right": { "slow": 0.028260538929823966, "alfven_n": 0.07549549218336729, "fast": 0.6945666541044185 } }, "front_relative_normal_velocity": { "left": -0.640702400718989, "right": -0.9995468206278512 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600797179879005, "pressure_ratio": 2.518176844515671, "entropy_over_cv": 0.18230696324069973, "tangential_field_ratio": 1.5651091026272559 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.75, "theta_Bn_degrees": 83.25, "compression": 1.5600714211586015, "u2x_km_s": -384.29607553389997, "u2y_km_s": -9.874757244188505, "speed2_km_s": 384.4229240060855, "signed_deflection_degrees": 1.471931347628721, "p2_over_p1": 2.5181494971898157, "B2_over_B1": 1.5587274705274867, "entropy_over_cv": 0.18230496691587514, "upstream_fast_Mach": 1.4390839663696142, "downstream_fast_Mach": 0.7369372182748609, "downstream_alfven_margin": 0.5800302845324445, "state_global_normalized": { "rho": "1.56007142115860147810259347318366324490885785406974794221512665982270330380091427016085154", "p": "0.102136143606018921940186939948398998056607656975544162767877625664735132913426792425356284", "u": [ "-0.640493459223166598739489367803018378372472910550148106622531309724700983651883856947540435", "-0.0164579287403141761723111279908250960639361361658713202478653441793685823531967707930367630", "0E-91" ], "B": [ "0.0451389828148215939911888385202988190560171230550424801539729091208915516455867475914441509", "1.00387722204755308017308484194231353339851299654514230279245456610530879053074137943255719", "0E-91" ] }, "root_record": { "r": "1.56007142115860147810259347318366324490885785406974794221512665982270330380091427016085154", "b": "0.0405978615977604845185443247353864617725322852736537877924575201012345393727006003561898848", "h": "0.00574718732783186661374987539723789009831461489100720952323248786166608981899309058466219225", "A": "0.410262278482653144858525031881777688054397703511209567180554526553201040554954884918407369", "denominator": "0.991033977297804634597678145261019152129256704833837753161672416607906670505096805132781471", "polynomial_residual": "-6.60861139557672476299949E-66", "bracket_initial_signs": [ "1.46116531284321634546873543626461640533150913303150769374076875656294501139963305524515330", "-1.98861838100051525094915922417323740380190593915853001656700689065368546002716899491029436" ], "bracket_derivative_max": "-5.51860451807047427515536460453693663232456537606156677881025666410404324217373256612004810", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.04161797993802566406696836740058506384017464495540436932806534834786602985873290712409917E-90", "3E-91", "0E-182", "1E-90", "0E-182", "3.81869555922499458923134763556862264850768605229452431349265463399780491802956393764679585E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_1.75", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.01682398928178669, 0.0 ], "rh_scaled_inf": 1.7882359920389019e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7882359920389019e-16, "t1_momentum": -6.938893903907228e-18, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.023050071135927608, "alfven_n": 0.0606670433465574, "fast": 0.8694055775590319 }, "right": { "slow": 0.02836528549022697, "alfven_n": 0.07577484738615457, "fast": 0.6945623842632632 } }, "front_relative_normal_velocity": { "left": -0.6406973278790019, "right": -0.9995335908367129 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600714211586015, "pressure_ratio": 2.5181494971898157, "entropy_over_cv": 0.18230496691587506, "tangential_field_ratio": 1.5651384654698883 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.775, "theta_Bn_degrees": 83.225, "compression": 1.560062853880469, "u2x_km_s": -384.2949006791718, "u2y_km_s": -9.84165460683065, "speed2_km_s": 384.4209006459127, "signed_deflection_degrees": 1.4670037111285197, "p2_over_p1": 2.5181209341955455, "B2_over_B1": 1.5587089637335942, "entropy_over_cv": 0.18230277668167771, "upstream_fast_Mach": 1.43907352395713, "downstream_fast_Mach": 0.7369393607262699, "downstream_alfven_margin": 0.5798013870384041, "state_global_normalized": { "rho": "1.56006285388046905441706810213510273025165466847029000373949914492207082954699720746981156", "p": "0.102134985090971330592178255047131114549037981237389596836249349589706321519780544096603376", "u": [ "-0.640491501131952975587015157386537818105155701467469997971920847580478828886243682826444029", "-0.0164027576780510839994451312387135259280485685440110694438018017915800281321783336378119845", "0E-91" ], "B": [ "0.0449811873509782558932957416638891378039552531795956614834438393556318460741830608207771566", "1.00387236177506868688462049972722893331612879134224947923182498232368466791512036067393020", "0E-91" ] }, "root_record": { "r": "1.56006285388046905441706810213510273025165466847029000373949914492207082954699720746981156", "b": "0.0405989517819466481778426964217815995360986334486813058793043341975043983749411127484091933", "h": "0.00578979442948926292766179713574534140928649272526173284890841668662941504458296637875087875", "A": "0.410230842583691459008613784249593984139970916087927974645921083301091996695951845936490918", "denominator": "0.990967556778949738317603184533766764689881173374929431293039664444847539319720780106631795", "polynomial_residual": "-2.9966022687436868190186E-67", "bracket_initial_signs": [ "1.46103098487478470101020232350901506354608014945223282609595160888506050406159456189614449", "-1.98851327984506113329688114140705340507619526787215148920712455159057788130800782294796401" ], "bracket_derivative_max": "-5.51833620735847898396328817561339506038533823659845415131265078085344424526509686874242752", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.04182782470669520384192973553405548264005187306928848832078209377107286069559550939326019E-90", "2E-91", "0E-182", "1E-90", "0E-182", "1.73175066968799236760792664216847181881070403518650813431283954850785399596144201076335819E-68", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_1.775", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.017209372513416917, 0.0 ], "rh_scaled_inf": 1.7883357132845842e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7883357132845842e-16, "t1_momentum": 6.938893903907228e-18, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02313529092234936, "alfven_n": 0.06089085703516108, "fast": 0.8693961514583085 }, "right": { "slow": 0.02847002858088116, "alfven_n": 0.07605418816248054, "fast": 0.6945580987412174 } }, "front_relative_normal_velocity": { "left": -0.6406922440735652, "right": -0.9995201707484881 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.560062853880469, "pressure_ratio": 2.5181209341955455, "entropy_over_cv": 0.18230277668167771, "tangential_field_ratio": 1.5651676990323506 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.8, "theta_Bn_degrees": 83.2, "compression": 1.5600540161343555, "u2x_km_s": -384.293821362128, "u2y_km_s": -9.808550802084259, "speed2_km_s": 384.4189756059712, "signed_deflection_degrees": 1.4620754855324787, "p2_over_p1": 2.518091155491325, "B2_over_B1": 1.5586901510885507, "entropy_over_cv": 0.18230039253039837, "upstream_fast_Mach": 1.4390628399206675, "downstream_fast_Mach": 0.7369415833221321, "downstream_alfven_margin": 0.5795724836510674, "state_global_normalized": { "rho": "1.56005401613435550141109843856863819520562082531825230857077584445202196747261257857851488", "p": "0.102133777266728137328074660411823360928382191296807978524253342629343005927957189141900643", "u": [ "-0.640489702270213358984127225730284854391198539465532633587992797029701712722486137566522927", "-0.0163475846701404307243226132298425521881564136291422113234033826191155447429505552910320813", "0E-91" ], "B": [ "0.0448233988494742397556836561120230927090042269165828386004636296388389277462681850542112885", "1.00386727913174239581031139539197392782940026293261070690262185186878231958112530986655738", "0E-91" ] }, "root_record": { "r": "1.56005401613435550141109843856863819520562082531825230857077584445202196747261257857851488", "b": "0.0406000574696076588081240566946062239101533061317363059701826437634104215281958230121886096", "h": "0.00583256004214797277296299637050711525882837829513409782656304280023788457425491152450270835", "A": "0.410199407039048835281553069156806936014916893802611127288484495254650812446132435847324347", "denominator": "0.990900891281902289280307292968566286064442184481417491947620713739931813926086541019287911", "polynomial_residual": "-7.6201153328441299169242E-67", "bracket_initial_signs": [ "1.46089506472316364206977692349094657678534000847847658757816092374921503184433151447303986", "-1.98840951687301546490165117982781324703537514116756671449281122590507891620770660846519605" ], "bracket_derivative_max": "-5.51806788620927160634881522547761077037233472425439803205017348533736685617766657798132432", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.04203921155808549914224270818379133250014621382054453415184902335702670944160024516672551E-90", "-5E-91", "0E-182", "1E-90", "0E-182", "4.40422236573981804216166794789191081916256179748608495317285943330740605441954608316994846E-68", "2E-91" ], "diagnosis": { "case_id": "R95_phi_1.8", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.01759475434211023, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.023220509462135497, "alfven_n": 0.06111466565828812, "fast": 0.8693866159935478 }, "right": { "slow": 0.028574768188833657, "alfven_n": 0.07633351445916262, "fast": 0.6945537975400936 } }, "front_relative_normal_velocity": { "left": -0.6406871493093556, "right": -0.9995065603657316 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600540161343555, "pressure_ratio": 2.518091155491325, "entropy_over_cv": 0.18230039253039831, "tangential_field_ratio": 1.5651968032946548 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.825, "theta_Bn_degrees": 83.17500000000001, "compression": 1.5600449079009577, "u2x_km_s": -384.29283758865034, "u2y_km_s": -9.775445899500276, "speed2_km_s": 384.4171488948833, "signed_deflection_degrees": 1.4571466849173353, "p2_over_p1": 2.518060161037073, "B2_over_B1": 1.558671032597614, "entropy_over_cv": 0.18229781445452217, "upstream_fast_Mach": 1.439051914254976, "downstream_fast_Mach": 0.7369438860707233, "downstream_alfven_margin": 0.5793435743611743, "state_global_normalized": { "rho": "1.56004490790095782571834139323368878585131711834980274553336612593374865538809946899757397", "p": "0.102132520131663693116021952292199517003497622270498081091628984260403847562372787422366763", "u": [ "-0.640488062647750584956963699442917528581556377039032761212762360711677264561956381012326968", "-0.0162924098325004629578889060344182363726455039192884794168167010238049838219702100279250564", "0E-91" ], "B": [ "0.0446656175415346618981857787496794530852911757671536906556424102110136309757675774372736269", "1.00386197411773121156181178484303050229401689026939322961825750982151251438809920750618273", "0E-91" ] }, "root_record": { "r": "1.56004490790095782571834139323368878585131711834980274553336612593374865538809946899757397", "b": "0.0406011786624300358360214075692020689332842475050291943674863737813704058747684720889482075", "h": "0.00587548419499622749349732086028889809215665489306202777753020678425635941343482187230916660", "A": "0.410167971836818938919680408346702878300159490647457257210289245685073190140306419121056741", "denominator": "0.990833980800143576949189848465458789681834943726284975914907695716341104384883725832970720", "polynomial_residual": "-1.049341213727124701395183E-65", "bracket_initial_signs": [ "1.46075755248895907379189731428578593991253897813245971059749826845353544402856599635384694", "-1.98830709169900269338854954006608486026145868489007714123834463083592193522970685758744672" ], "bracket_derivative_max": "-5.51779955420106113151759064387529979312765378119235414140110357586387302292240741524060534", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "-4E-91", "0E-182", "-5E-90", "0E-182", "6.06562911017392926902750041527681748888622818133920772268815539862948038300141305687824287E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_1.825", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.017980134730358376, 0.0 ], "rh_scaled_inf": 2.1964859984297853e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7885374965112893e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.1964859984297853e-16 }, "characteristics": { "left": { "slow": 0.023305726753761587, "alfven_n": 0.061338469231950944, "fast": 0.86937697116825 }, "right": { "slow": 0.028679504301130466, "alfven_n": 0.07661282622302104, "fast": 0.6945494806617111 } }, "front_relative_normal_velocity": { "left": -0.6406820435931253, "right": -0.9994927596910347 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600449079009577, "pressure_ratio": 2.5180601610370736, "entropy_over_cv": 0.18229781445452242, "tangential_field_ratio": 1.5652257782365275 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.85, "theta_Bn_degrees": 83.15, "compression": 1.5600355291608177, "u2x_km_s": -384.291949364629, "u2y_km_s": -9.742339968629471, "speed2_km_s": 384.4154205212518, "signed_deflection_degrees": 1.452217323361342, "p2_over_p1": 2.5180279507941674, "B2_over_B1": 1.5586516082660467, "entropy_over_cv": 0.18229504244672862, "upstream_fast_Mach": 1.4390407469548097, "downstream_fast_Mach": 0.7369462689804482, "downstream_alfven_margin": 0.57911465915953, "state_global_normalized": { "rho": "1.56003552916081770127463934832517939470649742270499313769815896759733190306844623195137037", "p": "0.102131213684211423457372307631829715730520159369219241978783317678626807767099004463010380", "u": [ "-0.640486582274381569959025938588596820330156761474913491304667991211149017115652799113355414", "-0.0162372332810491189190494072845030383760107432138306724590441233282636049706793667318288362", "0E-91" ], "B": [ "0.0445078436583934522893984190659019805603259229218229404084717388581579172493350950081561557", "1.00385644673330828539902371133789713809491962626193773344515722916862559040778043635228088", "0E-91" ] }, "root_record": { "r": "1.56003552916081770127463934832517939470649742270499313769815896759733190306844623195137037", "b": "0.0406023153621240192254908545229094914962608233972943929540393913459473448986102123784914481", "h": "0.00591856691746479690313556518441983493819227358075455950627998840877022420182917021862346581", "A": "0.410136536965095962898110178946560621523043515044944561427265571093400715526891361242496851", "denominator": "0.990766825327039095897832530061183941317629821582724100146389758530037242810206222824897821", "polynomial_residual": "-5.68119599487736161956127E-66", "bracket_initial_signs": [ "1.46061844827210032655684259773037483491698390814810041371374602996634877935608307917613543", "-1.98820600393675498511670678242922009756085018899423635974747460054540267772050527291584285" ], "bracket_derivative_max": "-5.51753121090997241696500892526875640046784829598519958820057403444755397629953516055494173", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "2E-91", "0E-182", "3E-90", "0E-182", "3.28435667644403004365406274857757456956512241877556091875235466509833812563436256277068817E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_1.85", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.01836551364066253, 0.0 ], "rh_scaled_inf": 2.1966279432662026e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.1966279432662026e-16 }, "characteristics": { "left": { "slow": 0.023390942795705815, "alfven_n": 0.061562267772172406, "fast": 0.8693672169859374 }, "right": { "slow": 0.028784236904816445, "alfven_n": 0.0768921234008788, "fast": 0.6945451481078955 } }, "front_relative_normal_velocity": { "left": -0.6406769269317023, "right": -0.9994787687270248 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600355291608177, "pressure_ratio": 2.5180279507941674, "entropy_over_cv": 0.18229504244672867, "tangential_field_ratio": 1.5652546238374072 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.875, "theta_Bn_degrees": 83.12500000000001, "compression": 1.5600258798943214, "u2x_km_s": -384.2911566959624, "u2y_km_s": -9.709233079022365, "speed2_km_s": 384.41379049366, "signed_deflection_degrees": 1.4472874149442205, "p2_over_p1": 2.51799452472544, "B2_over_B1": 1.5586318780991162, "entropy_over_cv": 0.18229207649989157, "upstream_fast_Mach": 1.4390293380149284, "downstream_fast_Mach": 0.736948732059841, "downstream_alfven_margin": 0.5788857380370039, "state_global_normalized": { "rho": "1.56002587989432146221951251900097836347606103305868658836136529381473369403491602105027642", "p": "0.102129857922863837983175135932617142626838918566579579364145401314812722447179994405609203", "u": [ "-0.640485261159937348794505154421984402054545622589538241121515382669124948061295923079547412", "-0.0161820551317039414255763015479452493491065898139463853967524591031929218180343398006543350", "0E-91" ], "B": [ "0.0443500774312933808466589811251366680923359996480587846079665567227808638390434706709519970", "1.00385069697886288932090183339393655446388673511949279508207184629501686543516216083177876", "0E-91" ] }, "root_record": { "r": "1.56002587989432146221951251900097836347606103305868658836136529381473369403491602105027642", "b": "0.0406034675704235750243569326638990505195648199830563868277089192452689492954573627983402794", "h": "0.00596180823922706410879105052809462828472375354100160821388661309504420752333277272788176275", "A": "0.410105102411974609937602176910790224649282047084952801709694260808454832783696483008535248", "denominator": "0.990699424855838583971116004504440503683216351024613677361872295962745985112916715187995360", "polynomial_residual": "-1.244528238317413447125488E-65", "bracket_initial_signs": [ "1.46047775217184097841324996185081793193004375535306558377963640555243625910559632777484193", "-1.98810625319911053036377071713599071260573180014736518786111092866743610588854348252809355" ], "bracket_derivative_max": "-5.51726285591004460438547991473465632412757952042000226046644414993168974401831410179275183", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.04268262663703590152482523468618146558884780460179100466352415177691787804314750215307036E-90", "-1E-91", "0E-182", "-1E-90", "0E-182", "7.19559503928343280440959355335806268769544616461173988378337832510056701672847897665129042E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_1.875", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.018750891035533384, 0.0 ], "rh_scaled_inf": 2.1967710249942347e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -2.1967710249942347e-16 }, "characteristics": { "left": { "slow": 0.023476157586449088, "alfven_n": 0.061786061294985886, "fast": 0.8693573534501537 }, "right": { "slow": 0.02888896598693531, "alfven_n": 0.07717140593956164, "fast": 0.6945407998804799 } }, "front_relative_normal_velocity": { "left": -0.6406717993319899, "right": -0.9994645874763657 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600258798943214, "pressure_ratio": 2.51799452472544, "entropy_over_cv": 0.18229207649989165, "tangential_field_ratio": 1.565283340076445 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.9, "theta_Bn_degrees": 83.10000000000001, "compression": 1.5600159600817, "u2x_km_s": -384.29045958855784, "u2y_km_s": -9.676125300229195, "speed2_km_s": 384.4122588206713, "signed_deflection_degrees": 1.4423569737471198, "p2_over_p1": 2.517959882795181, "B2_over_B1": 1.5586118421020942, "entropy_over_cv": 0.18228891660707927, "upstream_fast_Mach": 1.4390176874300968, "downstream_fast_Mach": 0.7369512753175648, "downstream_alfven_margin": 0.5786568109845315, "state_global_normalized": { "rho": "1.56001596008170009594423626507321768093992978576561662821875735955702835575449289550978602", "p": "0.102128452846172540010705131490152500467265020827082288285771005125938025549103142486511348", "u": [ "-0.640484099314263113047079224699811533889304239327044557725064484292847124794779014589621955", "-0.0161268755003819908413875017411933408677936257852786854427535618935670239809740277671206762", "0E-91" ], "B": [ "0.0441923190914860838366335277293096067183109551646580673078699393335132170091502952715241124", "1.00384472485490038995703290949076443883670781717726629698599335355031254897221382606585479", "0E-91" ] }, "root_record": { "r": "1.56001596008170009594423626507321768093992978576561662821875735955702835575449289550978602", "b": "0.0406046352890864009881217950026087034997326902250311555362438040168963944466714267507766117", "h": "0.00600520819019910112348632852736461980599203162811236319592825925091792211167081226547059616", "A": "0.410073668165550074519107899618455644986956495875667056426946205199263371560709390519197569", "denominator": "0.990631779379676060584403016672303760322987541892250949330005464107963076530856475410014544", "polynomial_residual": "-1.101901063321951847136255E-65", "bracket_initial_signs": [ "1.46033546428675968225907607048825376520989249439427108191331996676416189894910519273561505", "-1.98800783909801183518490654282486369954704056631592742609120700776076373293818197598043806" ], "bracket_derivative_max": "-5.51699448877322952155492887276834748530086576466679147458253321983217317136868155360004907", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-3E-91", "0E-182", "3E-90", "0E-182", "6.37170955589982201033512272624539168356615029121961669070490604778364291467548477722264095E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.9", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.01913626687749132, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02356137112447506, "alfven_n": 0.06200984981643539, "fast": 0.869347380564465 }, "right": { "slow": 0.028993691534529638, "alfven_n": 0.07745067378589811, "fast": 0.6945364359813037 } }, "front_relative_normal_velocity": { "left": -0.6406666608009668, "right": -0.9994502159417572 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600159600817, "pressure_ratio": 2.5179598827951812, "entropy_over_cv": 0.18228891660707947, "tangential_field_ratio": 1.5653119269325044 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.925, "theta_Bn_degrees": 83.075, "compression": 1.5600057697030292, "u2x_km_s": -384.289858048331, "u2y_km_s": -9.643016701799855, "speed2_km_s": 384.4108255108297, "signed_deflection_degrees": 1.4374260138525699, "p2_over_p1": 2.517924024969138, "B2_over_B1": 1.558591500280258, "entropy_over_cv": 0.18228556276155441, "upstream_fast_Mach": 1.4390057951950859, "downstream_fast_Mach": 0.7369538987624119, "downstream_alfven_margin": 0.5784278779931119, "state_global_normalized": { "rho": "1.56000576970302923628670184720758854795543899049519433564547252281154593027851627562126940", "p": "0.102126998452748236060035405805930594107294799941215733132726506319591604416977184759725494", "u": [ "-0.640483096747218250014524503372990372672808340924792392362187362027993297632513579146647959", "-0.0160716945029997579799809115382376489348932443752221130679882194208256685489491423123744348", "0E-91" ], "B": [ "0.0440345688702320903773490370592852483680871631327968452566385389529623999884764338367496788", "1.00383853036204222225987886076160319992085025380471946766821011270457403290721416611627322", "0E-91" ] }, "root_record": { "r": "1.56000576970302923628670184720758854795543899049519433564547252281154593027851627562126940", "b": "0.0406058185198939322810695844306621319313971522661782436539568925697134744486155302120076097", "h": "0.00604876680053974526984952618585031837514777160349882857139994070228052557188743873922864797", "A": "0.410042234213918024899936985550176997830930308254733878784511275434670866598710017399425896", "denominator": "0.990563888891569865160984463268417330652061941981885669260361784835493579687973034558339356", "polynomial_residual": "-3.48575313898978557602334E-66", "bracket_initial_signs": [ "1.46019158471476099777806983757869335049683812721643116807137030875565001167221611980320986", "-1.98791076124450399993548410642229712029606201513880281939159296078375257894170408959624766" ], "bracket_derivative_max": "-5.51672610906939007017705377928504539162675076588407526968504558584798980362145141830319692", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "4E-91", "0E-182", "2E-90", "0E-182", "2.01586479582701622857220982937296914150033422645573149807532677148749311103440039328115812E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_1.925", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.019521641129066493, 0.0 ], "rh_scaled_inf": 2.1970606001999604e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.788950431127184e-16, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.1970606001999604e-16 }, "characteristics": { "left": { "slow": 0.023646583408270236, "alfven_n": 0.06223363335257568, "fast": 0.869337298332459 }, "right": { "slow": 0.02909841353464084, "alfven_n": 0.07772992688671956, "fast": 0.6945320564122135 } }, "front_relative_normal_velocity": { "left": -0.6406615113456876, "right": -0.9994356541259355 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5600057697030292, "pressure_ratio": 2.517924024969138, "entropy_over_cv": 0.1822855627615545, "tangential_field_ratio": 1.5653403843841607 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.95, "theta_Bn_degrees": 83.05, "compression": 1.5599953087382292, "u2x_km_s": -384.28935208120583, "u2y_km_s": -9.609907353283846, "speed2_km_s": 384.4094905726596, "signed_deflection_degrees": 1.4324945493444403, "p2_over_p1": 2.5178869512145154, "B2_over_B1": 1.5585708526388884, "entropy_over_cv": 0.18228201495677412, "upstream_fast_Mach": 1.438993661304671, "downstream_fast_Mach": 0.7369566024033039, "downstream_alfven_margin": 0.5781989390538099, "state_global_normalized": { "rho": "1.55999530873822915687326144215076214708548217953845052438807203492809776564896749353602233", "p": "0.102125494741260745330663409666636774648748383440563600025518110861871757061801913651804821", "u": [ "-0.640482253468676382149490596341077676226746492939930725955323143807799032040477118377569372", "-0.0160165122554730769638065667670212334912664348989096805315555757950561695091142645027675862", "0E-91" ], "B": [ "0.0438768269988008490425063154216650837925386449335439811058085616835077396254914389875241372", "1.00383211350102586299757184698441604115647545823436113237383500741815137395673181850312282", "0E-91" ] }, "root_record": { "r": "1.55999530873822915687326144215076214708548217953845052438807203492809776564896749353602233", "b": "0.0406070172646513472546977437961573054250418379445099693939520008953419599999475084698444732", "h": "0.00609248410065067637442327444600415222737734030010188288680895583003930806413773913685542105", "A": "0.410010800545174585131486258170277706195117560130007380217391182615936617215858974033208184", "denominator": "0.990495753384422695707986141335502790522641127666992914503895794960485017285429868719019613", "polynomial_residual": "9.97368896711555049553166E-66", "bracket_initial_signs": [ "1.46004611355307622813889234252902606432296588667500364687928174641284947072792735867111136", "-1.98781501924873298444648028869226646090021532847716998440155658806865430011957465374451363" ], "bracket_derivative_max": "-5.51645771636629859968374965482321617574616669170246956593113494146775410332557163315704153", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "6E-91", "0E-182", "6E-90", "0E-182", "-5.76862081873675569424326864539603728943409596404712088955255279923652165826495427152671789E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_1.95", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.01990701375279895, 0.0 ], "rh_scaled_inf": 2.7755575615628914e-17, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -2.7755575615628914e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.023731794436323988, "alfven_n": 0.06245741191947236, "fast": 0.8693271067577454 }, "right": { "slow": 0.029203131974309186, "alfven_n": 0.07800916518886014, "fast": 0.6945276611750623 } }, "front_relative_normal_velocity": { "left": -0.6406563509732823, "right": -0.9994209020316729 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599953087382292, "pressure_ratio": 2.5178869512145154, "entropy_over_cv": 0.18228201495677399, "tangential_field_ratio": 1.5653687124097022 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 1.975, "theta_Bn_degrees": 83.025, "compression": 1.5599845771670648, "u2x_km_s": -384.28894169311525, "u2y_km_s": -9.576797324230222, "speed2_km_s": 384.40825401466594, "signed_deflection_degrees": 1.4275625943078942, "p2_over_p1": 2.5178486614999755, "B2_over_B1": 1.5585498991832718, "entropy_over_cv": 0.18227827318639006, "upstream_fast_Mach": 1.4389812857536335, "downstream_fast_Mach": 0.7369593862492915, "downstream_alfven_margin": 0.5779699941577545, "state_global_normalized": { "rho": "1.55998457716706476460776055372027284004550327083599410014776914297917879012436558335278994", "p": "0.102123941710439009138197183896093497794889229760032617638915027580499464698634831694321108", "u": [ "-0.640481569488525407006789254025513414002162252730398214111879519672181042375752153467740367", "-0.0159613288737170380393586667456624039106578806178255504447991090894846337542063699841714824", "0E-91" ], "B": [ "0.0437190937084707545689103891792078137945134520185091304358803434372583192298000621302078273", "1.00382547427270480404714930403478431881687563211455422384731094074169297282908812493394170", "0E-91" ] }, "root_record": { "r": "1.55998457716706476460776055372027284004550327083599410014776914297917879012436558335278994", "b": "0.0406082315251875733035074515186291559286840409720130372892427163630388594160452763805034441", "h": "0.00613636012117649475317359165444280856904537310575800722110482532212795345273879147319799862", "A": "0.409979367147416317078473830025838985163091591085293613108339632668884511291443905145785279", "denominator": "0.990427372851021647530934975092013893769131777934167300144781619446873904346566473311521082", "polynomial_residual": "-4.21556399006283159510353E-66", "bracket_initial_signs": [ "1.45989905089826426146408842084908473613937736418918850475201783315011133261950936390799716", "-1.98772061271994385984149856371716227401961295151228629441011944813471098443017323028648855" ], "bracket_derivative_max": "-5.51618931022963526697999646069625179243586861439242644621165709700623955159339936551215350", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "2E-91", "0E-182", "2E-90", "0E-182", "2.43850276313740675560962774798864819396211446760008262828524569744740264956430798036338525E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_1.975", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.020292384711238783, 0.0 ], "rh_scaled_inf": 2.1973547262181632e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.1973547262181632e-16 }, "characteristics": { "left": { "slow": 0.02381700420712866, "alfven_n": 0.06268118553320197, "fast": 0.8693168058439562 }, "right": { "slow": 0.029307846840573786, "alfven_n": 0.07828838863915683, "fast": 0.6945232502717101 } }, "front_relative_normal_velocity": { "left": -0.6406511796909565, "right": -0.999405959661778 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599845771670648, "pressure_ratio": 2.5178486614999755, "entropy_over_cv": 0.1822782731863899, "tangential_field_ratio": 1.5653969109871284 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.0, "theta_Bn_degrees": 83.0, "compression": 1.5599735749691457, "u2x_km_s": -384.28862689000056, "u2y_km_s": -9.54368668418754, "speed2_km_s": 384.4071158453339, "signed_deflection_degrees": 1.422630162829345, "p2_over_p1": 2.5178091557956384, "B2_over_B1": 1.5585286399186986, "entropy_over_cv": 0.1822743374442484, "upstream_fast_Mach": 1.43896866853676, "downstream_fast_Mach": 0.736962250309555, "downstream_alfven_margin": 0.5777410432961393, "state_global_normalized": { "rho": "1.55997357496914559330796328054822682111645577334554506390940551518092951186393375649951112", "p": "0.102122339359071100311109307129665926358865670409518324088303030168353340238573010385961613", "u": [ "-0.640481044816667537697551714826667287830659136485036087806409081362822176865221553646284944", "-0.0159061444736459003477689553891446023841361975037837862117779133814737151124968542599309088", "0E-91" ], "B": [ "0.0435613692305291746678560645224111890931947674323107609769447705306595237257865166595581367", "1.00381861267804852548811640254046608888232787674909208475632284091922590893476443646646470", "0E-91" ] }, "root_record": { "r": "1.55997357496914559330796328054822682111645577334554506390940551518092951186393375649951112", "b": "0.0406094613033552927981858035155180014119351468064519928298560736420293693219251953792719458", "h": "0.00618039489300479998859052494141138554719197175852415934253333648947380546927332900469227687", "A": "0.409947934008740202439620731645126427258035332077868956532180688863917232692134433675530543", "denominator": "0.990358747284038252087184636461488117249462866708452600124849214251777734864894413371518317", "polynomial_residual": "1.21906629164875390801639E-66", "bracket_initial_signs": [ "1.45975039684621241707618332158526935512814955949162546978545428590294898762462815993240750", "-1.98762754126647904698418173585607200982349075859225987271045125895564333448764707105583124" ], "bracket_derivative_max": "-5.51592089022298638212339384848618730527108074265914493719517173759484696948278192520626730", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "3E-91", "0E-182", "3E-90", "0E-182", "-7.05255167074766732055672065121903623851085849537670147462859715243509729279766298298952263E-68", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_2", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.02067775396694622, 0.0 ], "rh_scaled_inf": 2.1975034964698916e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -2.1975034964698916e-16 }, "characteristics": { "left": { "slow": 0.023902212719179614, "alfven_n": 0.0629049542098521, "fast": 0.8693063955947448 }, "right": { "slow": 0.029412558120472578, "alfven_n": 0.0785675971844494, "fast": 0.6945188237040237 } }, "front_relative_normal_velocity": { "left": -0.6406459975059914, "right": -0.9993908270190958 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599735749691457, "pressure_ratio": 2.517809155795639, "entropy_over_cv": 0.18227433744424837, "tangential_field_ratio": 1.5654249800941509 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.025, "theta_Bn_degrees": 82.97500000000001, "compression": 1.5599623021239257, "u2x_km_s": -384.2884076778116, "u2y_km_s": -9.510575502703803, "speed2_km_s": 384.4060760731294, "signed_deflection_degrees": 1.417697268996411, "p2_over_p1": 2.5177684340730826, "B2_over_B1": 1.5585070748504646, "entropy_over_cv": 0.1822702077243898, "upstream_fast_Mach": 1.438955809648842, "downstream_fast_Mach": 0.7369651945934037, "downstream_alfven_margin": 0.5775120864602223, "state_global_normalized": { "rho": "1.55996230212392579748957822788478460974569319482915024827880431836995602683475818178107759", "p": "0.102120687686004232547565738131614000785011826655903098998712091598398281437003962297598290", "u": [ "-0.640480679463019343850612021109633304788752623312855371532270919667397984803638928827127586", "-0.0158509591711730046506823567030889090139182348715174217869070851842910092601112976188652276", "0E-91" ], "B": [ "0.0434036537962724769413072154580240552262211385168888041123985837121819439975644160878426893", "1.00381152871814246849622289777342047863034465784152503948198907617321708071454032298594056", "0E-91" ] }, "root_record": { "r": "1.55996230212392579748957822788478460974569319482915024827880431836995602683475818178107759", "b": "0.0406107066010309490962127958183312883241917488774882797851146005375647578142961911318092914", "h": "0.00622458844726627049877678747683129382565267676801724659990383892097678586471341159050308178", "A": "0.409916501117243624769722538073735850945212050463918321917730413934068461381826160104586870", "denominator": "0.990289876676028515978401586399374258537094943785066780836224014595246080945974181208298438", "polynomial_residual": "-1.620628018709010269604102E-65", "bracket_initial_signs": [ "1.45960015149213729652824676109178956396233672050971889264686152494274708136585485070195823", "-1.98753580449577654154466772306145846194104484414562380982472567457790789578645063374267136" ], "bracket_derivative_max": "-5.51565245590784273992841266170798873530699179927438114088671744162390091972907669390106152", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "0E-91", "0E-182", "2E-90", "0E-182", "9.37677898167644978128490198237255244249171267459022459851342091352263528602672269544471639E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_2.025", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.021063121482491766, 0.0 ], "rh_scaled_inf": 2.1976534052545985e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7893758667846474e-16, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.1976534052545985e-16 }, "characteristics": { "left": { "slow": 0.023987419970975286, "alfven_n": 0.06312871796552148, "fast": 0.8692958760137868 }, "right": { "slow": 0.029517265801042327, "alfven_n": 0.0788467907715805, "fast": 0.6945143814738768 } }, "front_relative_normal_velocity": { "left": -0.6406408044257438, "right": -0.999375504106507 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599623021239257, "pressure_ratio": 2.5177684340730826, "entropy_over_cv": 0.18227020772438984, "tangential_field_ratio": 1.565452919708192 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.05, "theta_Bn_degrees": 82.95, "compression": 1.5599507586107042, "u2x_km_s": -384.2882840625071, "u2y_km_s": -9.47746384932641, "speed2_km_s": 384.4051347064987, "signed_deflection_degrees": 1.4127639268978733, "p2_over_p1": 2.5177264963053445, "B2_over_B1": 1.5584852039838695, "entropy_over_cv": 0.1822658840210496, "upstream_fast_Mach": 1.438942709084677, "downstream_fast_Mach": 0.7369682191102767, "downstream_alfven_margin": 0.5772831236413261, "state_global_normalized": { "rho": "1.55995075861070414629809517915424497446665951139394356044819533520426940669961698750303399", "p": "0.102118986690144769732336579170696979103734813385950229568804593946746723505198458628049350", "u": [ "-0.640480473437511793081477021252290212881138542508551656907616472691344446426299331088559090", "-0.0157957730822106860111952099650864508284330939692857831288345927902827197644212929173200554", "0E-91" ], "B": [ "0.0432459476370060559037092382595802556347165282531144152094125857301934148170298538331927498", "1.00380422239418800803734084981981899476040526230092323665710610656910194620704908236543805", "0E-91" ] }, "root_record": { "r": "1.55995075861070414629809517915424497446665951139394356044819533520426940669961698750303399", "b": "0.0406119674201147526299265961445888275384075124752440283387815779472982000163248293656113135", "h": "0.00626894081533474389892506770765201464207595483096349801761271863384562301814211107060006067", "A": "0.409885068461024351503053473827840335691431936019868319440745183173322759036374470471848346", "denominator": "0.990220761019432960082313675731870604523009181102968573309745540360796041025961593349925579", "polynomial_residual": "-1.563467665738603062465898E-65", "bracket_initial_signs": [ "1.45944831493058563942633572220936270592489288173039516591862429516100532628947182421100673", "-1.98744540201436812567361202948089149343818901456508335422277819847960438571348459096020051" ], "bracket_derivative_max": "-5.51538400684359793748531964757458975007146053777216864013988512201484364272264800547597103", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.04423793982066635525844776094207390695411309132451812272299846462984025772119709332585754E-90", "1E-91", "0E-182", "-2E-90", "0E-182", "9.04712555307774449557045860840372487983375615596912142723332786223586268234955323315437412E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_2.05", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.02144848722045631, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 2.220446049250313e-16, "t2_induction": 0.0, "energy": 2.1978044528534062e-16 }, "characteristics": { "left": { "slow": 0.024072625961017256, "alfven_n": 0.06335247681632014, "fast": 0.8692852471047797 }, "right": { "slow": 0.029621969869318664, "alfven_n": 0.07912596934739562, "fast": 0.6945099235831494 } }, "front_relative_normal_velocity": { "left": -0.6406356004576462, "right": -0.9993599909269292 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599507586107042, "pressure_ratio": 2.5177264963053445, "entropy_over_cv": 0.18226588402104948, "tangential_field_ratio": 1.5654807298063866 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.075, "theta_Bn_degrees": 82.92500000000001, "compression": 1.559938944408624, "u2x_km_s": -384.2882560500542, "u2y_km_s": -9.444351793602111, "speed2_km_s": 384.40429175386856, "signed_deflection_degrees": 1.4078301506236308, "p2_over_p1": 2.517683342466919, "B2_over_B1": 1.5584630273242177, "entropy_over_cv": 0.1822613663286577, "upstream_fast_Mach": 1.4389293668390677, "downstream_fast_Mach": 0.7369713238697421, "downstream_alfven_margin": 0.5770541548308372, "state_global_normalized": { "rho": "1.55993894440862401758864497343047846083768784414589045149427617780757026068875641544176732", "p": "0.102117236370458235213795615785931953917564791594939298685777852003387516003405624616422486", "u": [ "-0.640480426750090292969246967523843558254108892717882859689090813602148094784003786390116533", "-0.0157405863226701864296358864660105551278281274574789772468160993922650512642336657895611635", "0E-91" ], "B": [ "0.0430882509840443601102749946576839477980931785193134419516299389481565484300512377527965152", "1.00379669370750242536132920077318226992963398735305297855755851882082909875723530646598897", "0E-91" ] }, "root_record": { "r": "1.55993894440862401758864497343047846083768784414589045149427617780757026068875641544176732", "b": "0.0406132437625306870720810268648128958864732989077044208295467279158660503887615629619760721", "h": "0.00631345202882729815558912806144255010735859251821512654155786988958567200372175298727571404", "A": "0.409853636028180515978045484670177162178831017308350474099809832337559849233973393446526951", "denominator": "0.990151400306576658823924555700595375502464007896269467306773111806844047019256833590758103", "polynomial_residual": "-1.000406335327416056762811E-65", "bracket_initial_signs": [ "1.45929488725543518405129644993759819014761144815020145686816709844684815562635860536977660", "-1.98735633342787756627217423169761245041383412246492666379817299327459157955176474095051792" ], "bracket_derivative_max": "-5.51511554258754667758361831344053132965603588874290874355346908270111677035793697818916761", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.04446630324817076941604781117572096428156642682005713471250108726371276263721497947445448E-90", "3E-91", "0E-182", "1E-90", "0E-182", "5.78961278019545509986429704129588334299390460962810484857321167628761538270852604404296777E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_2.075", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.02183385114343126, 0.0 ], "rh_scaled_inf": 2.1979566395496037e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.789593276400674e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -2.1979566395496037e-16 }, "characteristics": { "left": { "slow": 0.024157830687810324, "alfven_n": 0.06357623077836944, "fast": 0.8692745088714423 }, "right": { "slow": 0.029726670312335987, "alfven_n": 0.07940513285874308, "fast": 0.6945054500337292 } }, "front_relative_normal_velocity": { "left": -0.6406303856092067, "right": -0.9993442874833157 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559938944408624, "pressure_ratio": 2.517683342466919, "entropy_over_cv": 0.18226136632865775, "tangential_field_ratio": 1.565508410365579 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.1, "theta_Bn_degrees": 82.9, "compression": 1.5599268594966733, "u2x_km_s": -384.2883236464288, "u2y_km_s": -9.411239405076941, "speed2_km_s": 384.4035472236464, "signed_deflection_degrees": 1.4028959542646549, "p2_over_p1": 2.5176389725337605, "B2_over_B1": 1.5584405448768186, "entropy_over_cv": 0.18225665464183868, "upstream_fast_Mach": 1.438915782906822, "downstream_fast_Mach": 0.7369745088814975, "downstream_alfven_margin": 0.5768251800202069, "state_global_normalized": { "rho": "1.55992685949667339215409736757418142162689724865322083657261373575635234267504394133919435", "p": "0.102115436725969321041015316910423688242260532384559886478424244437950060269866530174325208", "u": [ "-0.640480539410714733541853820180409626814784312135721445786123245908832672112597908006045385", "-0.0156853990084615674339670021338514543474286940074040223076774321359809804408343116172158316", "0E-91" ], "B": [ "0.0429305640687109193925854562560434149856848943276206330070514757965662362393380369316193440", "1.00378894265951888029577070209124322552086348970574494605493038739583868476035595974731227", "0E-91" ] }, "root_record": { "r": "1.55992685949667339215409736757418142162689724865322083657261373575635234267504394133919435", "b": "0.0406145356302265155789296162659897297936191273227543338501491111486594501511785323720904265", "h": "0.00635812211960433353415825525742875091772014675671363900510796804338883558590128771135139992", "A": "0.409822203806810599463184771925959250942867407237961866260645445044495488537515281412244730", "denominator": "0.990081794529669279586398259751703001184203043965887719607359904313547788616393926928824285", "polynomial_residual": "-2.72501474875177625435085E-66", "bracket_initial_signs": [ "1.45913986855989553278747528012686588825704704516134871577581875457227611738412344472871472", "-1.98726859834101879984623939044244723674780910381406862810464713932802344437366994805108864" ], "bracket_derivative_max": "-5.51484706269488305802973525957431967210820823201638233663511354057662148278812919521162760", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "-1E-91", "0E-182", "-7E-90", "0E-182", "1.57722375073005274940455864279398533218530089944882495845166624667477021428916423666940902E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_2.1", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.02221921321401866, 0.0 ], "rh_scaled_inf": 1.7897031548514696e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7897031548514696e-16, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02424303414986255, "alfven_n": 0.06379997986780221, "fast": 0.8692636613175164 }, "right": { "slow": 0.029831367117127562, "alfven_n": 0.0796842812524741, "fast": 0.6945009608275097 } }, "front_relative_normal_velocity": { "left": -0.640625159888009, "right": -0.9993283937786562 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599268594966733, "pressure_ratio": 2.5176389725337605, "entropy_over_cv": 0.18225665464183882, "tangential_field_ratio": 1.5655359613623259 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.125, "theta_Bn_degrees": 82.875, "compression": 1.5599145038536848, "u2x_km_s": -384.28848685761574, "u2y_km_s": -9.378126753296174, "speed2_km_s": 384.4029011242199, "signed_deflection_degrees": 1.3979613519129466, "p2_over_p1": 2.5175933864832816, "B2_over_B1": 1.5584177566469857, "entropy_over_cv": 0.18225174895541182, "upstream_fast_Mach": 1.4389019572827533, "downstream_fast_Mach": 0.7369777741553704, "downstream_alfven_margin": 0.5765961992009498, "state_global_normalized": { "rho": "1.55991450385368484810161399646672038818706285098960475921362450879967751355074361054298187", "p": "0.102113587755761897160963807774259202588547665889331957531417912530247489243310481731771737", "u": [ "-0.640480811429359530269987573203796064144450707897657585397016731161952018218845743048112722", "-0.0156302112554936226245878686809411252484587361655370912654730543832410713874461810910013017", "0E-91" ], "B": [ "0.0427728871223383722023471590555575389999374982090295526771736201044029319780258041611635287", "1.00378096925178638333946619033438214638352715670327145249028971596172137383078686474268234", "0E-91" ] }, "root_record": { "r": "1.55991450385368484810161399646672038818706285098960475921362450879967751355074361054298187", "b": "0.0406158430251737871108710097678169078172472040870784348301316731229305278135527477839679188", "h": "0.00640295111976965533994907233665316166635029463622565722196509528769592944335701007440420568", "A": "0.409790771785013413184068292052795070730702539866551191581159269016407516489909663875258698", "denominator": "0.990011943680805122261819429314300965379603123194051928190768890291419793719700782295922251", "polynomial_residual": "-5.65162715643228523729031E-66", "bracket_initial_signs": [ "1.45898325893650902236595720751991059464438710279496229146317213470584377200211455464115080", "-1.98718219635759410393301879180935633801709353789696059466857058123527465014624610793043348" ], "bracket_derivative_max": "-5.51457856671869884684856763628441540906705508346867892002178704328061453549800688995440419", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.04492766414181615362048317634963685527640720646805757780465835630540131144200526065465422E-90", "-4E-91", "0E-182", "-2E-90", "0E-182", "3.27151800816551203251950901369990659891908827287213164274837952482333873406834232519821834E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.125", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.022604573394831302, 0.0 ], "rh_scaled_inf": 1.7898138159998065e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7898138159998065e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.024328236345685327, "alfven_n": 0.06402372410076283, "fast": 0.8692527044467648 }, "right": { "slow": 0.029936060270725436, "alfven_n": 0.07996341447544278, "fast": 0.694496455966392 } }, "front_relative_normal_velocity": { "left": -0.6406199233017127, "right": -0.9993123098159769 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599145038536848, "pressure_ratio": 2.5175933864832816, "entropy_over_cv": 0.18225174895541185, "tangential_field_ratio": 1.565563382772895 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.15, "theta_Bn_degrees": 82.85, "compression": 1.5599018774583355, "u2x_km_s": -384.2887456896082, "u2y_km_s": -9.345013907804274, "speed2_km_s": 384.40235346395764, "signed_deflection_degrees": 1.3930263576614912, "p2_over_p1": 2.5175465842943545, "B2_over_B1": 1.5583946626400373, "entropy_over_cv": 0.1822466492643911, "upstream_fast_Mach": 1.4388878899616806, "downstream_fast_Mach": 0.7369811197013173, "downstream_alfven_margin": 0.5763672123646454, "state_global_normalized": { "rho": "1.55990187745833555537787588159899918661634165319030194341134748064164262208005980184198951", "p": "0.102111689458979020575810156275233324021621801466688129761554359640468971594615551144947216", "u": [ "-0.640481242816013667570084126608159857814637783848611942079268809660107595471045246851503099", "-0.0155750231796737901733152500919051154116794560617358781393416829440289619821726228073507986", "0E-91" ], "B": [ "0.0426152203762684930641494795656110332599799900650149134683476705848645237397750440354803882", "1.00377277348596976755557071325341524562740079422594271472411912639516288565197422180320963", "0E-91" ] }, "root_record": { "r": "1.55990187745833555537787588159899918661634165319030194341134748064164262208005980184198951", "b": "0.0406171659493678428306909677993943033292139535700487472545950170824594846987395612602462597", "h": "0.00644793906167055745333317384578895861636826138425006941521773188402079837963729939617609749", "A": "0.409759339950888080351562730861015672134814402779952316787222540112907438455443531438417274", "denominator": "0.989941847751963158942035767376628262591198868794019698661576784190755426784535785952226377", "polynomial_residual": "-2.75137232111788795359153E-66", "bracket_initial_signs": [ "1.45882505847715159893002045458574449470941858449155125463274202346307468313126924764500186", "-1.98709712708049225508804781759641175827710400126728771880116070937858361978901788007701247" ], "bracket_derivative_max": "-5.51431005420998174335839360797843309183299515644404328166792170206526076470842764949870464", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.04516066204941644200924166426601823142239539530578186249425637019424079228756178970353329E-90", "3E-91", "0E-182", "4E-90", "0E-182", "1.59285605737080603068441393800488481548396450880437898232388442315680921500719416683577977E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_2.15", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.022989931648492865, 0.0 ], "rh_scaled_inf": 2.1984200370878815e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.1984200370878815e-16 }, "characteristics": { "left": { "slow": 0.024413437273793442, "alfven_n": 0.06424746349340738, "fast": 0.8692416382629724 }, "right": { "slow": 0.030040749760160496, "alfven_n": 0.08024253247450606, "fast": 0.6944919354522833 } }, "front_relative_normal_velocity": { "left": -0.6406146758580528, "right": -0.9992960355983396 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5599018774583355, "pressure_ratio": 2.517546584294355, "entropy_over_cv": 0.18224664926439127, "tangential_field_ratio": 1.5655906745732633 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.175, "theta_Bn_degrees": 82.825, "compression": 1.5598889802891474, "u2x_km_s": -384.28910014840847, "u2y_km_s": -9.31190093814484, "speed2_km_s": 384.4019042512085, "signed_deflection_degrees": 1.3880909856042165, "p2_over_p1": 2.5174985659473115, "B2_over_B1": 1.558371262861296, "entropy_over_cv": 0.1822413555639853, "upstream_fast_Mach": 1.4388735809384277, "downstream_fast_Mach": 0.7369845455294245, "downstream_alfven_margin": 0.5761382195029363, "state_global_normalized": { "rho": "1.55988898028914727044320727724360817983080347942205185246556924072268960390750983505300298", "p": "0.102109741834822944460344141586273782964225282604521137424471947724184345010241132904832461", "u": [ "-0.640481833580680742816751444234440479489236714805064140909998015556453782739305837407147639", "-0.0155198348969080652763199112941556977168927949345542410414908523444787092406791324660702031", "0E-91" ], "B": [ "0.0424575640618522201380656527917322648625830794735644135774753403571854130158145508300871609", "1.00376435536384966026425551060802781426007784354452050947175633667131982706820703399124478", "0E-91" ] }, "root_record": { "r": "1.55988898028914727044320727724360817983080347942205185246556924072268960390750983505300298", "b": "0.0406185044048278225794366123955506702669826462111121366582442580421231653483785280050242077", "h": "0.00649308597789790665932350032260269790406389641820101019431713822738844420422412131382137249", "A": "0.409727908292534018191008468148596675229596941589166947568960018027471764931697548226074483", "denominator": "0.989871506735007073749790414585314614205017384415888723717149258966970385134632820808174449", "polynomial_residual": "3.19754198397032857853070E-66", "bracket_initial_signs": [ "1.45866526727303369793056474395253206430816621838800464689749357021116283137115569792071629", "-1.98701339011168667342047204204117225524646279573664925866776510284871547535392012659951907" ], "bracket_derivative_max": "-5.51404152471761362510853385834636303653889878810136136036997732017737699940730987140376454", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-2E-91", "0E-182", "-5E-90", "0E-182", "-1.85137661244074529611657498851521028326943392842265691649611795369044173028395295200890372E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.175", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.02337528793763803, 0.0 ], "rh_scaled_inf": 3.580074974409875e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -3.580074974409875e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.1985767830498208e-16 }, "characteristics": { "left": { "slow": 0.024498636932705157, "alfven_n": 0.06447119806190368, "fast": 0.8692304627699461 }, "right": { "slow": 0.030145435572462416, "alfven_n": 0.08052163519652385, "fast": 0.6944873992870982 } }, "front_relative_normal_velocity": { "left": -0.64060941756484, "right": -0.9992795711288428 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598889802891474, "pressure_ratio": 2.5174985659473115, "entropy_over_cv": 0.18224135556398524, "tangential_field_ratio": 1.5656178367391196 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.2, "theta_Bn_degrees": 82.8, "compression": 1.5598758123244862, "u2x_km_s": -384.2895502400274, "u2y_km_s": -9.278787913860548, "speed2_km_s": 384.4015534943023, "signed_deflection_degrees": 1.3831552498359456, "p2_over_p1": 2.517449331423943, "B2_over_B1": 1.5583475573160892, "entropy_over_cv": 0.182235867849598, "upstream_fast_Mach": 1.4388590302078244, "downstream_fast_Mach": 0.736988051649908, "downstream_alfven_margin": 0.5759092206075295, "state_global_normalized": { "rho": "1.55987581232448633109481998456932061802090914985117165695879475294593888059169014790776685", "p": "0.102107744882555127239516501658495775746292291989011039396705404721940331707551348042099902", "u": [ "-0.640482583733379010865013954482213387677135606261278856628458773692173407671139355947353233", "-0.0154646465231009125607958617150109087846169236569405892181756258910821523295694809434706448", "0E-91" ], "B": [ "0.0422999184104496828929423674246078946243517527626846790323871972698367250572268176405742155", "1.00375571488732245453477935516507999930436430015612775608627394066077881264758749556521838", "0E-91" ] }, "root_record": { "r": "1.55987581232448633109481998456932061802090914985117165695879475294593888059169014790776685", "b": "0.0406198583935966714299590202274631174009983608945226917875647941638058205815759228875598646", "h": "0.00653839190128622777204682637339549356956382680420999624450778879002041529845480470031830911", "A": "0.409696476798050919972411054568183265258141281495636795666876822972063350847807294204479618", "denominator": "0.989800920621685302810353053359006779206069689327537425721188111285943028982737161634316654", "polynomial_residual": "1.064947226940155512703804E-65", "bracket_initial_signs": [ "1.45850388541470112885934050580759756185599446733625710218286988561430934783497110369537184", "-1.98693098505223355366438585059148167317612809231547736078663073688524716590786315839449277" ], "bracket_derivative_max": "-5.51377297778836878066903823840248268783922699844198421338746432286807309860540499809825362", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.04563129390102385715378052362111754138120377662368104364173460926562650973407142428158549E-90", "4E-91", "0E-182", "4E-90", "0E-182", "-6.16677282116848714643086704176777153099287842666013279146663877868703363046474793366077226E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_2.2", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.0237606422249126, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 2.220446049250313e-16, "t2_induction": 0.0, "energy": 2.1987346695580798e-16 }, "characteristics": { "left": { "slow": 0.024583835320942243, "alfven_n": 0.0646949278224315, "fast": 0.8692191779715145 }, "right": { "slow": 0.030250117694659674, "alfven_n": 0.08080072258835891, "fast": 0.6944828474727581 } }, "front_relative_normal_velocity": { "left": -0.6406041484299609, "right": -0.9992629164106211 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598758123244862, "pressure_ratio": 2.517449331423943, "entropy_over_cv": 0.1822358678495981, "tangential_field_ratio": 1.5656448692458613 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.225, "theta_Bn_degrees": 82.775, "compression": 1.5598623735425636, "u2x_km_s": -384.29009597048486, "u2y_km_s": -9.245674904493107, "speed2_km_s": 384.4013012015491, "signed_deflection_degrees": 1.378219164452354, "p2_over_p1": 2.517398880707501, "B2_over_B1": 1.5583235460097482, "entropy_over_cv": 0.18223018611682762, "upstream_fast_Mach": 1.4388442377647055, "downstream_fast_Mach": 0.7369916380731132, "downstream_alfven_margin": 0.5756802156701954, "state_global_normalized": { "rho": "1.55986237354256365143940460736361297996843450930911706479743112644023394780821747690581258", "p": "0.102105698601496241626105483976461986683596988449658266877726224295712628558908710289978509", "u": [ "-0.640483493284141429082758374530805729983715267301193894706309682382929067225928569141481958", "-0.0154094581741551784451386081192920149711739237822116443266086076437559858155177323640291572", "0E-91" ], "B": [ "0.0421422836534302298912236948299247288430003071006758695968882448904011660049627591926473521", "1.00374685205840028047685225903920354005156768954647692773784956459679607836813295417790618", "0E-91" ] }, "root_record": { "r": "1.55986237354256365143940460736361297996843450930911706479743112644023394780821747690581258", "b": "0.0406212279177411463181606957453660196178913961310062328658885980754207271331211654008466143", "h": "0.00658385686491378955453419824226274259070357707549422823182842941859615329242129020673583518", "A": "0.409665045455538737041562728282631472381785294282435197846828904456519881951703090962119350", "denominator": "0.989730089403631074363859656118552199647869352165006779962897251552114499057403084953020745", "polynomial_residual": "6.94199751199119132858911E-66", "bracket_initial_signs": [ "1.45834091299203596482787586833788367247622117652721538468589778662004521725134874676610638", "-1.98684991150226998277386097411605977674070976875501380542533352915875302438430982895341743" ], "bracket_derivative_max": "-5.51350441296691212826155764147249970566982369562327022097475485127034484872971946395413014", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "2E-91", "0E-182", "1E-90", "0E-182", "-4.02036659786112326020004057195683963315030609174475886109312316652734148709418669474104494E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_2.225", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.024145994472973623, 0.0 ], "rh_scaled_inf": 2.198893696908951e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.198893696908951e-16 }, "characteristics": { "left": { "slow": 0.024669032437030065, "alfven_n": 0.06491865279118249, "fast": 0.869207783871528 }, "right": { "slow": 0.03035479611377956, "alfven_n": 0.08107979459687693, "fast": 0.6944782800111907 } }, "front_relative_normal_velocity": { "left": -0.6405988684613779, "right": -0.9992460714468455 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598623735425636, "pressure_ratio": 2.517398880707501, "entropy_over_cv": 0.18223018611682762, "tangential_field_ratio": 1.5656717720685978 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.25, "theta_Bn_degrees": 82.75, "compression": 1.5598486639214346, "u2x_km_s": -384.2907373458095, "u2y_km_s": -9.212561979583203, "speed2_km_s": 384.40114738123964, "signed_deflection_degrees": 1.3732827435499255, "p2_over_p1": 2.517347213782697, "B2_over_B1": 1.5582992289476096, "entropy_over_cv": 0.18222431036146744, "upstream_fast_Mach": 1.4388292036039116, "downstream_fast_Mach": 0.7369953048095155, "downstream_alfven_margin": 0.5754512046827684, "state_global_normalized": { "rho": "1.55984866392143471701529756852614556713016088843709814796813831538095842271986556032696419", "p": "0.102103602991026183618515351425077069030279227598700609193206902075907719283108998956956222", "u": [ "-0.640484562243015702893767366314161453512060893597066355450348536673947823064756647370421139", "-0.0153542699659720034524081386281430343920681761680574160606844222968191544873400211496074724", "0E-91" ], "B": [ "0.0419846600221724566861560359645107047244381019153674131397974654797499892963942429194401707", "1.00373776687921097633117404888734900623154604163500429377956955187172455212044308451602334", "0E-91" ] }, "root_record": { "r": "1.55984866392143471701529756852614556713016088843709814796813831538095842271986556032696419", "b": "0.0406226129793518227519848943857063198149714045290817573028625064245740349115534945320207048", "h": "0.00662948090210269143426562188704320206689478187866456609978628156919808008740986160293214676", "A": "0.409633614253097660852036504390020556568694374552859207219647091821906757230987740390956986", "denominator": "0.989659013072362449018571904187568567572184591979723918167133976052112510047226134266763924", "polynomial_residual": "5.36329275370573716353650E-66", "bracket_initial_signs": [ "1.45817635009425743700006798508096403880396471417971928144474359696975264096901044820229116", "-1.98677016906101204402917532777952202998210156904276973676042199667628113544718051519874538" ], "bracket_derivative_max": "-5.51323582979579742022044708524709314693289368915658080695138710231375299093158804373127054", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.04610810863841310406204057714539585888121493685863448563079273417848256312493641150818198E-90", "-2E-91", "0E-182", "1E-90", "0E-182", "-3.10644765856849948338950067425628306555622180199439011302494397160529417688942241316171640E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.25", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.024531344644489517, 0.0 ], "rh_scaled_inf": 1.3877787807814457e-17, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02475422827949764, "alfven_n": 0.06514237298436049, "fast": 0.8691962804738592 }, "right": { "slow": 0.03045947081684814, "alfven_n": 0.08135885116894657, "fast": 0.694473696904331 } }, "front_relative_normal_velocity": { "left": -0.640593577667129, "right": -0.9992290362407229 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598486639214346, "pressure_ratio": 2.517347213782697, "entropy_over_cv": 0.18222431036146758, "tangential_field_ratio": 1.5656985451821466 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.275, "theta_Bn_degrees": 82.72500000000001, "compression": 1.5598346834389996, "u2x_km_s": -384.2914743720386, "u2y_km_s": -9.179449208670441, "speed2_km_s": 384.40109204164565, "signed_deflection_degrees": 1.3683460012259079, "p2_over_p1": 2.517294330635702, "B2_over_B1": 1.558274606135014, "entropy_over_cv": 0.18221824057950572, "upstream_fast_Mach": 1.4388139277202885, "downstream_fast_Mach": 0.7369990518697197, "downstream_alfven_margin": 0.5752221876371463, "state_global_normalized": { "rho": "1.55983468343899958006445505419890120007695385843370112127301638924979151180203796473775894", "p": "0.102101458050584081458712322433224079693968811456383176112044695517045914902944880971144997", "u": [ "-0.640485790620064331831730664875117861952998352449483957909257051334328568196441916722690170", "-0.0152990820144507344768517631333754741519177526146710815708283158803381330555446529458054395", "0E-91" ], "B": [ "0.0418270477480642338322217041347602187261329199809375179112949901913784378613921245720497668", "1.00372845935199805935902981044500427868741018438647226611001013731970142891377502946252298", "0E-91" ] }, "root_record": { "r": "1.55983468343899958006445505419890120007695385843370112127301638924979151180203796473775894", "b": "0.0406240135805431015981842023848344712397530322955677058936690487664388001736054434356267404", "h": "0.00667526404641895101490977123576491984110644619013064690478050687485788933502053656144026770", "A": "0.409602183178828104997995375209317895919978022097618573510999475443417182731307256362694871", "denominator": "0.989587691619282360145268414205368234662777798854610263147117825858174686073824441264438094", "polynomial_residual": "-2.11128516498697056885903E-66", "bracket_initial_signs": [ "1.45801019680992283388647504889411423069974071727866338117086207169819446870822345774120713", "-1.98669175732675290764162543634848263434145336856533292802927431027566085491947249108131317" ], "bracket_derivative_max": "-5.51296722781546543327303178961444045523236152035698805497652347137441946613660554320802736", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "1E-91", "0E-182", "5E-90", "0E-182", "1.22301212476829531183312427354646532617701999565711424189943229568185219565950511967703166E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_2.275", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.024916692702140184, 0.0 ], "rh_scaled_inf": 2.1992151753345611e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.1992151753345611e-16 }, "characteristics": { "left": { "slow": 0.024839422846877686, "alfven_n": 0.06536608841818142, "fast": 0.8691846677824021 }, "right": { "slow": 0.030564141790890283, "alfven_n": 0.08163789225143937, "fast": 0.6944690981541204 } }, "front_relative_normal_velocity": { "left": -0.6405882760553278, "right": -0.9992118107954966 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598346834389996, "pressure_ratio": 2.5172943306357025, "entropy_over_cv": 0.18221824057950586, "tangential_field_ratio": 1.5657251885610368 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.3, "theta_Bn_degrees": 82.7, "compression": 1.559820432073003, "u2x_km_s": -384.29230705521877, "u2y_km_s": -9.146336661293303, "speed2_km_s": 384.4011351910193, "signed_deflection_degrees": 1.3634089515782684, "p2_over_p1": 2.5172402312541493, "B2_over_B1": 1.5582496775773058, "entropy_over_cv": 0.1822119767671257, "upstream_fast_Mach": 1.438798410108687, "downstream_fast_Mach": 0.7370028792644606, "downstream_alfven_margin": 0.5749931645252901, "state_global_normalized": { "rho": "1.55982043207300285495446740232181198194669374413322654677944079411168190565332830756775377", "p": "0.102099263779668304550303251665369256279813393480595031207969811767524241554263611428822314", "u": [ "-0.640487178425364656105626556772622587100037841300667645995233500964999282933044662917637882", "-0.0152438944354888370032613344313345318918640815245990053028921442401082257347967120328284670", "0E-91" ], "B": [ "0.0416694470625027350096497015814375386984967878065460176689577097644007177463717226385820957", "1.00371892947912069653082369848542648774633796389255846232579235149127152518807069283365612", "0E-91" ] }, "root_record": { "r": "1.55982043207300285495446740232181198194669374413322654677944079411168190565332830756775377", "b": "0.0406254297234532159469062166499790500017852167061706864701054108794780278097642385188911196", "h": "0.00672120633167259238470395853866573525736818740069960508723190978444803153468059855957183645", "A": "0.409570752220830687247759164313835478405122837448166259142538725755594770641629387375532686", "denominator": "0.989516125035678654412981019014585814910132458888321311431534580354588714720328295170206346", "polynomial_residual": "4.20736262234930802931604E-66", "bracket_initial_signs": [ "1.45784245322692840550841522907730083055532386761858692575962759488594424114621224105116673", "-1.98661467589686090784417851562317447972576489942875526461983315510070943628452804893253108" ], "bracket_derivative_max": "-5.51269860656424214462785375900589123287495505441516970055828847516694811235299917093398088", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "3E-91", "0E-182", "-1E-90", "0E-182", "-2.43750286715591566025406103933788055375174295992716661249182775427224090647912711346236756E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_2.3", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.02530203860861715, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": 0.0, "energy": 2.1993776270127484e-16 }, "characteristics": { "left": { "slow": 0.024924616137706714, "alfven_n": 0.06558979910887362, "fast": 0.8691729458010728 }, "right": { "slow": 0.03066880902292964, "alfven_n": 0.08191691779122987, "fast": 0.6944644837625076 } }, "front_relative_normal_velocity": { "left": -0.6405829636341638, "right": -0.999194395114446 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559820432073003, "pressure_ratio": 2.5172402312541493, "entropy_over_cv": 0.18221197676712553, "tangential_field_ratio": 1.5657517021795047 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.325, "theta_Bn_degrees": 82.675, "compression": 1.5598059098010337, "u2x_km_s": -384.29323540140535, "u2y_km_s": -9.113224406989085, "speed2_km_s": 384.40127683759334, "signed_deflection_degrees": 1.3584716087056488, "p2_over_p1": 2.5171849156271318, "B2_over_B1": 1.558224443279835, "entropy_over_cv": 0.18220551892070555, "upstream_fast_Mach": 1.438782650763964, "downstream_fast_Mach": 0.7370067870046029, "downstream_alfven_margin": 0.5747641353392247, "state_global_normalized": { "rho": "1.55980590980103371375084980456108868783296750279579377303071982239966606939121480027499449", "p": "0.102097020177836472336762184436532046888749412530754841761236070444685082968966775423136767", "u": [ "-0.640488725669008903676869827988224203306149183696538220284638519786528247618128487239776442", "-0.0151887073449818072789387692954942773034719652716223547346787229041225116881824363241819394", "0E-91" ], "B": [ "0.0415118581968944652638531942338366870277443236385500876280121994980655148019353235816862699", "1.00370917726305367501343210248512268854879667254759291649198806487796582710124714696038529", "0E-91" ] }, "root_record": { "r": "1.55980590980103371375084980456108868783296750279579377303071982239966606939121480027499449", "b": "0.0406268614102442380541346053695967828503069592215331760647789345144148776326361786574392707", "h": "0.00676730779191773522192408459293947529713450670272503761341963358140600976564495157273386721", "A": "0.409539321367206211578071581681349399220968524976223084459890022465066409108934988660750310", "denominator": "0.989444313312724132466290459934182254141927130036498651616894023672870939395020452693382387", "polynomial_residual": "-3.3612215699757415195821E-67", "bracket_initial_signs": [ "1.45767311943251027244004874695687127882343195598726564014346686874780112155380286312099420", "-1.98653892436777760645509296166573846542146621214087566990178643652716155350818930847922479" ], "bracket_derivative_max": "-5.51242996557833689385960200831332318175917061118749067854808125726148455465335074546924164", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.04683492765543987132149348062166530396825566478934457397039852719465979174783865329672278E-90", "3E-91", "0E-182", "4E-90", "0E-182", "1.94752773821367704581630903757514179938857480771064674011716070914411341807054602218764862E-68", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_2.325", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.025687382326623664, 0.0 ], "rh_scaled_inf": 2.1995412207404457e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.1995412207404457e-16 }, "characteristics": { "left": { "slow": 0.02500980815052507, "alfven_n": 0.06581350507267776, "fast": 0.8691611145338093 }, "right": { "slow": 0.03077347249998865, "alfven_n": 0.08219592773519553, "fast": 0.6944598537314475 } }, "front_relative_normal_velocity": { "left": -0.6405776404119023, "right": -0.9991767892008868 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5598059098010337, "pressure_ratio": 2.517184915627132, "entropy_over_cv": 0.18220551892070558, "tangential_field_ratio": 1.5657780860114974 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.35, "theta_Bn_degrees": 82.65, "compression": 1.5597911166005258, "u2x_km_s": -384.29425941666256, "u2y_km_s": -9.080112515293852, "speed2_km_s": 384.4015169895815, "signed_deflection_degrees": 1.3535339867073228, "p2_over_p1": 2.5171283837452036, "B2_over_B1": 1.558198903247955, "entropy_over_cv": 0.18219886703681856, "upstream_fast_Mach": 1.4387666496809814, "downstream_fast_Mach": 0.7370107751011407, "downstream_alfven_margin": 0.5745351000710378, "state_global_normalized": { "rho": "1.55979111660052588193984754496600003944387437516275245309496412709208106048858449021459672", "p": "0.102094727244705463139809744725846978965168505882276865542211003407202690531233307598355988", "u": [ "-0.640490432361104237848625547314239815297234570586046983389064615177826225083857377658399407", "-0.0151335208588230844380431793770226306971883958612706743862120261588960534381942085600734374", "0E-91" ], "B": [ "0.0413542813826552893606441416392154964332572545776423846040905194328692749709103306360242658", "1.00369920270638737245625665107966130950348336358734598419656311346055776806091660085334738", "0E-91" ] }, "root_record": { "r": "1.55979111660052588193984754496600003944387437516275245309496412709208106048858449021459672", "b": "0.0406283086431020863620242676029807432258663187386752231484191002585465270959077779313866200", "h": "0.00681356846145268469789876613874787998696800466757920927364608000893488910184288949381695585", "A": "0.409507890606055650209010031497301529306593071393702396825323085686979274071355702356231176", "denominator": "0.989372256441476589744396957100444486260165202502793770084027168423064754204676800860596626", "polynomial_residual": "-1.306565769043176390790975E-65", "bracket_initial_signs": [ "1.45750219551324533973668937690313643996500283038614126598608185617038257595165597919599291", "-1.98646450233501584290150857418432336643112372475795539233880004418593592074302664604510571" ], "bracket_derivative_max": "-5.51216130439184053057931511093582267372130035777233508320554466197442478233652204645313035", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "2E-91", "0E-182", "0E-90", "0E-182", "7.57127638511704675128950597646568654060515619892435900308889248743512289873342797623192789E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_2.35", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.02607272381887485, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.025094998883876996, "alfven_n": 0.06603720632584696, "fast": 0.8691491739845708 }, "right": { "slow": 0.030878132209088506, "alfven_n": 0.0824749220302168, "fast": 0.6944552080629024 } }, "front_relative_normal_velocity": { "left": -0.6405723063968848, "right": -0.999158993058171 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5597911166005258, "pressure_ratio": 2.5171283837452036, "entropy_over_cv": 0.18219886703681853, "tangential_field_ratio": 1.5658043400306711 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.375, "theta_Bn_degrees": 82.625, "compression": 1.5597760524487576, "u2x_km_s": -384.2953791070637, "u2y_km_s": -9.047001055742378, "speed2_km_s": 384.40185565517817, "signed_deflection_degrees": 1.34859609968315, "p2_over_p1": 2.5170706356003802, "B2_over_B1": 1.5581730574870243, "entropy_over_cv": 0.18219202111223318, "upstream_fast_Mach": 1.4387504068546069, "downstream_fast_Mach": 0.7370148435651983, "downstream_alfven_margin": 0.5743060587128807, "state_global_normalized": { "rho": "1.55977605244875763430199635538343927562590808342762688379418475523952184863491194193336928", "p": "0.102092384979951422957950143157036578811268837568408700880890526321521815261163946163592801", "u": [ "-0.640492298511772805367691302543751365897302188377941814080787676283283914783275310376031524", "-0.0150783350929039625780923082566351260569289846684293842466009120375027995992358903079958111", "0E-91" ], "B": [ "0.0411967168512104602580764980537920595430293861459567280173897963369134478427701431425902443", "1.00368900581182772707585702978434952909109581842209486194226436778229630749500986959445561", "0E-91" ] }, "root_record": { "r": "1.55977605244875763430199635538343927562590808342762688379418475523952184863491194193336928", "b": "0.0406297714242365325971697479770140774080533237776944576536096429643981181848434889261427091", "h": "0.00685998837482002217802632094429811079674718505816840145097286276133073855636047335164475575", "A": "0.409476459925480125639480728000903990367192092497191159956073869457290360203034806116218198", "denominator": "0.989299954412878857442182234149810752801676985501354656839929334398270188639586204041504329", "polynomial_residual": "-6.36453717901041926818202E-66", "bracket_initial_signs": [ "1.45732968155505221575766182527117110069361030754692850781089396135877376802587918601800710", "-1.98639140939315777068988030649286407850376280197422651338871183261002113260925086977364615" ], "bracket_derivative_max": "-5.51189262253672354787833019505837372981416735827419289207005118771581364679611256802781228", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "-3E-91", "0E-182", "1E-90", "0E-182", "3.68855243277141457785246088530256192514104937506743063172299445025726652207516169105180880E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_2.375", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.026458063048097794, 0.0 ], "rh_scaled_inf": 1.7909635213629265e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7909635213629265e-16, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.0251801883363107, "alfven_n": 0.06626090288464706, "fast": 0.8691371241573393 }, "right": { "slow": 0.0309827881372492, "alfven_n": 0.08275390062317708, "fast": 0.6944505467588412 } }, "front_relative_normal_velocity": { "left": -0.6405669615975278, "right": -0.9991410066896868 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5597760524487576, "pressure_ratio": 2.5170706356003802, "entropy_over_cv": 0.1821920211122332, "tangential_field_ratio": 1.5658304642103906 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.4, "theta_Bn_degrees": 82.60000000000001, "compression": 1.5597607173228518, "u2x_km_s": -384.2965944786911, "u2y_km_s": -9.013890097868101, "speed2_km_s": 384.4022928425583, "signed_deflection_degrees": 1.3436579617335331, "p2_over_p1": 2.5170116711861383, "B2_over_B1": 1.558146906002405, "entropy_over_cv": 0.18218498114391288, "upstream_fast_Mach": 1.4387339222797126, "downstream_fast_Mach": 0.7370189924080301, "downstream_alfven_margin": 0.5740770112569676, "state_global_normalized": { "rho": "1.55976071732285179093668082661318613661095173940187313663763800290025494097008176523845707", "p": "0.102089993383309774225170417598070166988151116351590633970102505205121111491810671134612827", "u": [ "-0.640494324131151785039353762960506265799557821014711816362947291239493811310807893114532497", "-0.0150231501631135027883903531583210275869593471461679721638461346660776560980804364913774816", "0E-91" ], "B": [ "0.0410391648339946476957703659928683410386902724135444496277190933578427795216597652502492380", "1.00367858658219620753904307642499422607300819592442951643915232812488510808528179005243680", "0E-91" ] }, "root_record": { "r": "1.55976071732285179093668082661318613661095173940187313663763800290025494097008176523845707", "b": "0.0406312497558812089468465008399451380029892488505831159958482921869695045816430798661240576", "h": "0.00690656756680669672125777805351541363533751871461702940712397405278932788158999883197644471", "A": "0.409445029313580892683241678303257878931819717125742341904819171149969719116112636382531915", "denominator": "0.989227407217758843613480682923440411010862281192168368817930866256628691434135437497262804", "polynomial_residual": "-8.11835321809700273265950E-66", "bracket_initial_signs": [ "1.45715557764319213589209170007558661256863384650888776048431563269915235749838178011877578", "-1.98631964513585288031000169056046137773967823732276584175209855346852387895346349128063755" ], "bracket_derivative_max": "-5.51162391954283420153433786872667420424221361482022519906927168572753691013229307268194883", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.04757566854126351627553840171849431941288486507476936321310941043820724933512259193420115E-90", "8E-91", "0E-182", "6E-90", "0E-182", "4.70552820287097553478294208317161846843351092831793886201107900103609338387123072806128791E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_2.4", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.026843399977031702, 0.0 ], "rh_scaled_inf": 4.40007771460622e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -4.40007771460622e-16 }, "characteristics": { "left": { "slow": 0.025265376506378463, "alfven_n": 0.06648459476535655, "fast": 0.8691249650561176 }, "right": { "slow": 0.031087440271489485, "alfven_n": 0.08303286346096284, "fast": 0.6944458698212392 } }, "front_relative_normal_velocity": { "left": -0.6405616060223241, "right": -0.9991228300988584 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5597607173228518, "pressure_ratio": 2.5170116711861383, "entropy_over_cv": 0.18218498114391268, "tangential_field_ratio": 1.565856458523729 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.425, "theta_Bn_degrees": 82.575, "compression": 1.5597451111997758, "u2x_km_s": -384.29790553763604, "u2y_km_s": -8.980779711203066, "speed2_km_s": 384.40282855987806, "signed_deflection_degrees": 1.338719586959372, "p2_over_p1": 2.5169514904974166, "B2_over_B1": 1.558120448799464, "entropy_over_cv": 0.18217774712901647, "upstream_fast_Mach": 1.4387171959511775, "downstream_fast_Mach": 0.7370232216410202, "downstream_alfven_margin": 0.573847957695576, "state_global_normalized": { "rho": "1.55974511119977571343793617553526055154839824993803568020465582658152693844075990028013329", "p": "0.102087552454575224529806345104698212640275264525652948705799401370179767683394844669276481", "u": [ "-0.640496509229393436855628702683479710449012058321962350065944126731165376988849760721140916", "-0.0149679661853384451301536277650363426456509996998189604747100304463850425969344897189311258", "0E-91" ], "B": [ "0.0408816255624519669025704551934017117710952154518178003387501104113141961357622269621430565", "1.00366794502042978264430510726546912916647571061508976438745958699892552083146893242747027", "0E-91" ] }, "root_record": { "r": "1.55974511119977571343793617553526055154839824993803568020465582658152693844075990028013329", "b": "0.0406327436402936153132650367818066732551448240966162714904721981215069417562904553575541087", "h": "0.00695330607244411737851357140068315909144717355018474733208253580313344248199670731883737577", "A": "0.409413598758459320505396094331810843233295135795106258264126273087647565260091424667542302", "denominator": "0.989154614846829574416778463089994500830913656634796240723795117953995447290471662305290664", "polynomial_residual": "-6.18208081030250953287651E-66", "bracket_initial_signs": [ "1.45697988386226989119608514029367583794751403255475896383701462453679438238674845358406924", "-1.98624920915581600855923633045136878252815963093729517802924600953596274800478972925467267" ], "bracket_derivative_max": "-5.51135519493789661496778781452973180058512823985232003142866216108595497382092992024949838", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.04782567701837962435676976937025741137246897517124944133792693032725142829401879640947817E-90", "0E-91", "0E-182", "-1E-90", "0E-182", "3.58365682837670828080646197386273640563627293627490913146072556718359690304359072206604135E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.425", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.027228734568428, 0.0 ], "rh_scaled_inf": 2.20020702232225e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.20020702232225e-16 }, "characteristics": { "left": { "slow": 0.025350563392636586, "alfven_n": 0.0667082819842667, "fast": 0.8691126966849309 }, "right": { "slow": 0.03119208859882687, "alfven_n": 0.08331181049046343, "fast": 0.6944411772520794 } }, "front_relative_normal_velocity": { "left": -0.6405562396798427, "right": -0.9991044632891464 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5597451111997758, "pressure_ratio": 2.5169514904974166, "entropy_over_cv": 0.18217774712901624, "tangential_field_ratio": 1.5658823229434684 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.45, "theta_Bn_degrees": 82.55000000000001, "compression": 1.5597292340563413, "u2x_km_s": -384.2993122899991, "u2y_km_s": -8.947669965277871, "speed2_km_s": 384.403462815274, "signed_deflection_degrees": 1.3337809894620198, "p2_over_p1": 2.5168900935306158, "B2_over_B1": 1.5580936858835726, "entropy_over_cv": 0.1821703190648979, "upstream_fast_Mach": 1.438700227863885, "downstream_fast_Mach": 0.7370275312756829, "downstream_alfven_margin": 0.5736188980210458, "state_global_normalized": { "rho": "1.55972923405634130122174103199912070969935931578110554523536309260966796245122165671419745", "p": "0.102085062193601775293579289791018478509421621241831374349974717241210438054625609575520254", "u": [ "-0.640498853816665151637296885394964222842424158657310905498834610251256482224974430694415417", "-0.0149127832754631205681048962371937882430345469650606435717755468044585403836332086045246077", "0E-91" ], "B": [ "0.0407240992680360074233931779562529118616782739175320714059429811028703247119315745155075834", "1.00365708112958089080146091392170126814192392145382887705111006199045770986596892132733790", "0E-91" ] }, "root_record": { "r": "1.55972923405634130122174103199912070969935931578110554523536309260966796245122165671419745", "b": "0.0406342530797551266458784233323851866570693476529385811990016800576588427517928316683934235", "h": "0.00700020392700824629050606954106562316835948666735347125478088995891383695344887013177000465", "A": "0.409382168248216874659298798966644035126155066005878258825472839521583112150257192629289278", "denominator": "0.989081577290689235503560440605648342131990432204883114439082303800455708777839852044595768", "polynomial_residual": "2.37419309388192385272953E-66", "bracket_initial_signs": [ "1.45680260029623476194982562649547922130878135540191019199123957089799250226530208787744074", "-1.98618010104482533427344798959549312729424887012072008539327931889376395260824089643370239" ], "bracket_derivative_max": "-5.51108644824750886993677495960446377785762649529422391431290513796954855093578599347421962", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "1E-91", "0E-182", "-2E-90", "0E-182", "-1.37644565415511530311402658350057139885660476498505807196542252562900468128588884467763366E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_2.45", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.027614066785050462, 0.0 ], "rh_scaled_inf": 4.400752661896993e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 4.400752661896993e-16 }, "characteristics": { "left": { "slow": 0.025435748993645594, "alfven_n": 0.0669319645576818, "fast": 0.869100319047826 }, "right": { "slow": 0.03129673310627763, "alfven_n": 0.08359074165857133, "fast": 0.6944364690533508 } }, "front_relative_normal_velocity": { "left": -0.6405508625787276, "right": -0.9990859062640476 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5597292340563413, "pressure_ratio": 2.5168900935306158, "entropy_over_cv": 0.18217031906489778, "tangential_field_ratio": 1.5659080574420992 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.475, "theta_Bn_degrees": 82.525, "compression": 1.559713085869205, "u2x_km_s": -384.3008147418897, "u2y_km_s": -8.914560929621617, "speed2_km_s": 384.4041956168639, "signed_deflection_degrees": 1.3288421833432402, "p2_over_p1": 2.516827480283598, "B2_over_B1": 1.5580666172601056, "entropy_over_cv": 0.1821626969491065, "upstream_fast_Mach": 1.4386830180127244, "downstream_fast_Mach": 0.7370319213236624, "downstream_alfven_margin": 0.5733898322257804, "state_global_normalized": { "rho": "1.55971308586920498800505127514764744956430355356448029509516504040855571490004278039979682", "p": "0.102082522600302730410808076852337039115901017879505561725005365079137074597300707569561616", "u": [ "-0.640501357903149501190151481911341779629570399031559207761473161396641931355546812978563493", "-0.0148576015493693628533065779156358640734138985654713698734758855313853498317075621102320598", "0E-91" ], "B": [ "0.0405665861822098620661176962211699780340512456457037096446694413306508707609413733439330009", "1.00364599491281740930939735680649845675232368277588258718024752133005729932576505197439959", "0E-91" ] }, "root_record": { "r": "1.55971308586920498800505127514764744956430355356448029509516504040855571490004278039979682", "b": "0.0406357780765710003517840508942493169925391729255713574610603070735359258042878349303477697", "h": "0.00704726116601969258544459264370505346535915720419474590418797739220872034934880554490999507", "A": "0.409350737770955099123818194031225424663702278084859991116100158849856700388315926523876493", "denominator": "0.989008294539821213549525977754436532845677279763555257936453565915444202910286725282647911", "polynomial_residual": "-5.67707266657474454307756E-66", "bracket_initial_signs": [ "1.45662372702838145614318604498363773544585238967666805086655707664011659974689888558772531", "-1.98611232039372036045099181547790450607441078197835619308742920185196213976750684725794106" ], "bracket_derivative_max": "-5.51081767899514108295842119510229267736579186919693806470698072037682600513012560457010959", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "4E-91", "0E-182", "3E-90", "0E-182", "3.29168883478317851664704905957749992293715149738591081812993947772620243727969626580237212E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_2.475", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.02799939658967534, 0.0 ], "rh_scaled_inf": 2.2005467834999108e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.791445371995725e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.2005467834999108e-16 }, "characteristics": { "left": { "slow": 0.025520933307970197, "alfven_n": 0.06715564250191905, "fast": 0.8690878321488716 }, "right": { "slow": 0.031401373780856806, "alfven_n": 0.08386965691218194, "fast": 0.6944317452270495 } }, "front_relative_normal_velocity": { "left": -0.6405454747276994, "right": -0.999067159027095 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559713085869205, "pressure_ratio": 2.516827480283598, "entropy_over_cv": 0.18216269694910647, "tangential_field_ratio": 1.5659336619918194 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.5, "theta_Bn_degrees": 82.50000000000001, "compression": 1.5596966666148677, "u2x_km_s": -384.3024128994266, "u2y_km_s": -8.881452673761853, "speed2_km_s": 384.40502697274604, "signed_deflection_degrees": 1.3239031827051606, "p2_over_p1": 2.516763650755688, "B2_over_B1": 1.5580392429344434, "entropy_over_cv": 0.18215488077938688, "upstream_fast_Mach": 1.4386655663925898, "downstream_fast_Mach": 0.7370363917967331, "downstream_alfven_margin": 0.5731607603022455, "state_global_normalized": { "rho": "1.55969666661486773843682731707185759364293871237248087779822589647482781508356886005527898", "p": "0.102079933674650704847799808388919156263597528282195449040843819028438856942531172036022372", "u": [ "-0.640504021499044288975875967981008003166361500051555208169833926724465408501042667068941434", "-0.0148024211229364203570023872805675203470835171294283507330140792154009459177120440817430590", "0E-91" ], "B": [ "0.0404090865364461559693772264991930251377963571399760086944382344540126382515621902860013995", "1.00363468637342262343178396504686840026140503721612722422741162680423684440644825575382437", "0E-91" ] }, "root_record": { "r": "1.55969666661486773843682731707185759364293871237248087779822589647482781508356886005527898", "b": "0.0406373186330703837842610145640548515515129909529069202724336944610542349275950097944161131", "h": "0.00709447782524380707710407018107180978771540689510303132576689766166619488247303798131341817", "A": "0.409319307314775598340896360083418654270758150344569100095738982487780365284979134982991797", "denominator": "0.988934766584594137928895696133117871523653045849523819405752613017517907062065146747990543", "polynomial_residual": "-2.94585907880740561889195E-66", "bracket_initial_signs": [ "1.45644326414135105289852472675144420336923868820250380812974479026952141256819618224683606", "-1.98604586679239988275600114815106093512874227283704944142670701402502633991642249327227403" ], "bracket_derivative_max": "-5.51054888670213346744465259007406502691899746107709677398367300426161554438113025510200369", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "-2E-91", "0E-182", "-1E-90", "0E-182", "1.70827416745131073607990415579691020126534391703584557432985630223835623673552164190998065E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.5", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.028384723945091478, 0.0 ], "rh_scaled_inf": 1.7915677988588733e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7915677988588733e-16, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.025606116334179408, "alfven_n": 0.06737931583330883, "fast": 0.869075235992158 }, "right": { "slow": 0.03150601060957816, "alfven_n": 0.08414855619819375, "fast": 0.6944270057751788 } }, "front_relative_normal_velocity": { "left": -0.6405400761355544, "right": -0.9990482215818578 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5596966666148677, "pressure_ratio": 2.516763650755688, "entropy_over_cv": 0.1821548807793869, "tangential_field_ratio": 1.5659591365645358 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.525, "theta_Bn_degrees": 82.47500000000001, "compression": 1.5596799762696751, "u2x_km_s": -384.3041067687376, "u2y_km_s": -8.848345267224522, "speed2_km_s": 384.4059568909999, "signed_deflection_degrees": 1.3189640016502293, "p2_over_p1": 2.5166986049476736, "B2_over_B1": 1.558011562911969, "entropy_over_cv": 0.18214687055367912, "upstream_fast_Mach": 1.4386478729983816, "downstream_fast_Mach": 0.7370409427067997, "downstream_alfven_margin": 0.5729316822429698, "state_global_normalized": { "rho": "1.55967997626967504488130960227009354173234983040780529649735574556888873178546683235269750", "p": "0.102077295416677633202423361881362809060734954444845371463476490728726166849348622397513545", "u": [ "-0.640506844614562601297974730653187123284632880083667968786941478949898938511918448742326422", "-0.0147472421120408678552363345253804799421059300683033939068481340649162365696478275584259815", "0E-91" ], "B": [ "0.0402516005622270757921079059585553363811206419531583857848123842021933795327738725503893943", "1.00362315551479519527063543554560039039124834429165124411128967228910597868598473507666310", "0E-91" ] }, "root_record": { "r": "1.55967997626967504488130960227009354173234983040780529649735574556888873178546683235269750", "b": "0.0406388747516063218094849024439497608255964361914250302641591681613102431449605948415954381", "h": "0.00714185394069077776374299896886864069465748857732440102221618178676786653688218620328817968", "A": "0.409287876867780019253349859921717087074479293022522879325961223737293021657760885986721485", "denominator": "0.988860993415261922532032442358294029301171275451890808104416183542213484151808316645790112", "polynomial_residual": "-5.45638464303703826253136E-66", "bracket_initial_signs": [ "1.45626121171713195083940493129674989773194025448185538283617167334882504035795179772850927", "-1.98598073982981994438707614511126431681922406800730585743450044748868270559958448352528418" ], "bracket_derivative_max": "-5.51028007088769438154015691680308652952897799573847679280206494483574206145414552216250773", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "5E-91", "0E-182", "2E-90", "0E-182", "3.16447641918926146287246228287785249621127969785093250969495396752538410078860506408009032E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_2.525", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.02877004881410044, 0.0 ], "rh_scaled_inf": 2.2008911216614012e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7916910118530354e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.2008911216614012e-16 }, "characteristics": { "left": { "slow": 0.025691298070846573, "alfven_n": 0.06760298456819479, "fast": 0.869062530581797 }, "right": { "slow": 0.03161064357945424, "alfven_n": 0.08442743946350828, "fast": 0.6944222506997481 } }, "front_relative_normal_velocity": { "left": -0.6405346668111646, "right": -0.9990290939319414 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5596799762696751, "pressure_ratio": 2.5166986049476736, "entropy_over_cv": 0.18214687055367906, "tangential_field_ratio": 1.5659844811318626 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.55, "theta_Bn_degrees": 82.45, "compression": 1.559663014809817, "u2x_km_s": -384.3058963559597, "u2y_km_s": -8.815238779533912, "speed2_km_s": 384.40698537968564, "signed_deflection_degrees": 1.3140246542811707, "p2_over_p1": 2.5166323428618043, "B2_over_B1": 1.5579835771980712, "entropy_over_cv": 0.1821386662701187, "upstream_fast_Mach": 1.4386299378250051, "downstream_fast_Mach": 0.7370455740658968, "downstream_alfven_margin": 0.5727025980405444, "state_global_normalized": { "rho": "1.55966301480981692435379946433305168412538676753448185003509958349040417266325535473742516", "p": "0.102074607826474778223869137146848345262741779626919918539868449550070584660946887954011456", "u": [ "-0.640509827259932859003181897593620347718985239617379029177675068948180274611158770784767904", "-0.0146920646325565182640173685780701359449771341677037721549867367734399390211399278292409304", "0E-91" ], "B": [ "0.0400941284910443990257135265453830297274631912304881774006865199794008377727559672249586781", "1.00361140234044913243759940511233266235408197765491738348587570575966656062666553034951016", "0E-91" ] }, "root_record": { "r": "1.55966301480981692435379946433305168412538676753448185003509958349040417266325535473742516", "b": "0.0406404464345557644514622213502006927996707470224797255349252644862752348461190052866785596", "h": "0.00718938954861572612836087139691784565727859299523869042361521773523679145461543425172712130", "A": "0.409256446418070033342853819376901422075343945602229518003512484342704098075998506538436475", "denominator": "0.988786975021963807726600794474939208351985672489699661178848655507307038480815187600099257", "polynomial_residual": "-3.36393535959155403950731E-66", "bracket_initial_signs": [ "1.45607756983706082141404809462622474200010291638253939695134980274860385752492892086983798", "-1.98591693909399177729735212319629137095768179771194495175419076440685408145358626238709683" ], "bracket_derivative_max": "-5.51001123106889836165019107681241615782341735899352856325320122353566365574236241836538705", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-4E-91", "0E-182", "-4E-90", "0E-182", "1.95117311373618308617764305630108856808630141655519683689386508364979733354430853306540691E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.55", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.029155371159516635, 0.0 ], "rh_scaled_inf": 1.7918150112053095e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7918150112053095e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.025776478516549475, "alfven_n": 0.06782664872293385, "fast": 0.8690497159219229 }, "right": { "slow": 0.03171527267749632, "alfven_n": 0.08470630665503008, "fast": 0.694417480002774 } }, "front_relative_normal_velocity": { "left": -0.6405292467634781, "right": -0.9990097760809875 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559663014809817, "pressure_ratio": 2.5166323428618043, "entropy_over_cv": 0.18213866627011865, "tangential_field_ratio": 1.5660096956651208 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.575, "theta_Bn_degrees": 82.425, "compression": 1.5596457822113279, "u2x_km_s": -384.3077816672393, "u2y_km_s": -8.7821332802126, "speed2_km_s": 384.4081124468446, "signed_deflection_degrees": 1.3090851547009406, "p2_over_p1": 2.5165648645017935, "B2_over_B1": 1.557955285798142, "entropy_over_cv": 0.18213026792703663, "upstream_fast_Mach": 1.4386117608673712, "downstream_fast_Mach": 0.7370502858861896, "downstream_alfven_margin": 0.5724735076876227, "state_global_normalized": { "rho": "1.55964578221132791560920485660845864201963189763343431571705942252981329928776984628763605", "p": "0.102071870904192739292598442357994250363849891043612331546871537012430720993753963230750499", "u": [ "-0.640512969445398869698777194867438080656917807115431053069955551257733181340003932687235755", "-0.0146368888003543343247972965515929268190254153170355157830819915567765652205078589393408874", "0E-91" ], "B": [ "0.0399366705543995234297054540337301432172078847921006441713844159112202163765345112043859085", "1.00359942685401375652284534935652130356103270465606657389726370715212455061796844731271508", "0E-91" ] }, "root_record": { "r": "1.55964578221132791560920485660845864201963189763343431571705942252981329928776984628763605", "b": "0.0406420336843195746152271314919522720649036967322964861248971996800094571454337306849766914", "h": "0.00723708468551880424078975788761046115169530410509741547975836577792663186115362940748032532", "A": "0.409225015953747318668051860300613547708240880045094217270251064554687607821010707704742742", "denominator": "0.988712711394724402462490555030183101575205673536179291312279437364655428422246853672067873", "polynomial_residual": "1.158739297974688420112876E-65", "bracket_initial_signs": [ "1.45589233858182356718240211161424410313954020513984554798048978367191516288127721110329221", "-1.98585446417197972975179706690821898226581546120858824655056152133831229499065920449689692" ], "bracket_derivative_max": "-5.50974236676068414164579268795671575966404166764068521428112796367829054328084526226144185", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "3E-91", "0E-182", "5E-90", "0E-182", "-6.72179351831914721972324055799539591892307261275029445774538074034549597706854238780034652E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_2.575", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.02954069094416743, 0.0 ], "rh_scaled_inf": 1.3877787807814457e-17, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02586165766987035, "alfven_n": 0.06805030831389638, "fast": 0.8690367920166909 }, "right": { "slow": 0.03181989789071439, "alfven_n": 0.08498515771966678, "fast": 0.6944126936862801 } }, "front_relative_normal_velocity": { "left": -0.6405238160015191, "right": -0.9989902680326739 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5596457822113279, "pressure_ratio": 2.5165648645017935, "entropy_over_cv": 0.18213026792703668, "tangential_field_ratio": 1.5660347801353391 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.6, "theta_Bn_degrees": 82.4, "compression": 1.559628278450087, "u2x_km_s": -384.30976270873197, "u2y_km_s": -8.749028838781404, "speed2_km_s": 384.40933810049887, "signed_deflection_degrees": 1.304145517012682, "p2_over_p1": 2.516496169872817, "B2_over_B1": 1.5579266887175776, "entropy_over_cv": 0.18212167552295946, "upstream_fast_Mach": 1.4385933421203962, "downstream_fast_Mach": 0.7370550781799733, "downstream_alfven_margin": 0.572244411176921, "state_global_normalized": { "rho": "1.55962827845008707638361285133151672658157438998860550674910819786766093677493882412266949", "p": "0.102069084650041460860485734230050455431570725683702276248559261999132544162017147391705018", "u": [ "-0.640516271181219880486240935005137485436006628539826373198483788684792071765165201054275159", "-0.0145817147313023402400289614165185114621180730894337217283610751480507527506346186655034241", "0E-91" ], "B": [ "0.0397792269838034965916780653550006318402662455717838904521513546618120222682798820107157771", "1.00358722905923367136142994030603757605337750764376190501560902076548437358504103827070166", "0E-91" ] }, "root_record": { "r": "1.55962827845008707638361285133151672658157438998860550674910819786766093677493882412266949", "b": "0.0406436365033225358883436027231162648778970980701357413250424790912896849754788966971568530", "h": "0.00728493938814529266211924586083435824304526554351162907718867509496313033763123141201137156", "A": "0.409193585462913541902734461689713913539493504328610681426986986203343991622595701861839339", "denominator": "0.988638202523453726520730784539487084297688119379304705332851895239912032493465240874572917", "polynomial_residual": "4.2000910039519778018782E-67", "bracket_initial_signs": [ "1.45570551803145628507577697621017647446067870509911415120214346572972928499036418041658604", "-1.98579331464989918020745918059722440967127541603540554803896008118339822907095509105149534" ], "bracket_derivative_max": "-5.50947347747585265773383466204499441254414176551788743764895536133158728164459262331014212", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-2E-91", "0E-182", "0E-90", "0E-182", "-2.43674115163567460468245289563642203422852819380802911748528527382660359643526547633829020E-68", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.6", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.0299260081308933, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.025946835529395987, "alfven_n": 0.06827396335746636, "fast": 0.8690237588702786 }, "right": { "slow": 0.03192451920611722, "alfven_n": 0.08526399260432907, "fast": 0.6944078917522966 } }, "front_relative_normal_velocity": { "left": -0.6405183745343874, "right": -0.9989705697907147 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559628278450087, "pressure_ratio": 2.516496169872817, "entropy_over_cv": 0.18212167552295966, "tangential_field_ratio": 1.5660597345132543 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.625, "theta_Bn_degrees": 82.375, "compression": 1.559610503501818, "u2x_km_s": -384.31183948660237, "u2y_km_s": -8.71592552475932, "speed2_km_s": 384.41066234865184, "signed_deflection_degrees": 1.299205755319682, "p2_over_p1": 2.516426258981515, "B2_over_B1": 1.5578977859617786, "entropy_over_cv": 0.1821128890566094, "upstream_fast_Mach": 1.438574681579002, "downstream_fast_Mach": 0.7370599509596736, "downstream_alfven_margin": 0.5720153085012177, "state_global_normalized": { "rho": "1.55961050350181798078915318185446722137435136381290565700949862660513397257895869616520412", "p": "0.102066249064290240851156751775251963900405418902161427363781735611941958026971444501912570", "u": [ "-0.640519732477670631211683538653771538705609300397575087363073749256906276519245849040824336", "-0.0145265425412655332585710031530944470576262503121840202553183991644106202679172281390306752", "0E-91" ], "B": [ "0.0396217980107770456124810604689769287159477901211623143186611420878343101926087095602074890", "1.00357480895996873109701367148089535725749503057269401402720854569324726662535257906038251", "0E-91" ] }, "root_record": { "r": "1.55961050350181798078915318185446722137435136381290565700949862660513397257895869616520412", "b": "0.0406452548940133604207565463685775625849262250525659985082467968645127475352035077483344632", "h": "0.00733295369348569915195845981263576261106377554609565672348151514342229858909950837650386793", "A": "0.409162154933670340374028325598756734500460535762211013099967608249616406511800074292300146", "denominator": "0.988563448397947252906622036609580638140565641471679670474668822454136135822602694685726708", "polynomial_residual": "1.522772097654745861403666E-65", "bracket_initial_signs": [ "1.45551710826534623463807125978533923157992942339652689775489168714722259128353989251566699", "-1.98573349011291443750225666791061233170718338360287056308499585821131401689454392911312342" ], "bracket_derivative_max": "-5.50920456272506503897924606819174909633024303324314002659036475719328951972772983403783495", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "1E-91", "0E-182", "1E-90", "0E-182", "-8.83561673096827121637635385843289554661293203573057302852733014995305870658325225365590050E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_2.625", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03031132268254791, 0.0 ], "rh_scaled_inf": 4.403187078647153e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7921917297039493e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 4.403187078647153e-16 }, "characteristics": { "left": { "slow": 0.02603201209371777, "alfven_n": 0.0684976138700413, "fast": 0.8690106164868848 }, "right": { "slow": 0.03202913661071227, "alfven_n": 0.08554281125593072, "fast": 0.6944030742028604 } }, "front_relative_normal_velocity": { "left": -0.640512922371259, "right": -0.9989506813588601 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559610503501818, "pressure_ratio": 2.516426258981515, "entropy_over_cv": 0.1821128890566095, "tangential_field_ratio": 1.5660845587693086 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.65, "theta_Bn_degrees": 82.35000000000001, "compression": 1.5595924573420887, "u2x_km_s": -384.3140120070248, "u2y_km_s": -8.682823407663477, "speed2_km_s": 384.41208519928756, "signed_deflection_degrees": 1.294265883725324, "p2_over_p1": 2.5163551318359896, "B2_over_B1": 1.55786857753615, "entropy_over_cv": 0.1821039085269043, "upstream_fast_Mach": 1.4385557792381158, "downstream_fast_Mach": 0.7370649042378465, "downstream_alfven_margin": 0.5717861996533533, "state_global_normalized": { "rho": "1.55959245734208871686241948518582522036899902651512383837467130563031467128574333285774636", "p": "0.102063364147267739020525407082897889082327135523839462324217344101423348814467198767126080", "u": [ "-0.640523353345041408233488299831595967092632318914802298212705793082320313066696105991730923", "-0.0144713723461057952107048677436748485571125223081847466909090166963128750353131410718629008", "0E-91" ], "B": [ "0.0394643838668506069174510344219712808178379870241201154787017250781316136289320468374386363", "1.00356216656019400804280303440216285105893370099194060477741454180666162943757789021642684", "0E-91" ] }, "root_record": { "r": "1.55959245734208871686241948518582522036899902651512383837467130563031467128574333285774636", "b": "0.0406468888588646968830359183960108310091634446038644196566077540353949019388169511644799448", "h": "0.00738112763877585817904341356816705165971746712348285645631083705086458831823651100053890512", "A": "0.409130724354119304100539324892486309048021956476876102822711029944608652073811144243954065", "denominator": "0.988488449007885950387315563288964210148533170535089883147481096426661384988034887741651302", "polynomial_residual": "1.85491416082172633690462E-66", "bracket_initial_signs": [ "1.45532710936223281125768416914612594693982909504900839299843255488650748504891307250143964", "-1.98567499014523662733777310446750201332070710073190244995191163314898050417635805849963161" ], "bracket_derivative_max": "-5.50893562201684058346660693842265241614345922560114810863883410804596106388833621256007803", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "-1E-91", "0E-182", "1E-90", "0E-182", "-1.07640828462077916659649676749156551923179319240124561632653084274155196284823890023105610E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_2.65", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03069663456199827, 0.0 ], "rh_scaled_inf": 2.2017720084404273e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.2017720084404273e-16 }, "characteristics": { "left": { "slow": 0.02611718736143177, "alfven_n": 0.0687212598680326, "fast": 0.8689973648707304 }, "right": { "slow": 0.03213375009150576, "alfven_n": 0.0858216136213886, "fast": 0.6943982410400157 } }, "front_relative_normal_velocity": { "left": -0.6405074595213859, "right": -0.9989306027408966 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5595924573420887, "pressure_ratio": 2.5163551318359896, "entropy_over_cv": 0.18210390852690428, "tangential_field_ratio": 1.5661092528736513 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.675, "theta_Bn_degrees": 82.325, "compression": 1.5595741399463119, "u2x_km_s": -384.31628027618285, "u2y_km_s": -8.649722557009081, "speed2_km_s": 384.41360666037144, "signed_deflection_degrees": 1.2893259163330468, "p2_over_p1": 2.516282788445808, "B2_over_B1": 1.5578390634461006, "entropy_over_cv": 0.18209473393295772, "upstream_fast_Mach": 1.43853663509267, "downstream_fast_Mach": 0.7370699380271787, "downstream_alfven_margin": 0.5715570846262306, "state_global_normalized": { "rho": "1.55957413994631188426671728707210011886308815632732671329214367723402955216186593950848763", "p": "0.102060429899361985277532120407671226762890030673810382407442964938148324751870670872826590", "u": [ "-0.640527133793638098707609416789990663557708735137283891214365167521358732537364365851166699", "-0.0144162042616818039925290630985977355293717355113199358182244184563433752485506347521019200", "0E-91" ], "B": [ "0.0393069847835643561945657311066176931974882155290696881700388883070860729310244291126370022", "1.00354930186399976033959200424172429336324401320811442049001987394540093890532556728347558", "0E-91" ] }, "root_record": { "r": "1.55957413994631188426671728707210011886308815632732671329214367723402955216186593950848763", "b": "0.0406485384003731385030582318504429096788272228411880111666818081609339564665341731706374917", "h": "0.00742946126149703123570247638684240583604213591930241121687293776665676097733625149458204701", "A": "0.409099293712361957830391609975935526751452690920272769179507990729095970445737260104348972", "denominator": "0.988413204342836326174069366287684214726684193955620568834162654131724130779673300782356224", "polynomial_residual": "-1.264416969366686113431077E-65", "bracket_initial_signs": [ "1.45513552140020852439927929238404262646836726021690489703789398384849075127226084033357862", "-1.98561781433012156504139282751345729324711459250442485815022665511644717168577040488695119" ], "bracket_derivative_max": "-5.50866665485755472008820892782856491238985806349316296940684915985431319771432477426525033", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-2E-91", "0E-182", "-4E-90", "0E-182", "7.33828851437591808286097031966603665973402878708125929999802157846063931175969820745267668E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.675", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03108194373212487, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.026202361331138763, "alfven_n": 0.06894490136786541, "fast": 0.8689840040260578 }, "right": { "slow": 0.03223835963550259, "alfven_n": 0.08610039964762267, "fast": 0.6943933922658129 } }, "front_relative_normal_velocity": { "left": -0.640501985994096, "right": -0.998910333940647 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5595741399463119, "pressure_ratio": 2.516282788445808, "entropy_over_cv": 0.1820947339329576, "tangential_field_ratio": 1.566133816796139 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.7, "theta_Bn_degrees": 82.30000000000001, "compression": 1.5595555512897445, "u2x_km_s": -384.31864430026934, "u2y_km_s": -8.616623042309367, "speed2_km_s": 384.4152267398499, "signed_deflection_degrees": 1.2843858672462989, "p2_over_p1": 2.5162092288220017, "B2_over_B1": 1.557809243697043, "entropy_over_cv": 0.18208536527407906, "upstream_fast_Mach": 1.4385172491376035, "downstream_fast_Mach": 0.7370750523404871, "downstream_alfven_margin": 0.5713279634128144, "state_global_normalized": { "rho": "1.55955555128974459214841015933722306307565750873616728387602170796761143613551258248909801", "p": "0.102057446321020387965086110434425733840271599488269370349340790485179723604534457551395621", "u": [ "-0.640531073833782245390970627781039807188996631366874464748678089459037292029077568768229097", "-0.0143610384038489449994949913571728324385636629317971731334852903031984839709484974698284885", "0E-91" ], "B": [ "0.0391496009924682384603854426072077892905180039722835412726595105369310624216382519134297436", "1.00353621487559139941077606450947714046783840897583490288144883418295294962253778559385217", "0E-91" ] }, "root_record": { "r": "1.55955555128974459214841015933722306307565750873616728387602170796761143613551258248909801", "b": "0.0406502035210592311811703589940935150126216155831259211805428584132196741709956798909440253", "h": "0.00747795459937600795669726941822094401841369992353577616991605210037758511501598988524898041", "A": "0.409067862996499743079105451411498545860232817000327249375513534895949294958479361883649913", "denominator": "0.988337714392250468749412076538659068819345177702806601756344299045319007161582646095214725", "polynomial_residual": "6.86394631703954530059084E-66", "bracket_initial_signs": [ "1.45494234445671998084463761375939358792063765970571963362242517113509566372236556325257862", "-1.98556196224986761459298169798976213383809502583203572404159382516704552700531552835514004" ], "bracket_derivative_max": "-5.50839766075143695594555789062885624268628562582783167727520675867303667532218334551815736", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.05067798027304448409808699144959615816921337276303773848098498734954764406775002171717226E-90", "-2E-91", "0E-182", "-4E-90", "0E-182", "-3.98409414617611214155497919156298000442326236159262476744167374399644099809239243292814321E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_2.7", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03146725015582174, 0.0 ], "rh_scaled_inf": 1.7925755337430386e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7925755337430386e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.026287534001444342, "alfven_n": 0.06916853838597888, "fast": 0.8689705339571311 }, "right": { "slow": 0.03234296522970642, "alfven_n": 0.08637916928155602, "fast": 0.6943885278823095 } }, "front_relative_normal_velocity": { "left": -0.6404965017987932, "right": -0.99888987496197 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5595555512897445, "pressure_ratio": 2.5162092288220017, "entropy_over_cv": 0.18208536527407915, "tangential_field_ratio": 1.5661582505063334 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.725, "theta_Bn_degrees": 82.27499999999999, "compression": 1.5595366913474884, "u2x_km_s": -384.3211040854867, "u2y_km_s": -8.583524933075534, "speed2_km_s": 384.4169454456504, "signed_deflection_degrees": 1.2794457505684926, "p2_over_p1": 2.516134452977065, "B2_over_B1": 1.5577791182943943, "entropy_over_cv": 0.1820758025497735, "upstream_fast_Mach": 1.438497621367859, "downstream_fast_Mach": 0.7370802471907191, "downstream_alfven_margin": 0.5710988360061315, "state_global_normalized": { "rho": "1.55953669134748845714763786915256264843263228735826444114378697846652556908303751946615325", "p": "0.102054413412749742101213973932686934600316768214694779699434729283806175722829620824122577", "u": [ "-0.640535173475811101963413113672381221217504233387227147076772188136444293713384930931933793", "-0.0143058748884592225088480129585218949512756643173169373625512661520047298715681513841626523", "0E-91" ], "B": [ "0.0389922327251219982546470668990244524852192444866385312508954089099652516193817913228140696", "1.00352290559928945721421147132099456025623572146738999455921586702590338194809856406800103", "0E-91" ] }, "root_record": { "r": "1.55953669134748845714763786915256264843263228735826444114378697846652556908303751946615325", "b": "0.0406518842234674816838809465028070012627966483326951314451068498900751276422151371534310047", "h": "0.00752660769038520804296084807017308164843138245494962435155215478243321851090552991994403021", "A": "0.409036432194634000167256394790255310378508010359776348423584709981501941037606736269604835", "denominator": "0.988261979145466090839446751158260318533873639560986191365289971420914149184842583092599289", "polynomial_residual": "-1.33498164058908383685409E-66", "bracket_initial_signs": [ "1.45474757860856887295190895919743563707619736366204253497711532537903388624675404728743609", "-1.98550743348581353390118939466686701642819205773555535352928321683633470703648101872047086" ], "bracket_derivative_max": "-5.50812863920056880935117847473150780157576810271683444042724032727122630621780499499241409", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "-2E-91", "0E-182", "-3E-90", "0E-182", "7.74965288030074098467432829759438910893726385086173587700143131246338654615436448187478526E-68", "0E-91" ], "diagnosis": { "case_id": "R95_phi_2.725", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03185255379599667, 0.0 ], "rh_scaled_inf": 2.202314296434365e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.792705044085038e-16, "t1_momentum": 2.7755575615628914e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.202314296434365e-16 }, "characteristics": { "left": { "slow": 0.02637270537095896, "alfven_n": 0.06939217093882626, "fast": 0.8689569546682361 }, "right": { "slow": 0.03244756686111961, "alfven_n": 0.08665792247011485, "fast": 0.6943836478915703 } }, "front_relative_normal_velocity": { "left": -0.6404910069449579, "right": -0.9988692258087608 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5595366913474884, "pressure_ratio": 2.516134452977065, "entropy_over_cv": 0.18207580254977374, "tangential_field_ratio": 1.566182553973503 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.75, "theta_Bn_degrees": 82.25, "compression": 1.5595175600944895, "u2x_km_s": -384.32365963804665, "u2y_km_s": -8.550428298816703, "speed2_km_s": 384.41876278568185, "signed_deflection_degrees": 1.2745055804029621, "p2_over_p1": 2.5160584609249566, "B2_over_B1": 1.5577486872435755, "entropy_over_cv": 0.18206604575974225, "upstream_fast_Mach": 1.4384777517783864, "downstream_fast_Mach": 0.737085522590953, "downstream_alfven_margin": 0.5708697023992707, "state_global_normalized": { "rho": "1.55951756009448960156368273235844322020689246634921019236913172664891241481358973397263965", "p": "0.102051331175116237580416712115989191082369959599952609302944669114404285210892101330887247", "u": [ "-0.640539432730077688868644657382576290174770809428479729820123825260821463025499442699368197", "-0.0142507138313611710107367194225713319003002611781984129254533876606549136011193676437901218", "0E-91" ], "B": [ "0.0388348802130952099643773920847267782983951380101038917931361449603814034542259561668324689", "1.00350937403952955329079192688083538940406906887134673801782068619274829871644870908526003", "0E-91" ] }, "root_record": { "r": "1.55951756009448960156368273235844322020689246634921019236913172664891241481358973397263965", "b": "0.0406535805101663659161252103663820073269658375777977249329305747722269477951224486522656723", "h": "0.00757542057274278399075956919561899756406221731587354639919807983226800151214628363262350278", "A": "0.409005001294865950257858303368845111245026775304300125355255387572476968252256995457267263", "denominator": "0.988185998591706572531527783199273023491309135244841756552283069038841895623756424051747106", "polynomial_residual": "-1.025447454666642305488558E-65", "bracket_initial_signs": [ "1.45455122393191297194264272268982550111024739607836634871898737701135056030479700013165280", "-1.98545422761833630631432007538750285703020555725584835377025991962661204766242890938284404" ], "bracket_derivative_max": "-5.50785958970488172841746476962202784533914541882743704750232986757200308588217096712998696", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "1E-91", "0E-182", "1E-90", "0E-182", "5.95348970411167403414308892555777877612483122076563104349460048640048391297691972400201391E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_2.75", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03223785461557124, 0.0 ], "rh_scaled_inf": 1.3877787807814457e-17, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.026457875438297983, "alfven_n": 0.06961579904287489, "fast": 0.8689432661636801 }, "right": { "slow": 0.032552164516743205, "alfven_n": 0.08693665916022845, "fast": 0.6943787522956659 } }, "front_relative_normal_velocity": { "left": -0.6404855014421457, "right": -0.9988483864849507 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5595175600944895, "pressure_ratio": 2.5160584609249566, "entropy_over_cv": 0.1820660457597424, "tangential_field_ratio": 1.5662067271666213 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.775, "theta_Bn_degrees": 82.225, "compression": 1.5594981575055387, "u2x_km_s": -384.3263109641705, "u2y_km_s": -8.51733320903986, "speed2_km_s": 384.4206787678338, "signed_deflection_degrees": 1.269565370852917, "p2_over_p1": 2.5159812526811014, "B2_over_B1": 1.5577179505500118, "entropy_over_cv": 0.1820560949038823, "upstream_fast_Mach": 1.4384576403641398, "downstream_fast_Mach": 0.7370908785543973, "downstream_alfven_margin": 0.5706405625853824, "state_global_normalized": { "rho": "1.55949815750553865167526277791162099254644426027879915501287791792870945610432824109894526", "p": "0.102048199608745467335237183877440456248304437346656048897639613497609602533026686169953147", "u": [ "-0.640543851606950849674645383570158058458033950949663853922567520491257937821599839301560610", "-0.0141955553483997664877527089074205547182437996640479650431536931094558541379683374900613590", "0E-91" ], "B": [ "0.0386775436879673082783932373104757891667897638138528620566688057432276584713593948036881806", "1.00349562020086236160961429934469434589873206954688270971230755862788674031807335309262547", "0E-91" ] }, "root_record": { "r": "1.55949815750553865167526277791162099254644426027879915501287791792870945610432824109894526", "b": "0.0406552923837483372721493208271496084931206860253366763478593578922911390698910258171606241", "h": "0.00762439328491272462680958966986800320814151265786999197134004900710918688377921439265217328", "A": "0.408973570285296677393412862813316228834803858381627004128653136117000468618902413064939060", "denominator": "0.988109772720081004537545225669881936559972303147882697070598537464816195373215947598362878", "polynomial_residual": "1.280584667623385918330052E-65", "bracket_initial_signs": [ "1.45435328050226712622605052191753812593302001139504907582881516256194498874333803354560564", "-1.98540234422684895835058878568772533393811074964724619414577066265643573130722774826393933" ], "bracket_derivative_max": "-5.50759051176215499521920486453370249831685898064513007624712480316523571521283813622621847", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.05148842869269572978585474857409348663264620618103850630376484331802736988348787770650590E-90", "-1E-91", "0E-182", "-3E-90", "0E-182", "-7.43562924947188886124585386397101361481849713585386004834337053360010833515593596024081828E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.775", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03262315257748102, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02654304420208177, "alfven_n": 0.06983942271460647, "fast": 0.8689294684477926 }, "right": { "slow": 0.03265675818357699, "alfven_n": 0.08721537929882933, "fast": 0.694373841096675 } }, "front_relative_normal_velocity": { "left": -0.640479985299989, "right": -0.9988273569945072 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5594981575055387, "pressure_ratio": 2.5159812526811014, "entropy_over_cv": 0.1820560949038823, "tangential_field_ratio": 1.5662307700543687 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.8, "theta_Bn_degrees": 82.2, "compression": 1.5594784835552706, "u2x_km_s": -384.32905807008916, "u2y_km_s": -8.484239733249803, "speed2_km_s": 384.4226933999777, "signed_deflection_degrees": 1.264625136021399, "p2_over_p1": 2.5159028282623876, "B2_over_B1": 1.5576869082191322, "entropy_over_cv": 0.18204594998228688, "upstream_fast_Mach": 1.4384372871200795, "downstream_fast_Mach": 0.7370963150943918, "downstream_alfven_margin": 0.5704114165576788, "state_global_normalized": { "rho": "1.55947848355527073621603272800737104273306230830737135811149813680306385573451900118422107", "p": "0.102045018714322435458039788681107097301850766965992832937837891843312959128160969816426515", "u": [ "-0.640548430116815307953988740937633964079345071760882824619998177808313632739054997177704848", "-0.0141403995554163376426624713034018150993958372411962427693060699960812212667871180339366814", "0E-91" ], "B": [ "0.0385202233813276187730571490242531696839922313252099759948332489684976335194796495749597636", "1.00348164408795357720960449217757105220318202820265137903315174712183526384445185176756442", "0E-91" ] }, "root_record": { "r": "1.55947848355527073621603272800737104273306230830737135811149813680306385573451900118422107", "b": "0.0406570198468298350650610317730846858451018781839729294330052222099289697686086485207129499", "h": "0.00767352586560495944988349495669522139801898964428052266097495893702694934620710670467282462", "A": "0.408942139154027110532568120907612664869702332839414555183232502142636588916597863406672684", "denominator": "0.988033301519584231603051937113026059434655419317904557435456308082259856382787346434076034", "polynomial_residual": "-1.138327545461672645703566E-65", "bracket_initial_signs": [ "1.45415374839450426477002533972313014177466779219516779378953590863904213347135617689668801", "-1.98535178288979836363245140875824429882097845764202763053678297488869538555519435067117257" ], "bracket_derivative_max": "-5.50732140486801361551629088470505842647599492234496698095822770887258948966684481015104162", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.05176168048309541671027708500951372114244181345538408135264561020183240964309875485417576E-90", "-1E-91", "0E-182", "-2E-90", "0E-182", "6.61040250045054956627030699728901256465217753244889446151644334767488766574992921022347768E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.8", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.033008447644675615, 0.0 ], "rh_scaled_inf": 2.2028669125554368e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.2028669125554368e-16 }, "characteristics": { "left": { "slow": 0.02662821166093573, "alfven_n": 0.07006304197051703, "fast": 0.8689155615249243 }, "right": { "slow": 0.03276134784861942, "alfven_n": 0.08749408283285308, "fast": 0.6943689142966819 } }, "front_relative_normal_velocity": { "left": -0.6404744585281958, "right": -0.9988061373414341 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5594784835552706, "pressure_ratio": 2.5159028282623876, "entropy_over_cv": 0.18204594998228696, "tangential_field_ratio": 1.5662546826051298 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.825, "theta_Bn_degrees": 82.175, "compression": 1.5594585382181654, "u2x_km_s": -384.331900962043, "u2y_km_s": -8.451147940949086, "speed2_km_s": 384.4248066899657, "signed_deflection_degrees": 1.2596848900112365, "p2_over_p1": 2.5158231876871686, "B2_over_B1": 1.5576555602563695, "entropy_over_cv": 0.18203561099524512, "upstream_fast_Mach": 1.4384166920411707, "downstream_fast_Mach": 0.7371018322244063, "downstream_alfven_margin": 0.5701822643094338, "state_global_normalized": { "rho": "1.55945853821816548500557619843485674171565512652573570576209778407084109118785814092827516", "p": "0.102041788492591565283004004246475139066024081146631189027235910270164016813557171674649145", "u": [ "-0.640553168270071724684539733948094740704646031309550098201234004547173348822891740883225547", "-0.0140852465682484770740922978741248101047126931813222454058815033705697279985689247124994622", "0E-91" ], "B": [ "0.0383629195247753886301584263339094125072075115000751976936329044227999000994558675483734563", "1.00346744570558388263747403049518052989250407628364578591737612724898334774879019266797404", "0E-91" ] }, "root_record": { "r": "1.55945853821816548500557619843485674171565512652573570576209778407084109118785814092827516", "b": "0.0406587629020512930350936534824049998410695562354428956520653215961475813279750769560051958", "h": "0.00772281835377546377944711268717995456163870244639829736123308890247372902296616685904881255", "A": "0.408910707889158005586328633286688310905312189813649852747773919753302497320671195092975483", "denominator": "0.987956584979096896062470061596369078685391526927632422759616204868966702733313310523126242", "polynomial_residual": "4.41608270816612121197882E-66", "bracket_initial_signs": [ "1.45395262768285640552851372764085654541414068817078463759948561886998557593190315890753569", "-1.98530254318466303300956623151721092976547440865767383137774569321648739551797515557401034" ], "bracket_derivative_max": "-5.50705226851592619402300967197260227543792081356918791534832676579277156298487310545794964", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.05203648386750399580805673647132815535667608075097001169860531995380556557705326626475706E-90", "2E-91", "0E-182", "6E-90", "0E-182", "-2.56477388328440000207735777601931191134369588300846072510637579367578725446398335167799010E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_2.825", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03339373978011889, 0.0 ], "rh_scaled_inf": 2.2030534146805678e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": -1.793230970146214e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.2030534146805678e-16 }, "characteristics": { "left": { "slow": 0.026713377813490393, "alfven_n": 0.07028665682711713, "fast": 0.8689015453994474 }, "right": { "slow": 0.032865933498867676, "alfven_n": 0.0877727697092385, "fast": 0.6943639718977785 } }, "front_relative_normal_velocity": { "left": -0.6404689211365509, "right": -0.9987847275297711 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5594585382181654, "pressure_ratio": 2.5158231876871686, "entropy_over_cv": 0.18203561099524512, "tangential_field_ratio": 1.5662784647869952 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.85, "theta_Bn_degrees": 82.15, "compression": 1.559438321468547, "u2x_km_s": -384.33483964628203, "u2y_km_s": -8.41805790163797, "speed2_km_s": 384.42701864563145, "signed_deflection_degrees": 1.2547446469250005, "p2_over_p1": 2.515742330975264, "B2_over_B1": 1.5576239066671609, "entropy_over_cv": 0.18202507794324246, "upstream_fast_Mach": 1.438395855122385, "downstream_fast_Mach": 0.7371074299580421, "downstream_alfven_margin": 0.5699531058339825, "state_global_normalized": { "rho": "1.55943832146854702773617492628547058470389655105929779170224607537985508105627586812937272", "p": "0.102038508944356707428333226267899302622615146429841175748560839920592430596438235154703015", "u": [ "-0.640558066077136756170995760736853498907416641984895827908340817181554696663529692089912673", "-0.0140300965027299523999264342482920776550265469217185116013514487526006170282406731308505700", "0E-91" ], "B": [ "0.0382056323499198174877903309081818349659417225575993531809621567523961304942468723328936634", "1.00345302505864891418187739465197956968835322168828473357161410677826793391763116874590965", "0E-91" ] }, "root_record": { "r": "1.55943832146854702773617492628547058470389655105929779170224607537985508105627586812937272", "b": "0.0406605215520771479366309124998681246170506696929865118412068559019358826499394628827800478", "h": "0.00777227078862636471187112714046330122044150112594999673634620827229394651036763321483504213", "A": "0.408879276478789927453759784142652227002176651339309822412331397070232069347547600239855362", "denominator": "0.987879623087385481540614461249245719783957441577710559157703612206439119517273357659519807", "polynomial_residual": "6.74938541500648171159763E-66", "bracket_initial_signs": [ "1.45374991844091566893490977952492331639637484467087559341988821073303557741857041389645853", "-1.98525462468795089085481534813143517038474757535811589219483535350408537264178771512671287" ], "bracket_derivative_max": "-5.50678310219720279521019276083294329926998525122673605265716719487792290734688216622481407", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.05231283910943549362711399308549171808458957346956791261656811350772945528076147660688588E-90", "-3E-91", "0E-182", "-1E-90", "0E-182", "-3.92037249450690461053357271697123653761093330057764860973275891369202400894941661344186511E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.85", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.033779028946789004, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -2.220446049250313e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02679854265838147, "alfven_n": 0.07051026730093185, "fast": 0.8688874200757563 }, "right": { "slow": 0.0329705151213176, "alfven_n": 0.08805143987492754, "fast": 0.6943590139020634 } }, "front_relative_normal_velocity": { "left": -0.6404633731349144, "right": -0.9987631275635946 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559438321468547, "pressure_ratio": 2.515742330975264, "entropy_over_cv": 0.18202507794324252, "tangential_field_ratio": 1.5663021165677595 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.875, "theta_Bn_degrees": 82.125, "compression": 1.559417833280584, "u2x_km_s": -384.3378741290659, "u2y_km_s": -8.38496968481437, "speed2_km_s": 384.42932927479006, "signed_deflection_degrees": 1.249804420864961, "p2_over_p1": 2.5156602581479572, "B2_over_B1": 1.557591947456947, "entropy_over_cv": 0.1820143508269605, "upstream_fast_Mach": 1.4383747763586985, "downstream_fast_Mach": 0.7371131083090308, "downstream_alfven_margin": 0.569723941124722, "state_global_normalized": { "rho": "1.55941783328058399291564323726104451732168228892656107424259545579729072300098908825145774", "p": "0.102035180070481147798680179260120905147838564248206105801584445635738837831110344794766976", "u": [ "-0.640563123548443112487738769573948190396626455787081588819191907296831991314928929345825895", "-0.0139749494746906173281779948906224126390794286895957383524650168695477612285473786465545908", "0E-91" ], "B": [ "0.0380483620883800884250954251556500632122097815110270838398791885748478737015069092052380176", "1.00343838215215922790363959251145791318274381639562808631680717008479989167096327441405954", "0E-91" ] }, "root_record": { "r": "1.55941783328058399291564323726104451732168228892656107424259545579729072300098908825145774", "b": "0.0406622957995958482040406877146730681641172339705337376913196483158046237731241387740471743", "h": "0.00782188320960604788476667585947849133976998569624736382184478522437741152112567782994086545", "A": "0.408847844911023232057128848426832026255709126218581290746735971679169176650116120645484842", "denominator": "0.987802415833102356800771824494226157716621172150224107657381638216342996257707558959591846", "polynomial_residual": "-1.376850059380285836598872E-65", "bracket_initial_signs": [ "1.45354562074163529647121182838290465648119428144759111403521407165985665735774841432261774", "-1.98520802697519703751768413328688366719553302529381440764189874974668395535447483068427507" ], "bracket_derivative_max": "-5.50651390540099278962638767129234018573084325308673973186256526095911986648538000660310730", "iterations": 216 }, "flux_residuals": [ "0E-90", "1.61051814929478275658611576376772943421541468627836614044819973688488797209103637822119617E-89", "-1E-91", "0E-182", "-2E-90", "0E-182", "7.99836039498827328464528667378723486105307582042196378112748466776752280799492574715758131E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_2.875", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03416431510767856, 0.0 ], "rh_scaled_inf": 3.5869973347901587e-16, "rh_components": { "mass": 0.0, "normal_momentum": -3.5869973347901587e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.2034298661603607e-16 }, "characteristics": { "left": { "slow": 0.02688370619424991, "alfven_n": 0.07073387340850101, "fast": 0.8688731855582665 }, "right": { "slow": 0.03307509270296375, "alfven_n": 0.08833009327686533, "fast": 0.694354040311642 } }, "front_relative_normal_velocity": { "left": -0.640457814533223, "right": -0.9987413374470168 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559417833280584, "pressure_ratio": 2.5156602581479577, "entropy_over_cv": 0.1820143508269607, "tangential_field_ratio": 1.5663256379149233 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.9, "theta_Bn_degrees": 82.10000000000001, "compression": 1.5593970736282896, "u2x_km_s": -384.34100441666374, "u2y_km_s": -8.351883359973794, "speed2_km_s": 384.4317385852377, "signed_deflection_degrees": 1.2448642259330411, "p2_over_p1": 2.5155769692279986, "B2_over_B1": 1.5575596826311733, "entropy_over_cv": 0.18200342964727706, "upstream_fast_Mach": 1.4383534557450932, "downstream_fast_Mach": 0.7371188672912352, "downstream_alfven_margin": 0.5694947701751104, "state_global_normalized": { "rho": "1.55939707362828950696651837253743618445546924245566921463008613092469458836520053822594034", "p": "0.102031801871887615547789989212139352193663644130727502411077718113681401286576345105114291", "u": [ "-0.640568340694439616443470807435724784580402150700062994732783970029061432203596305195408868", "-0.0139198055999563226750914520232853326201842163191705272818662379693998178176902231273507258", "0E-91" ], "B": [ "0.0378911089717853990817520773298547868784970216416146764845250102807297710166928401008792072", "1.00342351699124026546192292139272126331412079315100459120097698211340619104937233000893955", "0E-91" ] }, "root_record": { "r": "1.55939707362828950696651837253743618445546924245566921463008613092469458836520053822594034", "b": "0.0406640856473198626963660574098711066867301741868604331143940084860869468188966814934708086", "h": "0.00787165565640926504999867949693674982053035853843897537101504644600930533029343917722306545", "A": "0.408816413173958048376425359331179075817777765823429818999076330163556383191980707881866645", "denominator": "0.987724963204785819739575277852317197418779834630589538710923845286436275192493276783288761", "polynomial_residual": "1.606400751559853390764810E-65", "bracket_initial_signs": [ "1.45333973465733067432275517880854334095747070476790725064090633722851193109615529565625005", "-1.98516274962096149791916689151118508739743343117766218199412765680045812497393248873885476" ], "bracket_derivative_max": "-5.50624467761428268572409579415659606659099154769512301811239274578023258332023417946809456", "iterations": 216 }, "flux_residuals": [ "2E-90", "8.05287020622747320493506614144948928824877796098319357890519968614309716586697266930710429E-90", "-3E-91", "0E-182", "-2E-90", "0E-182", "-9.33296059422322722416383903506341119940400413228325934065847365962484601777309058806106351E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_2.9", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03454959822579478, 0.0 ], "rh_scaled_inf": 1.7936337004350894e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7936337004350894e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.026968868419741984, "alfven_n": 0.07095747516637924, "fast": 0.8688588418514152 }, "right": { "slow": 0.03317966623079935, "alfven_n": 0.0886087298620002, "fast": 0.6943490511286263 } }, "front_relative_normal_velocity": { "left": -0.6404522453414896, "right": -0.9987193571841863 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5593970736282896, "pressure_ratio": 2.515576969227998, "entropy_over_cv": 0.18200342964727678, "tangential_field_ratio": 1.5663490287956905 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.925, "theta_Bn_degrees": 82.075, "compression": 1.5593760424855212, "u2x_km_s": -384.34423051535475, "u2y_km_s": -8.318798996609297, "speed2_km_s": 384.4342465847523, "signed_deflection_degrees": 1.239924076230773, "p2_over_p1": 2.515492464239603, "B2_over_B1": 1.5575271121952878, "entropy_over_cv": 0.18199231440526648, "upstream_fast_Mach": 1.438331893276557, "downstream_fast_Mach": 0.7371247069186488, "downstream_alfven_margin": 0.569265592978667, "state_global_normalized": { "rho": "1.55937604248552119348189970544422721731805365510232448531802546640812731247117344698281584", "p": "0.102028374349558291001361830062474581667942681233845224773555439995409780761796329209680467", "u": [ "-0.640573717525591263068108401115515402082433658147735018104539853609745607880738990787386565", "-0.0138646649943488273302348023181987146808048447280060142553485141002981572380513013989855114", "0E-91" ], "B": [ "0.0377338732317749929130762737592080943689394374849815242432350932999036206181235611634368973", "1.00340842958113231973620132862182088930249278306777383269115403245245377549651944068803891", "0E-91" ] }, "root_record": { "r": "1.55937604248552119348189970544422721731805365510232448531802546640812731247117344698281584", "b": "0.0406658910979856895209225381673541164924104923866126659840685157731227297558767251695378506", "h": "0.00792158816897724245593523040703861179131690251280370190701574013830290677213415628263225883", "A": "0.408784981255694260483203341779010119019285522694569094254565460084385504039267790446249604", "denominator": "0.987647265190860141528915433647177549245453416941748427959167782819306501762162796917127516", "polynomial_residual": "3.2998217622271100391391E-67", "bracket_initial_signs": [ "1.45313226025968036212840666190291664312159035703574150413461837829902924624126579018623624", "-1.98511879219882695627223652452947707076136581785421331619025402881940419825124454754887861" ], "bracket_derivative_max": "-5.50597541832189394717700528175211396474960347080177373815787901129225520359213499411403352", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.05315121863815919517031723855401730772508798424345307178808955500137676251066169816895406E-90", "1E-91", "0E-182", "-2E-90", "0E-182", "-1.91737572124102125306229334607416830101149266552853883669472327825836430995740814690191353E-68", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_2.925", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03493487826415955, 0.0 ], "rh_scaled_inf": 2.2038109163115407e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -2.2038109163115407e-16 }, "characteristics": { "left": { "slow": 0.027054029333509325, "alfven_n": 0.07118107259113607, "fast": 0.8688443889596615 }, "right": { "slow": 0.03328423569181631, "alfven_n": 0.08888734957728368, "fast": 0.6943440463551356 } }, "front_relative_normal_velocity": { "left": -0.640446665569803, "right": -0.9986971867792875 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5593760424855212, "pressure_ratio": 2.515492464239603, "entropy_over_cv": 0.18199231440526642, "tangential_field_ratio": 1.5663722891769698 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.95, "theta_Bn_degrees": 82.05, "compression": 1.5593547398259813, "u2x_km_s": -384.3475524314276, "u2y_km_s": -8.285716664211426, "speed2_km_s": 384.4368532810929, "signed_deflection_degrees": 1.234983985859254, "p2_over_p1": 2.515406743208452, "B2_over_B1": 1.5574942361547433, "entropy_over_cv": 0.1819810051021994, "upstream_fast_Mach": 1.4383100889480827, "downstream_fast_Mach": 0.7371306272053965, "downstream_alfven_margin": 0.5690364095289725, "state_global_normalized": { "rho": "1.55935473982598117263823229113835760759326834759727713459870165325408014163757716957485858", "p": "0.102024897504534813540129877076670048945633825868852794601022398695361633400244971176302115", "u": [ "-0.640579254052379279622414583885173591246272750514231959152459523552296562660716281504832132", "-0.0138095277736857091683388005226550703775197812936332281877334909590156350015206919020334387", "0E-91" ], "B": [ "0.0375766550999981905816139866035893275590712688061421142465653293767952218258766827306598575", "1.00339311992719050024391023591667323987269122331925699370067242008886897315499952118568009", "0E-91" ] }, "root_record": { "r": "1.55935473982598117263823229113835760759326834759727713459870165325408014163757716957485858", "b": "0.0406677121543538649358508430446885400201010072482569746013321717211126555297826400114680089", "h": "0.00797168078749779003949594451620399636953323786503865744072462574622930753371687383232674235", "A": "0.408753549144331489573687969287663171007569928215587913433183434099145503008586386566868998", "denominator": "0.987569321779635610905129910089915108053088507614936285779562371236498134773273447118714616", "polynomial_residual": "1.032244346907503270233490E-65", "bracket_initial_signs": [ "1.45292319761972712683617939026409230968961017753107797624979481868503971580430080139313901", "-1.98507615428139647691178565462779446771273638735145893566050245348768349338309929979892562" ], "bracket_derivative_max": "-5.50570612700648079567403037626086487536608202928062773018419035637902256157302462316770035", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "-2E-91", "0E-182", "-5E-90", "0E-182", "-5.99860766782797051567359096051703099170650647130281433153145260715027644647637801918626003E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_2.95", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.0353201551858096, 0.0 ], "rh_scaled_inf": 2.2040031667841747e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7939061365930366e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.2040031667841747e-16 }, "characteristics": { "left": { "slow": 0.027139188934209, "alfven_n": 0.07140466569935598, "fast": 0.8688298268874859 }, "right": { "slow": 0.0333888010730052, "alfven_n": 0.0891659523696705, "fast": 0.6943390259932956 } }, "front_relative_normal_velocity": { "left": -0.6404410752283285, "right": -0.9986748262365419 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5593547398259813, "pressure_ratio": 2.515406743208452, "entropy_over_cv": 0.18198100510219928, "tangential_field_ratio": 1.5663954190253742 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 2.975, "theta_Bn_degrees": 82.025, "compression": 1.559333165623216, "u2x_km_s": -384.3509701711807, "u2y_km_s": -8.252636432268167, "speed2_km_s": 384.43955868200015, "signed_deflection_degrees": 1.2300439689191007, "p2_over_p1": 2.5153198061616937, "B2_over_B1": 1.5574610545149965, "entropy_over_cv": 0.18196950173954293, "upstream_fast_Mach": 1.4382880427546685, "downstream_fast_Mach": 0.7371366281657337, "downstream_alfven_margin": 0.5688072198196688, "state_global_normalized": { "rho": "1.55933316562321606076533260799371806106078512810191309185489209983855661549609776989749460", "p": "0.102021371337918289443164121010263938137232495482006789978350559863050420384701089063768830", "u": [ "-0.640584950285301186130850759051567260446243898103591498923670313209673994659666660269085750", "-0.0137543940537802759076399305032124198814371776770008112541509334729587856537500250696810339", "0E-91" ], "B": [ "0.0374194548081144214861004604114739160728442548851497278142868876959614586514312080077920510", "1.00337758803488469835363914749063862067775366655656119297227041927766656686921364238181909", "0E-91" ] }, "root_record": { "r": "1.55933316562321606076533260799371806106078512810191309185489209983855661549609776989749460", "b": "0.0406695488192089723316749333941741972035901112788773418372247543297751172184165521291629816", "h": "0.00802193355240541142856676466130712383061860114531077779517741885959807920155525322048892580", "A": "0.408722116827969076001089197884216705236318832599139830026574562607973488765190126510819121", "denominator": "0.987491132959308578605714464086868714135800154743455431793747378814726557411813235269908518", "polynomial_residual": "1.482385889980626372522411E-65", "bracket_initial_signs": [ "1.45271254680787898167429879850341225291430357840304081710235897908460382330655189932810610", "-1.98503483544029121121781609694163003674770923637234699045165414840554743270187063378526870" ], "bracket_derivative_max": "-5.50543680314852799917585150774803603553477058834840030088569307516224356278397359026405376", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-2E-91", "0E-182", "-2E-90", "0E-182", "-8.61549862133845524403049220260746937536877885489471833720129077127868628674590964365140206E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_2.975", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03570542895379661, 0.0 ], "rh_scaled_inf": 2.2041965680034001e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -2.2041965680034001e-16 }, "characteristics": { "left": { "slow": 0.027224347220503597, "alfven_n": 0.07162825450763866, "fast": 0.8688151556393905 }, "right": { "slow": 0.03349336236135529, "alfven_n": 0.08944453818611862, "fast": 0.6943339900452389 } }, "front_relative_normal_velocity": { "left": -0.6404354743273074, "right": -0.9986522755602062 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559333165623216, "pressure_ratio": 2.5153198061616937, "entropy_over_cv": 0.18196950173954296, "tangential_field_ratio": 1.5664184183072198 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.0, "theta_Bn_degrees": 82.0, "compression": 1.559311319850617, "u2x_km_s": -384.3544837409225, "u2y_km_s": -8.219558370264885, "speed2_km_s": 384.4423627951962, "signed_deflection_degrees": 1.225104039510406, "p2_over_p1": 2.5152316531279415, "B2_over_B1": 1.5574275672815072, "entropy_over_cv": 0.1819578043189609, "upstream_fast_Mach": 1.438265754691319, "downstream_fast_Mach": 0.7371427098140474, "downstream_alfven_margin": 0.5685780238444584, "state_global_normalized": { "rho": "1.55931131985061697007395676761529646484994689851081126157198230108567565900036937623645753", "p": "0.102017795850869299691391417474902104840139622945827620166086884060574717785140061737047570", "u": [ "-0.640590806234870856438133975875799718752656747047304426194722044630476123877788670864618757", "-0.0136992639504414759144830609827178791965843917897843434295420217153046704483156521504217556", "0E-91" ], "B": [ "0.0372622725877932554286639023080151522526539474748416959782552687282695368368608215988238528", "1.00336183390979955229373381476173133489619235056085538901358719777056909701881541718918945", "0E-91" ] }, "root_record": { "r": "1.55931131985061697007395676761529646484994689851081126157198230108567565900036937623645753", "b": "0.0406714010953596512919155860744096970503401360309949381859732959224510964549519959902968743", "h": "0.00807234650438141475535329191625278569572633367988497826912644152659682375921731004524961748", "A": "0.408690684294706061307064926759953181726068834360406493064397711758160802344180329114035329", "denominator": "0.987412698717961501953799980673029235712662463349703186109346301613937511644973075810989199", "polynomial_residual": "-1.558342467447833638920805E-65", "bracket_initial_signs": [ "1.45250030789391023024782388080362413133310435421833002511995988348256646811347129397857890", "-1.98499483524614809061552288611637043018896883404190880501477295594487947414386113889060218" ], "bracket_derivative_max": "-5.50516744622634864561953327341020656359132430519868490742995213418626688393928214156063062", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "1E-91", "0E-182", "1E-90", "0E-182", "9.05801939498872581714673216282950542528668479198253768595546779488748958508209166517116272E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_3", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.036090699531187334, 0.0 ], "rh_scaled_inf": 4.408782240666799e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7941817345346578e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 4.408782240666799e-16 }, "characteristics": { "left": { "slow": 0.02730950419106125, "alfven_n": 0.07185183903259891, "fast": 0.8688003752198987 }, "right": { "slow": 0.033597919543854486, "alfven_n": 0.08972310697358923, "fast": 0.6943289385131054 } }, "front_relative_normal_velocity": { "left": -0.6404298628770573, "right": -0.9986295347545738 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559311319850617, "pressure_ratio": 2.5152316531279415, "entropy_over_cv": 0.18195780431896091, "tangential_field_ratio": 1.5664412869885274 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.025, "theta_Bn_degrees": 81.97500000000001, "compression": 1.5592892024814196, "u2x_km_s": -384.35809314697116, "u2y_km_s": -8.186482547684285, "speed2_km_s": 384.44526562838473, "signed_deflection_degrees": 1.220164211732694, "p2_over_p1": 2.515142284137276, "B2_over_B1": 1.55739377445974, "entropy_over_cv": 0.18194591284231357, "upstream_fast_Mach": 1.4382432247530432, "downstream_fast_Mach": 0.7371488721648555, "downstream_alfven_margin": 0.5683488215971051, "state_global_normalized": { "rho": "1.55928920248141950854121389123070659918046451345775902708907276721254673444771381129765371", "p": "0.102014171044607907731336966189277228280948978258923312388795025441161038117026212445740550", "u": [ "-0.640596821911618579789988583278774674443126797103399988046423405914421628763416755174661318", "-0.0136441375794738089539390054897416852961552298533655571297651770423531458510553783342875518", "0E-91" ], "B": [ "0.0371051086707144344211521889017281182935726292573439591204663290552065735319356831695711600", "1.00334585755763441195617418189181979814573538000088449833730290828267254908894232099363698", "0E-91" ] }, "root_record": { "r": "1.55928920248141950854121389123070659918046451345775902708907276721254673444771381129765371", "b": "0.0406732689856386067328101456142256374475986877499056560926193510986986571506397866900603663", "h": "0.00812291968435402428124931447708241510816172484294685126192294306908937862741630191863061741", "A": "0.408659251532641170252276231039711209767667527678367436024384066018992530006511724909273835", "denominator": "0.987334019043562989590640666228160270578310677794066589063267681538470963742782434353125861", "polynomial_residual": "1.234824385285104741373524E-65", "bracket_initial_signs": [ "1.45228648094696251577100048226415177213336474559108535200062238764772286433219860872858531", "-1.98495615326861750563578823153484716209696482038768045464191163571730268000120054452597075" ], "bracket_derivative_max": "-5.50489805571608190205668006742198333043157913642103828897893729046421062809366573308586807", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "4E-91", "0E-182", "3E-90", "0E-182", "-7.17838469554276290794611776806377360771848261669844364183177455866601597521775773560788782E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_3.025", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03647596688106373, 0.0 ], "rh_scaled_inf": 2.2045868241405679e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7943207198098628e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -2.2045868241405679e-16 }, "characteristics": { "left": { "slow": 0.02739465984455574, "alfven_n": 0.07207541929086697, "fast": 0.8687854856335561 }, "right": { "slow": 0.033702472607489375, "alfven_n": 0.09000165867904679, "fast": 0.6943238713990413 } }, "front_relative_normal_velocity": { "left": -0.640424240887972, "right": -0.9986066038239745 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5592892024814196, "pressure_ratio": 2.515142284137276, "entropy_over_cv": 0.18194591284231354, "tangential_field_ratio": 1.5664640250350197 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.05, "theta_Bn_degrees": 81.95, "compression": 1.5592668134887038, "u2x_km_s": -384.3617983956547, "u2y_km_s": -8.153409034006343, "speed2_km_s": 384.448267189251, "signed_deflection_degrees": 1.2152244996848751, "p2_over_p1": 2.515051699221244, "B2_over_B1": 1.5573596760551622, "entropy_over_cv": 0.18193382731165803, "upstream_fast_Mach": 1.4382204529348566, "downstream_fast_Mach": 0.7371551152328071, "downstream_alfven_margin": 0.5681196130714333, "state_global_normalized": { "rho": "1.55926681348870377995412977372911324763404276033613640473668816231969637037270248925350190", "p": "0.102010496920413667199086234787647743650187075650821770350319796323404191226177866719320617", "u": [ "-0.640602997326091122938584622585689106933835220703017328073546295564293328594760420969738379", "-0.0135890150566772368861914737255132145578911853161214559128406486258345798953745477660437448", "0E-91" ], "B": [ "0.0369479632885679046314623379714557999002773879531498053040308807420141573914853363909597491", "1.00332965898420330349559378604281319685046255217116964066148044853396745110395034666156488", "0E-91" ] }, "root_record": { "r": "1.55926681348870377995412977372911324763404276033613640473668816231969637037270248925350190", "b": "0.0406751524929026181221895791319937447570416729205847158429081182732949279806084537259800633", "h": "0.00817365313349849283380180148205183139945291605712604194928569197065612401820991635747930931", "A": "0.408627818529872792845977207418632814870874149154215013528185816027875401633711863838891878", "denominator": "0.987255093923967846356359895575933830387118495207750916490280344407179723481582306543249300", "polynomial_residual": "1.064937123032661487361188E-65", "bracket_initial_signs": [ "1.45207106603554587544559656617751003203939809996480996328664174043603643928153856073540623", "-1.98491878907636097101946979890780560778228167139964999013041972310337106394124300160459269" ], "bracket_derivative_max": "-5.50462863109169075921047166585700417390513459623371850188957996924658144724789290993341649", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.05457958003593413497778235544779814694962753552878637698448955044597336717895733931936775E-90", "-8E-91", "0E-182", "-5E-90", "0E-182", "-6.19151151913117299670283212655756441552686242004288325418637309553841445649029954237388087E-67", "4E-91" ], "diagnosis": { "case_id": "R95_phi_3.05", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03686123096652308, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02747981417966654, "alfven_n": 0.07229899529908844, "fast": 0.868770486884929 }, "right": { "slow": 0.033807021539245204, "alfven_n": 0.09028019324945896, "fast": 0.6943187887051999 } }, "front_relative_normal_velocity": { "left": -0.6404186083705218, "right": -0.9985834827727736 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5592668134887038, "pressure_ratio": 2.515051699221244, "entropy_over_cv": 0.18193382731165797, "tangential_field_ratio": 1.566486632412124 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.075, "theta_Bn_degrees": 81.92500000000001, "compression": 1.5592441528453944, "u2x_km_s": -384.36559949331104, "u2y_km_s": -8.120337898708256, "speed2_km_s": 384.45136748546184, "signed_deflection_degrees": 1.2102849174652015, "p2_over_p1": 2.5149598984128607, "B2_over_B1": 1.5573252720732458, "entropy_over_cv": 0.18192154772924815, "upstream_fast_Mach": 1.4381974392317798, "downstream_fast_Mach": 0.7371614390326827, "downstream_alfven_margin": 0.5678903982613285, "state_global_normalized": { "rho": "1.55924415284539438411166838282301914215905871057764729435016347957147280575168233004759072", "p": "0.102006773479625629604467161574305819214618151763285476847202313911619034693753352593639655", "u": [ "-0.640609332488851792773158722305179996134621237410176147578298838327908344540546596944217863", "-0.0135338964978470943084471646675059937600873522980268251368913345435009825538388494740848670", "0E-91" ], "B": [ "0.0367908366730538484707536347023820656097342872901218812394741916268657362184642794426017084", "1.00331323819543489372330573421445429470471972811026716548308007158577961708481158199469936", "0E-91" ] }, "root_record": { "r": "1.55924415284539438411166838282301914215905871057764729435016347957147280575168233004759072", "b": "0.0406770516200325487775644004939305084280661951502014197965597397025824313665235470090361569", "h": "0.00822454689323721505635823174623402507483635501469245267237043292649008610152757653768062533", "A": "0.408596385274498966374581968481038506824270461209604065238045056866590191276439421876270743", "denominator": "0.987175923346917118319201265693158469691954686424802956722749862002814625149510245998715190", "polynomial_residual": "1.142395115923575020572479E-65", "bracket_initial_signs": [ "1.45185406322753979999554256594563627074744966772742593544081951659639781649729069603654861", "-1.98488274223704877684873659310696756617596518819306447304511315269610530866705100379976906" ], "bracket_derivative_max": "-5.50435917182495976143680348235088942140799843051041986236044580238960872639647802046812544", "iterations": 216 }, "flux_residuals": [ "1E-90", "-8.05486991410303473442952368096325691899895184504261013096620188217494824509490395129153611E-90", "-3E-91", "0E-182", "1E-90", "0E-182", "-6.64263270825066970943708579765677557730710982779708202399897308498011210532498168855975031E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_3.075", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03724649175067812, 0.0 ], "rh_scaled_inf": 2.2049816876630484e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.2049816876630484e-16 }, "characteristics": { "left": { "slow": 0.027564967195078872, "alfven_n": 0.07252256707392445, "fast": 0.868755378978606 }, "right": { "slow": 0.033911566326105855, "alfven_n": 0.0905587106317967, "fast": 0.6943136904337412 } }, "front_relative_normal_velocity": { "left": -0.6404129653352529, "right": -0.9985601716053734 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5592441528453944, "pressure_ratio": 2.5149598984128607, "entropy_over_cv": 0.18192154772924818, "tangential_field_ratio": 1.5665091090849697 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.1, "theta_Bn_degrees": 81.9, "compression": 1.5592212205242604, "u2x_km_s": -384.3694964462883, "u2y_km_s": -8.087269211264399, "speed2_km_s": 384.45456652466584, "signed_deflection_degrees": 1.2053454791712228, "p2_over_p1": 2.5148668817466064, "B2_over_B1": 1.557290562519466, "entropy_over_cv": 0.18190907409753462, "upstream_fast_Mach": 1.4381741836388386, "downstream_fast_Mach": 0.7371678435793941, "downstream_alfven_margin": 0.5676611771607364, "state_global_normalized": { "rho": "1.55922122052426041718552116971742195995590134884139383856121849501131501942733094989413355", "p": "0.102003000723642351975452291050009902624550869053639443030133031468585370428204676147324941", "u": [ "-0.640615827410480499476316665637323174833577205919857298133696649841062204813794677217483633", "-0.0134787820187739991421220102578634539165736348652563293110088527867979593417330947364642631", "0E-91" ], "B": [ "0.0366337290558827168224264506963547089474081623256383337149091586369839840319680807245407389", "1.00329659519737245429619982481064263681805142179532846512763490761337226204146922829468123", "0E-91" ] }, "root_record": { "r": "1.55922122052426041718552116971742195995590134884139383856121849501131501942733094989413355", "b": "0.0406789663699333552434714793169889362813125785642578579517869470146807812368456239429603454", "h": "0.00827560100523984147098673483018358071585779422465569075341054150462945860592998146045873606", "A": "0.408564951754617357429151316264215624289197925304320487984044590575515830085525004248094976", "denominator": "0.987096507300038137953533511061064497040646935404339255505088329187809111883818319986316937", "polynomial_residual": "-1.403842333192786567837032E-65", "bracket_initial_signs": [ "1.45163547259019429836827323907490555561521130525551643095217993112598890226191034409864454", "-1.98484801231735762568857444631753365875730151703498416094756504885831039913072223435946669" ], "bracket_derivative_max": "-5.50408967738549272207463849630382350568329614306189730350318315534847674544008235452989802", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "5E-91", "0E-182", "-1E-90", "0E-182", "8.16381990644713594178842947932622750619931092484159636541753668677608254581284279712705095E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_3.1", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.037631749196657176, 0.0 ], "rh_scaled_inf": 2.2051808481222187e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.2051808481222187e-16 }, "characteristics": { "left": { "slow": 0.027650118889483797, "alfven_n": 0.07274613463205178, "fast": 0.8687401619191971 }, "right": { "slow": 0.03401610695505387, "alfven_n": 0.09083721077303424, "fast": 0.6943085765868324 } }, "front_relative_normal_velocity": { "left": -0.6404073117927882, "right": -0.9985366703262117 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5592212205242604, "pressure_ratio": 2.5148668817466064, "entropy_over_cv": 0.18190907409753465, "tangential_field_ratio": 1.566531455018389 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.125, "theta_Bn_degrees": 81.87500000000001, "compression": 1.5591980164979156, "u2x_km_s": -384.37348926094427, "u2y_km_s": -8.054203041146257, "speed2_km_s": 384.4578643144932, "signed_deflection_degrees": 1.200406198899742, "p2_over_p1": 2.5147726492584295, "B2_over_B1": 1.5572555473993017, "entropy_over_cv": 0.18189640641916505, "upstream_fast_Mach": 1.438150686151065, "downstream_fast_Mach": 0.7371743288879844, "downstream_alfven_margin": 0.5674319497636636, "state_global_normalized": { "rho": "1.55919801649791547223997659929882516274940727328025730931996344865983740944153043215023029", "p": "0.101999178653921904462780315193553608414465154455590967948613159613526363706492314068280459", "u": [ "-0.640622482101573820206520215099746911966317141576228725010094724224052672822531167352276009", "-0.0134236717352437631650558324555488945350581782778421935224353363527248977892621758086685261", "0E-91" ], "B": [ "0.0364766406687752614137499492041623736797241353697631542690882204752260879284795065551070055", "1.00327972999617382570037482665785863180719707223152718266531204680238746689006037236563623", "0E-91" ] }, "root_record": { "r": "1.55919801649791547223997659929882516274940727328025730931996344865983740944153043215023029", "b": "0.0406808967455340967481341999891783851397140986459976980231010462919464471279840153581034653", "h": "0.00832681551142339335526413417912556984874090719802847441547248270413791710946441079342968394", "A": "0.408533517958325243931741620063744649569242980641417961169336173676700704854840744273739105", "denominator": "0.987016845770844569466859037668201524235682246595802790198359206608475478683108176719250608", "polynomial_residual": "1.013759308800166148021765E-65", "bracket_initial_signs": [ "1.45141529419013096761324087258478073924747411158321333544582634587686308623383028763164467", "-1.98481459888296825572145169552612162074298229521657472534382516358601882410960582467190014" ], "bracket_derivative_max": "-5.50382014724071042417056001533260772343258454609439881678110446677218581389047121663243321", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-1E-91", "0E-182", "0E-90", "0E-182", "-5.89604937074863612605928790392455830170579814739242929324709107377335020689064061039995799E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_3.125", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.038017003267604245, 0.0 ], "rh_scaled_inf": 2.205381161546273e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7948845756166695e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.205381161546273e-16 }, "characteristics": { "left": { "slow": 0.02773526926157826, "alfven_n": 0.07296969799016295, "fast": 0.8687248357113333 }, "right": { "slow": 0.03412064341307044, "alfven_n": 0.09111569362014905, "fast": 0.694303447166647 } }, "front_relative_normal_velocity": { "left": -0.6404016477538266, "right": -0.9985129789397631 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5591980164979156, "pressure_ratio": 2.5147726492584295, "entropy_over_cv": 0.18189640641916482, "tangential_field_ratio": 1.5665536701769165 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.15, "theta_Bn_degrees": 81.85, "compression": 1.5591745407388176, "u2x_km_s": -384.377577943647, "u2y_km_s": -8.02113945782238, "speed2_km_s": 384.46126086255595, "signed_deflection_degrees": 1.1954670907467702, "p2_over_p1": 2.5146772009857465, "B2_over_B1": 1.5572202267182358, "entropy_over_cv": 0.18188354469698406, "upstream_fast_Mach": 1.4381269467634956, "downstream_fast_Mach": 0.7371808949736282, "downstream_alfven_margin": 0.567202716064177, "state_global_normalized": { "rho": "1.55917454073881763991118474221885122879811763976326675993816960145684395952554712285963065", "p": "0.101995307271981877904796312355783804157459029926526557320936281459409524026218319360643325", "u": [ "-0.640629296572745063307264198394147483422954404744809603304001084727648509228304112459757244", "-0.0133685657630373024885069257500090968050728507838622500789086665348155238993567388739634114", "0E-91" ], "B": [ "0.0363195717434625673310230320322487042052274972910189518833233051029170890401452959055971235", "1.00326264259811138102936937105986987223621948267330573833585043236887882658529087851709118", "0E-91" ] }, "root_record": { "r": "1.55917454073881763991118474221885122879811763976326675993816960145684395952554712285963065", "b": "0.0406828427497879447394888858965820145596576425652516855168054586824290185578255054731942560", "h": "0.00837819045395237843353159930313033533054639711764561326656629246397090482242638258725021888", "A": "0.408502083873719497160558417596571119440017721679112177612965103377759613728940562677197228", "denominator": "0.986936938746736454276076934319336066122720782143080095303098951933732158656883683585364140", "polynomial_residual": "-7.06373224501581289198242E-66", "bracket_initial_signs": [ "1.45119352809334406794814324523018258318840736290866320818341814276626781430489489281609286", "-1.98478250149856304985800406266862293030920186847343250246774469840463454576533857152692104" ], "bracket_derivative_max": "-5.50355058085584830656239646621876628777284868019690327002169191972743797331693910479276459", "iterations": 216 }, "flux_residuals": [ "-1E-90", "8.05575024488133359916149381540650954755490591709724207253088838035498172016986937984384522E-90", "-3E-91", "0E-182", "-2E-90", "0E-182", "4.10876834620177690277934765237271266967899380255809731157786329507383899913507879082935115E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_3.15", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03840225392667919, 0.0 ], "rh_scaled_inf": 1.7950275195477117e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7950275195477117e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.027820418310065168, "alfven_n": 0.07319325716496639, "fast": 0.8687094003596675 }, "right": { "slow": 0.03422517568713539, "alfven_n": 0.09139415912012197, "fast": 0.6942983021753659 } }, "front_relative_normal_velocity": { "left": -0.6403959732291434, "right": -0.9984890974505379 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5591745407388176, "pressure_ratio": 2.5146772009857465, "entropy_over_cv": 0.1818835446969842, "tangential_field_ratio": 1.566575754524789 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.175, "theta_Bn_degrees": 81.825, "compression": 1.5591507932192694, "u2x_km_s": -384.38176250077464, "u2y_km_s": -7.988078530758329, "speed2_km_s": 384.4647561764478, "signed_deflection_degrees": 1.1905281688074818, "p2_over_p1": 2.5145805369674408, "B2_over_B1": 1.5571846004817544, "entropy_over_cv": 0.18187048893403338, "upstream_fast_Mach": 1.4381029654711739, "downstream_fast_Mach": 0.7371875418516314, "downstream_alfven_margin": 0.5669734760564044, "state_global_normalized": { "rho": "1.55915079321926950924613420835913131561590310460559393515387898528947673339242690508360857", "p": "0.101991386579399391352509794211976926465261925622113751159355193375063369489489679801449280", "u": [ "-0.640636270834624333043453285447954351244127090206098207086251557419765910436460312390341004", "-0.0133134642179305479786773219277378245856509777356202852211967195458602100071616894777781514", "0E-91" ], "B": [ "0.0361625225116860856791540523803312230875636735539439749636322865130339005386032899920664436", "1.00324533300957198955685435360706247639782239699864943223976399537843800883617471533176116", "0E-91" ] }, "root_record": { "r": "1.55915079321926950924613420835913131561590310460559393515387898528947673339242690508360857", "b": "0.0406848043856721925006308545158717360424316896262832196500603998684251631327397262294800618", "h": "0.00842972587523890738322223615999446931761430285681037110634839941879274643312911508143600609", "A": "0.408470649488896563773857252443312064296615914687238734043979466962214640200191110110224222", "denominator": "0.986856786215000256633252421211309319903732731432210329936922337867398664164843764796129349", "polynomial_residual": "-1.215723438707678203673645E-65", "bracket_initial_signs": [ "1.45097017436520160302348343317632626584833545513797993274229697741016780626390127842821125", "-1.98475171972782363080646602806630272252439623389253181678534032272606294340530468484652623" ], "bracket_derivative_max": "-5.50328097769395413530667131260201386274938861947081356797544291637159594494031425770694029", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "4E-91", "0E-182", "0E-90", "0E-182", "7.07234413178078020357781956450338388226574074275238125687728722270037252799956339656784525E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_3.175", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03878750113705779, 0.0 ], "rh_scaled_inf": 2.2057852488011422e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7951712559968775e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -2.2057852488011422e-16 }, "characteristics": { "left": { "slow": 0.02790556603365343, "alfven_n": 0.07341681217318638, "fast": 0.8686938558688742 }, "right": { "slow": 0.03432970376422719, "alfven_n": 0.09167260721993709, "fast": 0.6942931416151764 } }, "front_relative_normal_velocity": { "left": -0.6403902882295907, "right": -0.9984650258630829 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5591507932192694, "pressure_ratio": 2.5145805369674408, "entropy_over_cv": 0.18187048893403357, "tangential_field_ratio": 1.5665977080259452 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.2, "theta_Bn_degrees": 81.8, "compression": 1.559126773911418, "u2x_km_s": -384.3860429387152, "u2y_km_s": -7.955020329416613, "speed2_km_s": 384.46835026374436, "signed_deflection_degrees": 1.1855894471761717, "p2_over_p1": 2.5144826572438634, "B2_over_B1": 1.5571486686953482, "entropy_over_cv": 0.1818572391335518, "upstream_fast_Mach": 1.4380787422691477, "downstream_fast_Mach": 0.7371942695374317, "downstream_alfven_margin": 0.566744229734533, "state_global_normalized": { "rho": "1.55912677391141816870166114104111834224462189070580144861605782475609290868275942767662353", "p": "0.101987416577811099554869489518999442420544083273464067409988127348946507802135137315734518", "u": [ "-0.640643404897858594865491318499371990762054510647875259606650847790800518714783566674741930", "-0.0132583672156943556225187339377986040143812002386048050294784990143753864794717885129187614", "0E-91" ], "B": [ "0.0360054932051976663865459934863163081632366309330025057774519824798746051666968441246536878", "1.00322780123705698010364918185600066251473869013040437780162806191890110169832166337600567", "0E-91" ] }, "root_record": { "r": "1.55912677391141816870166114104111834224462189070580144861605782475609290868275942767662353", "b": "0.0406867816561882648447339199576745643995553995255543585789741353139335232912816496009742704", "h": "0.00848142181794281115686957209131447685646659528798062324699754511094383496412567979033382574", "A": "0.408439214791952447832534254182217633745674038268173188393987693725048303576891576679398568", "denominator": "0.986776388162808909401145796699585183206076474269612925041706039145712097140600121349531843", "polynomial_residual": "1.290017972210987194500788E-65", "bracket_initial_signs": [ "1.45074523307044640539615235318336823636526323002385566424905587237717080786014063507931467", "-1.98472225313342844208344411170233312769353290268764708615303934653510717444430207350545674" ], "bracket_derivative_max": "-5.50301133721588566043451297197737433889626993466889951982688608670726164794413565419192215", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.05634490870156707010257381257667051546172197746901270868037015555018968578385434792761675E-90", "5E-91", "0E-182", "5E-90", "0E-182", "-7.50542897056968184390800046836612221150505216423456742194564274414250147803155815729476470E-67", "-4E-91" ], "diagnosis": { "case_id": "R95_phi_3.2", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03917274486193194, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02799071243105805, "alfven_n": 0.07364036303156332, "fast": 0.8686782022436491 }, "right": { "slow": 0.03443422763132293, "alfven_n": 0.0919510378665818, "fast": 0.6942879654882729 } }, "front_relative_normal_velocity": { "left": -0.6403845927660963, "right": -0.998440764181981 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.559126773911418, "pressure_ratio": 2.5144826572438634, "entropy_over_cv": 0.181857239133552, "tangential_field_ratio": 1.5666195306440263 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.225, "theta_Bn_degrees": 81.775, "compression": 1.5591024827872553, "u2x_km_s": -384.39041926386705, "u2y_km_s": -7.92196492325665, "speed2_km_s": 384.472043132003, "signed_deflection_degrees": 1.1806509399462082, "p2_over_p1": 2.5143835618568344, "B2_over_B1": 1.5571124313645102, "entropy_over_cv": 0.1818437952989755, "upstream_fast_Mach": 1.4380542771524711, "downstream_fast_Mach": 0.7372010780465985, "downstream_alfven_margin": 0.5665149770928111, "state_global_normalized": { "rho": "1.55910248278725520730381243400189287070734016792862499830449940156441905633934641010747681", "p": "0.101983397268913200404253611433576933169747342085874251933620508740568921346592929431759136", "u": [ "-0.640650698773111741201599495190215917912520112828863430435845120574592199805447366458194890", "-0.0132032748720944168375684111044097998658172833152602110233729312965144794756758871087562809", "0E-91" ], "B": [ "0.0358484840557595911561749954076700173727883185306085766935309351302697917097033511413701452", "1.00321004728718210419892364264468797267871437464620408872867769825116269444732192990120708", "0E-91" ] }, "root_record": { "r": "1.55910248278725520730381243400189287070734016792862499830449940156441905633934641010747681", "b": "0.0406887745643617278894976109336505592728024489089744896166314099024715874294584014300818356", "h": "0.00853327832497175912041052388881971639450338958299365413456986685221790722491337183411949943", "A": "0.408407779770982692821348960803740142254460406256828266329845586179595592021375062453182569", "denominator": "0.986695744577221859978755043792602697697509923168974654390250362153209655529311109684872009", "polynomial_residual": "1.225765952862616976745903E-65", "bracket_initial_signs": [ "1.45051870427319722722279887196499902238693313969321974842226027604648067739858360503761500", "-1.98469410127705031494849544605813686240702796325109505979938561925338590688571920195106671" ], "bracket_derivative_max": "-5.50274165888030825802054124800860360081857885236887606565905028143523488697661361288569864", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "5E-91", "0E-182", "4E-90", "0E-182", "-7.13244567033916833047161466651552867220024406382601681736566972328544088283556879915816919E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_3.225", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.039557985064509714, 0.0 ], "rh_scaled_inf": 2.206193952474071e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.206193952474071e-16 }, "characteristics": { "left": { "slow": 0.02807585750100019, "alfven_n": 0.07386390975685378, "fast": 0.8686624394887095 }, "right": { "slow": 0.03453874727539834, "alfven_n": 0.09222945100704685, "fast": 0.6942827737968567 } }, "front_relative_normal_velocity": { "left": -0.6403788868496648, "right": -0.9984163124118512 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5591024827872553, "pressure_ratio": 2.5143835618568344, "entropy_over_cv": 0.18184379529897543, "tangential_field_ratio": 1.5666412223423734 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.25, "theta_Bn_degrees": 81.75, "compression": 1.5590779198186167, "u2x_km_s": -384.39489148263874, "u2y_km_s": -7.888912381734701, "speed2_km_s": 384.4758347887632, "signed_deflection_degrees": 1.1757126612099906, "p2_over_p1": 2.514283250849641, "B2_over_B1": 1.5570758884947378, "entropy_over_cv": 0.18183015743393788, "upstream_fast_Mach": 1.4380295701162031, "downstream_fast_Mach": 0.7372079673948326, "downstream_alfven_margin": 0.5662857181255466, "state_global_normalized": { "rho": "1.55907791981861671596788777861032026214581725842772006409533564440408268633142855285773987", "p": "0.101979328654461442342174172864732795673593162387678371664037363140910034990049243043198119", "u": [ "-0.640658152471064657778883148931663588308076770441277959887195505808314485311157299288156903", "-0.0131481873028911687255633686703114876099626680014252644199300360570925082269652723805766754", "0E-91" ], "B": [ "0.0356914952951446065637513015710323003864737332902633898735025084929284951834887586916454671", "1.00319207116667749903544659870095636894494375704164098297225220181007652960907584545989361", "0E-91" ] }, "root_record": { "r": "1.55907791981861671596788777861032026214581725842772006409533564440408268633142855285773987", "b": "0.0406907831132422989111768239725352185280550575920809867256663002177705617908656482371956127", "h": "0.00858529543948137800840107487279189816047766444932263207700522803709939961014324781668343616", "A": "0.408376344414082363668721875856741007899683605895023721810885430341296038889239372964211499", "denominator": "0.986614855445185116377127358169420943184915662608201273536113368750615341148921064534362642", "polynomial_residual": "-5.19155662259213918359111E-66", "bracket_initial_signs": [ "1.45029058803694983618382637319022514192861967027437049982669649552489833984322401199853812", "-1.98466726371935402124484283726134225440122292744548478922373451949906009038464824297952655" ], "bracket_derivative_max": "-5.50247194214369255754912830560828241756286375488149558922515520600208989160420145127350870", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-3E-91", "0E-182", "-2E-90", "0E-182", "3.02120134245967911465689817156025622592945975509764071436254136181340991898428737754186457E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_3.25", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.03994322170801553, 0.0 ], "rh_scaled_inf": 2.206400036429037e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.206400036429037e-16 }, "characteristics": { "left": { "slow": 0.028161001242207207, "alfven_n": 0.0740874523658306, "fast": 0.8686465676087943 }, "right": { "slow": 0.03464326268342777, "alfven_n": 0.09250784658832632, "fast": 0.6942775665431355 } }, "front_relative_normal_velocity": { "left": -0.6403731704913772, "right": -0.9983916705573488 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5590779198186167, "pressure_ratio": 2.514283250849641, "entropy_over_cv": 0.18183015743393782, "tangential_field_ratio": 1.5666627830840303 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.275, "theta_Bn_degrees": 81.72500000000001, "compression": 1.5590530849771833, "u2x_km_s": -384.39945960144917, "u2y_km_s": -7.855862774303823, "speed2_km_s": 384.4797252415462, "signed_deflection_degrees": 1.170774625058903, "p2_over_p1": 2.51418172426704, "B2_over_B1": 1.5570390400915317, "entropy_over_cv": 0.1818163255422697, "upstream_fast_Mach": 1.438004621155409, "downstream_fast_Mach": 0.7372149375979665, "downstream_alfven_margin": 0.5660564528271079, "state_global_normalized": { "rho": "1.55905308497718328897948759706250598510523188368481276858639851630620556526702098903799296", "p": "0.101975210736271131725193731754483604226265426466653159480649653614456788362872230452277348", "u": [ "-0.640665766002415290473670321355168327477937297230439983744959939081531340614724380885649484", "-0.0130931046238397042695806807099332372479036645966323009650413087524608515387777978775858393", "0E-91" ], "B": [ "0.0355345271551359573038528928914747626780636260828516203155477287262110377223574934670751395", "1.00317387288238765021874215832487943397851704570255359814090963285784035619066411823060986", "0E-91" ] }, "root_record": { "r": "1.55905308497718328897948759706250598510523188368481276858639851630620556526702098903799296", "b": "0.0406928073059038562782490840316180535250125362309609152862464681266509807501046630579578236", "h": "0.00863747320487537169676752928776696472759211840764566666650490702716947087737342535859893437", "A": "0.408344908709346028765049245324935158599964710506783910443381548891893365208283356222497673", "denominator": "0.986533720753531293445695959413841996647832447716702670021722534091153058370428234706800303", "polynomial_residual": "7.03416576782016513372072E-66", "bracket_initial_signs": [ "1.45006088442457811664892886561300899265948966112439479758997138118400511018124202641092888", "-1.98464174001999381212842516681533157552739762069873008586987428498752352095187694971299038" ], "bracket_derivative_max": "-5.50220218646031205456231359449280918748899608574930547880950951719317107099018977452778635", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.05724857509336191968941801871545619210939609960710970371301919811983036096870051389058561E-90", "-2E-91", "0E-182", "-1E-90", "0E-182", "-4.09398101811505660663203965162721011316436525727875698662661421900018699122061674839836626E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_3.275", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04032845475569025, 0.0 ], "rh_scaled_inf": 0.0, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.028246143653412752, "alfven_n": 0.07431099087528296, "fast": 0.8686305866086633 }, "right": { "slow": 0.03474777384238417, "alfven_n": 0.0927862245574176, "fast": 0.6942723437293246 } }, "front_relative_normal_velocity": { "left": -0.640367443702391, "right": -0.9983668386231653 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5590530849771833, "pressure_ratio": 2.51418172426704, "entropy_over_cv": 0.18181632554226979, "tangential_field_ratio": 1.5666842128317409 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.3, "theta_Bn_degrees": 81.7, "compression": 1.55902797823448, "u2x_km_s": -384.40412362672726, "u2y_km_s": -7.82281617041381, "speed2_km_s": 384.48371449785526, "signed_deflection_degrees": 1.1658368455832713, "p2_over_p1": 2.514078982155255, "B2_over_B1": 1.5570018861603967, "entropy_over_cv": 0.1818022996279993, "upstream_fast_Mach": 1.437979430265159, "downstream_fast_Mach": 0.7372219886719648, "downstream_alfven_margin": 0.5658271811919232, "state_global_normalized": { "rho": "1.55902797823448002563689636838683164585556367004399509128741320304456732586723264083935885", "p": "0.101971043516217140151052765303640571833344300072195353135388862461385158023700043472280187", "u": [ "-0.640673539377878712691648778496359097347023166741363825658845622420219312362982673284095751", "-0.0130380269506896824744507468123825135220808648572837180830845121232430343849591669684063800", "0E-91" ], "B": [ "0.0353775798675274195849232803166359392230964888162257722524970929058706424600688089869415000", "1.00315545244127135431001339427048925091047977673857771070954283765968092327970518360157760", "0E-91" ] }, "root_record": { "r": "1.55902797823448002563689636838683164585556367004399509128741320304456732586723264083935885", "b": "0.0406948471454444494647750374441196470215143880662032202616414411399375370380350670749653966", "h": "0.00868981166480564179372085990317992254714709851009702470127255775401256739891007338780489682", "A": "0.408313472644867741979477531465174024468598176095736004849484268921143378869713528149449691", "denominator": "0.986452340488979659249399646689511176675204060464433358643668297014004605040643218478176119", "polynomial_residual": "6.41385632450169114821386E-66", "bracket_initial_signs": [ "1.44982959349833517609515403805407832897465957826366903325775358607992289578302998466804515", "-1.98461752973761094266734948280340791584092419450870803859707658543094195849421765129650055" ], "bracket_derivative_max": "-5.50193239128224070857353337083415457763225297732780821785871106429754102119992273800609154", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.05755291055590017726031546035510498504766840535916906613196281057421770647703906601254636E-90", "-6E-91", "0E-182", "-6E-90", "0E-182", "-3.73339207683584888998652353098937783199057016664209672549313802146528054979650421443816939E-67", "3E-91" ], "diagnosis": { "case_id": "R95_phi_3.3", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.040713684170791346, 0.0 ], "rh_scaled_inf": 2.2068156705188974e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.2068156705188974e-16 }, "characteristics": { "left": { "slow": 0.028331284733356797, "alfven_n": 0.07453452530201655, "fast": 0.8686144964930987 }, "right": { "slow": 0.034852280739239135, "alfven_n": 0.09306458486132146, "fast": 0.6942671053576457 } }, "front_relative_normal_velocity": { "left": -0.6403617064939398, "right": -0.9983418166140283 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.55902797823448, "pressure_ratio": 2.514078982155255, "entropy_over_cv": 0.18180229962799932, "tangential_field_ratio": 1.5667055115479505 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.325, "theta_Bn_degrees": 81.67500000000001, "compression": 1.5590025995618766, "u2x_km_s": -384.40888356491234, "u2y_km_s": -7.789772639511143, "speed2_km_s": 384.4878025651758, "signed_deflection_degrees": 1.1608993368723173, "p2_over_p1": 2.51397502456198, "B2_over_B1": 1.5569644267068403, "entropy_over_cv": 0.18178807969535246, "upstream_fast_Mach": 1.437953997440529, "downstream_fast_Mach": 0.7372291206329236, "downstream_alfven_margin": 0.5655979032144803, "state_global_normalized": { "rho": "1.55900259956187653205513330802240070898322742223708894175000691301704449548442718774774463", "p": "0.101966826996233911745005688981507359099762408046908510551318301931028701616386275691613409", "u": [ "-0.640681472608187193278331585525905306091705038501545601929518819544071304470483817369233352", "-0.0129829543991852384501896595868999895185579673067815985102712402553754078278394083477115114", "0E-91" ], "B": [ "0.0352206536641233346740261366063706307408636807045895740900484995142869848745876706274985171", "1.00313680985040168116269311850673059528794018035063603869697825184303686582276892916777239", "0E-91" ] }, "root_record": { "r": "1.55900259956187653205513330802240070898322742223708894175000691301704449548442718774774463", "b": "0.0406969026349863091435082554136430303601891613232939156437568139464879699827209843895923413", "h": "0.00874231086317240904946631748872407319404365109082441006985673758372135501576284331010516187", "A": "0.408282036208741024675080052757541185488130868918705602193419865025236431483753136565084209", "denominator": "0.986370714638136181596843659239673601528531438697874578806363810595743306086124961857471377", "polynomial_residual": "1.435292609386128738737791E-65", "bracket_initial_signs": [ "1.44959671531985445678855512043888823719401885577388674060249537351198425838663825226978600", "-1.98459463242983118229367846580619097080528892942641116404216625622597437218130366440581351" ], "bracket_derivative_max": "-5.50166255605935052623120657503406603654269865984286056841964770519951677939360678921330257", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "3E-91", "0E-182", "2E-90", "0E-182", "-8.35556779856424586705640426500002435424005556075314570430209913849233672158453243953808323E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_3.325", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.041098909916592964, 0.0 ], "rh_scaled_inf": 2.2070252214376452e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7960503325638176e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.2070252214376452e-16 }, "characteristics": { "left": { "slow": 0.028416424480785754, "alfven_n": 0.07475805566285365, "fast": 0.8685982972669034 }, "right": { "slow": 0.034956783360962855, "alfven_n": 0.09334292744704203, "fast": 0.6942618514303271 } }, "front_relative_normal_velocity": { "left": -0.640355958877334, "right": -0.9983166045347017 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5590025995618766, "pressure_ratio": 2.5139750245619803, "entropy_over_cv": 0.18178807969535238, "tangential_field_ratio": 1.566726679194804 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.35, "theta_Bn_degrees": 81.64999999999999, "compression": 1.558976948930587, "u2x_km_s": -384.41373942245417, "u2y_km_s": -7.756732251038936, "speed2_km_s": 384.49198945097515, "signed_deflection_degrees": 1.1559621130141144, "p2_over_p1": 2.5138698515363775, "B2_over_B1": 1.556926661736374, "entropy_over_cv": 0.18177366574875273, "upstream_fast_Mach": 1.4379283226766013, "downstream_fast_Mach": 0.7372363334970711, "downstream_alfven_margin": 0.5653686188893272, "state_global_normalized": { "rho": "1.55897694893058692313200481852595887511131092745860418127775474333670766670977209913351318", "p": "0.101962561178315470406363352676820952156427096976690296403490461030647496426723484932775986", "u": [ "-0.640689565704090264960384824380311219068844460156069465463897235534321353153161021394073703", "-0.0129278870850648934381960119735125394518230895573481885475495486962973031085503013342989508", "0E-91" ], "B": [ "0.0350637487767386425922506650329806087093480366425488114532996328753426198426265734508825531", "1.00311794511696593605248064829182921985456083366291679393526541364786350880792020912897101", "0E-91" ] }, "root_record": { "r": "1.55897694893058692313200481852595887511131092745860418127775474333670766670977209913351318", "b": "0.0406989737776758573588108800182687841214871042311782393479740782736664385768533568053377821", "h": "0.00879497084412433558534512885656513370251212610125925592817783093638581499624104934506778676", "A": "0.408250599389058847722378250720915445721952589762399738553146921125996649717735182981040252", "denominator": "0.986288843187493574719761500876519898481449430128244467697309548730164447638902065927475991", "polynomial_residual": "-9.67733856462223924614732E-66", "bracket_initial_signs": [ "1.44936224995015085274056799583315884992071591872687791775009628419992747250430896710875440", "-1.98457304765326231108935412945521607682705187937823497728487310619218844213962139666263278" ], "bracket_derivative_max": "-5.50139268023930912971609979537364887254420284121005872063775929443378097924918403867644990", "iterations": 216 }, "flux_residuals": [ "-1E-90", "-8.05816625323047144349498512704600294177580093711396776033124566846908835203653002586323364E-90", "5E-91", "0E-182", "2E-90", "0E-182", "5.63433409027802400275730076932684709069698792443253247546914808129131550860227921879488872E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_3.35", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.0414841319563861, 0.0 ], "rh_scaled_inf": 2.207235928798558e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.207235928798558e-16 }, "characteristics": { "left": { "slow": 0.028501562894452485, "alfven_n": 0.07498158197463323, "fast": 0.8685819889349017 }, "right": { "slow": 0.03506128169452414, "alfven_n": 0.09362125226158681, "fast": 0.6942565819496047 } }, "front_relative_normal_velocity": { "left": -0.6403502008639604, "right": -0.9982912023899855 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.558976948930587, "pressure_ratio": 2.5138698515363775, "entropy_over_cv": 0.18177366574875287, "tangential_field_ratio": 1.5667477157341476 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.375, "theta_Bn_degrees": 81.625, "compression": 1.55895102631167, "u2x_km_s": -384.4186912058129, "u2y_km_s": -7.723695074436879, "speed2_km_s": 384.49627516270294, "signed_deflection_degrees": 1.1510251880955447, "p2_over_p1": 2.5137634631290786, "B2_over_B1": 1.5568885912545125, "entropy_over_cv": 0.1817590577928213, "upstream_fast_Mach": 1.4379024059684624, "downstream_fast_Mach": 0.7372436272807673, "downstream_alfven_margin": 0.5651393282110715, "state_global_normalized": { "rho": "1.55895102631166982467649558862677410278766706767814364653592905362599094323844350581676555", "p": "0.101958246064515427015239662559886900846015955831613405277045516748136352357679674778045950", "u": [ "-0.640697818676354793318354514599779400544296523271514665076457924820605170762386605681565647", "-0.0128728251240614647799566905348953738943303743005506932661922356098715413754716941743366729", "0E-91" ], "B": [ "0.0349068654371989159616628264981243806455370141831662990211247796728490235909371503765906561", "1.00309885824826562160072292593836234650132758041418860882573197998980318308113703231953606", "0E-91" ] }, "root_record": { "r": "1.55895102631166982467649558862677410278766706767814364653592905362599094323844350581676555", "b": "0.0407010605766837177794320989228997851858848402041908612753751659366074798190826317633944652", "h": "0.00884779165205864794304977346585255761824857520606072141648763864857627965543768653976769066", "A": "0.408219162173913613511150035636578284917423747468857299015012146640447647420180663893451638", "denominator": "0.986206726123431346104038486022546821291875414080751998082113798125967327334555800299388644", "polynomial_residual": "5.86130641526437045852401E-66", "bracket_initial_signs": [ "1.44912619744962183195032472743230702413822451899944762057932946862789503101122037521852349", "-1.98455277496349160188792562718363372957202636022632896116346679961267194043305601446579448" ], "bracket_derivative_max": "-5.50112276326757731035627488117390322012271498517727591913035072976452232489211789615251971", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.05847526103169407046895845256895502786489255672868693025009444848217515483960828748957457E-90", "2E-91", "0E-182", "4E-90", "0E-182", "-3.41296805234331488448523695054568860821790483224974640384178634304695435910569689123218101E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_3.375", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04186935025347874, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.028586699973116417, "alfven_n": 0.07520510425421105, "fast": 0.8685655715019395 }, "right": { "slow": 0.03516577572689038, "alfven_n": 0.09389955925196669, "fast": 0.6942512969177206 } }, "front_relative_normal_velocity": { "left": -0.6403444324652825, "right": -0.9982656101847159 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.55895102631167, "pressure_ratio": 2.5137634631290786, "entropy_over_cv": 0.1817590577928211, "tangential_field_ratio": 1.5667686211275271 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.4, "theta_Bn_degrees": 81.6, "compression": 1.5589248316760285, "u2x_km_s": -384.423738921459, "u2y_km_s": -7.690661179141185, "speed2_km_s": 384.50065970779093, "signed_deflection_degrees": 1.146088576202251, "p2_over_p1": 2.513655859392184, "B2_over_B1": 1.5568502152667745, "entropy_over_cv": 0.18174425583237722, "upstream_fast_Mach": 1.4378762473112057, "downstream_fast_Mach": 0.7372510020005045, "downstream_alfven_margin": 0.5649100311743802, "state_global_normalized": { "rho": "1.55892483167602837569983768040207529966409335381749476371026774901337007903134850309102675", "p": "0.101953881656946986599499793129940446830396537816472001234752932496926603951173493768971496", "u": [ "-0.640706231535765046291333280092121753582780293722074899622706242086373260572667914610463883", "-0.0128177686319019758280054033475761764594158002165974723295829557496353018824299473771052321", "0E-91" ], "B": [ "0.0347500038773403940046987773278177296792838766383073254241984372447437769208044577159461225", "1.00307954925171639949099777976753854895454488416582500196279136838662774625826463796968101", "0E-91" ] }, "root_record": { "r": "1.55892483167602837569983768040207529966409335381749476371026774901337007903134850309102675", "b": "0.0407031630352047260312068897231098150630546608534707999206404834614805381120254103908239301", "h": "0.00890077333162126095455899720994269479822320703944281003999781905930472417570350619030009172", "A": "0.408187724551397137960467654196537402111226031988899170471214188435676799096177219895025567", "denominator": "0.986124363432215843472558862874212670256861270961235037100230300323321010052800764309863197", "polynomial_residual": "1.618473192074351342959328E-65", "bracket_initial_signs": [ "1.44888855787804856394418951777508689045624490409793729807486583589725301382750371054774920", "-1.98453381391508328817361588393969697178844548035021529560062647919546924813115070874635606" ], "bracket_derivative_max": "-5.50085280458740656744330346397163368908070350770136712736316233734864340886055975371274743", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.05878582687087343783987876093251641557500245651186307288177905475392630910034059924081042E-90", "0E-91", "0E-182", "1E-90", "0E-182", "-9.42528391286795761039980288682224398056393935349885254226809363729516273827931634347384527E-67", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_3.4", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04225456477119591, 0.0 ], "rh_scaled_inf": 2.2076608144391185e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.2076608144391185e-16 }, "characteristics": { "left": { "slow": 0.028671835715543544, "alfven_n": 0.07542862251845976, "fast": 0.8685490449728841 }, "right": { "slow": 0.035270265445027565, "alfven_n": 0.09417784836519594, "fast": 0.694245996336924 } }, "front_relative_normal_velocity": { "left": -0.64033865369284, "right": -0.9982398279237653 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5589248316760285, "pressure_ratio": 2.5136558593921845, "entropy_over_cv": 0.1817442558323772, "tangential_field_ratio": 1.5667893953361876 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.425, "theta_Bn_degrees": 81.575, "compression": 1.5588983649944101, "u2x_km_s": -384.4288825758737, "u2y_km_s": -7.657630634584539, "speed2_km_s": 384.50514309365303, "signed_deflection_degrees": 1.1411522914185956, "p2_over_p1": 2.5135470403792644, "B2_over_B1": 1.5568115337786812, "entropy_over_cv": 0.1817292598724374, "upstream_fast_Mach": 1.4378498466999288, "downstream_fast_Mach": 0.7372584576729069, "downstream_alfven_margin": 0.5646807277739804, "state_global_normalized": { "rho": "1.55889836499441023086959940980298238381322883157287278479289276484314626652050788267814464", "p": "0.101949467957782955461907269514743665945500753796361840619388418310696950012437643559669921", "u": [ "-0.640714804293122764214110793453789837246777481812850653652430700548681882993493464249270142", "-0.0127627177243075657988768887871264164986800093984321262750803290521599093649925789770176999", "0E-91" ], "B": [ "0.0345931643290100166968981077443313513371612616728624064195196515596085446448673012215064544", "1.00306001813484805197875653703972074829107146870478925092609118320536780852359483676275039", "0E-91" ] }, "root_record": { "r": "1.55889836499441023086959940980298238381322883157287278479289276484314626652050788267814464", "b": "0.0407052811564579401097329300609850831058887501399342108223072494900057439096403357279948019", "h": "0.00895391592770690243344339599419258963959897816763963603929733150435260291357297027906542228", "A": "0.408156286509600632526907512752433899769128195354996189276610265136824973907829750181066056", "denominator": "0.986041755100000301920139466870461565569903305769637076726645107657832464632498446868564200", "polynomial_residual": "3.88426966559128840274505E-66", "bracket_initial_signs": [ "1.44864933129459705262387810608847733792181152889443698382259412515580671104592733082820214", "-1.98451616406157601775912845301220310120222814925621475724925627834717574326410370333398288" ], "bracket_derivative_max": "-5.50058280363983663223331319989969928391912064097860106641896307502940942880463715651007613", "iterations": 216 }, "flux_residuals": [ "0E-90", "1.61181959020928277993586833805665063917363534242938182949576473332017791632566816949357884E-89", "-2E-91", "0E-182", "-1E-90", "0E-182", "-2.26229603389638037679134618836572209573552620567366957643629002092933604592683963097169169E-67", "3E-91" ], "diagnosis": { "case_id": "R95_phi_3.425", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04263977547287987, 0.0 ], "rh_scaled_inf": 2.207874993520475e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.796652268211344e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -2.207874993520475e-16 }, "characteristics": { "left": { "slow": 0.02875697012050656, "alfven_n": 0.07565213678426906, "fast": 0.8685324093526242 }, "right": { "slow": 0.03537475083590031, "alfven_n": 0.09445611954829225, "fast": 0.6942406802094709 } }, "front_relative_normal_velocity": { "left": -0.6403328645582494, "right": -0.9982138556120422 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5588983649944101, "pressure_ratio": 2.5135470403792644, "entropy_over_cv": 0.1817292598724375, "tangential_field_ratio": 1.5668100383210741 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.45, "theta_Bn_degrees": 81.55, "compression": 1.5588716262374076, "u2x_km_s": -384.43412217554834, "u2y_km_s": -7.62460351019604, "speed2_km_s": 384.5097253276855, "signed_deflection_degrees": 1.1362163478276142, "p2_over_p1": 2.5134370061453586, "B2_over_B1": 1.5567725467957583, "entropy_over_cv": 0.1817140699182168, "upstream_fast_Mach": 1.4378232041297363, "downstream_fast_Mach": 0.7372659943147308, "downstream_alfven_margin": 0.564451418004658, "state_global_normalized": { "rho": "1.55887162623740756312713829413795502099715761490872769783400607321737869197666587211663470", "p": "0.101945004969255748267467015368723473044885311175982806676536231284733626365964212987192829", "u": [ "-0.640723536959247230387355524934148695380796547986119995739528996020765062829087018402464458", "-0.0127076725169933995677989443983438533151934286175418630729596318190377259085040858265486805", "0E-91" ], "B": [ "0.0344363470240654590738757157411774143101387144276948341876619981437604416994891445780126477", "1.00304026490530444319388262109321969748702008922274647510922842837289460038749990914560546", "0E-91" ] }, "root_record": { "r": "1.55887162623740756312713829413795502099715761490872769783400607321737869197666587211663470", "b": "0.0407074149436866508730840253672498787699920300570410421154271860929961809429333190332443389", "h": "0.00900721948545923868819708110296466189794319533734516980854720183107118091154216708664633762", "A": "0.408124848036614686210874380185123425897416470057827004988306557221086041925253077702350155", "denominator": "0.985958901112824891200813954859459981631646141263821948384853357105686429255976164555437503", "polynomial_residual": "1.437380760742657966570459E-65", "bracket_initial_signs": [ "1.44840851775781927443459673465592297212436890887824829407680335025388752906726817985518016", "-1.98449982495548029222346251228954425942416724373779545980137276606706080980040216624971064" ], "bracket_derivative_max": "-5.50031275986369297711631095978910910560930905062476001448142259196537378674473911367815258", "iterations": 216 }, "flux_residuals": [ "-2E-90", "8.05941163385824488896523558503713605306784998348389565492350384458285503832944401238612410E-90", "4E-91", "0E-182", "1E-90", "0E-182", "-8.37265150720689383616072759680845699673774857669002777945333454231295754682075047451151397E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_3.45", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04302498232189025, 0.0 ], "rh_scaled_inf": 0.0, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.028842103186784873, "alfven_n": 0.07587564706854573, "fast": 0.8685156646460697 }, "right": { "slow": 0.03547923188647179, "alfven_n": 0.0947343727482767, "fast": 0.6942353485376245 } }, "front_relative_normal_velocity": { "left": -0.6403270650732038, "right": -0.9981876932544915 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5588716262374076, "pressure_ratio": 2.513437006145359, "entropy_over_cv": 0.18171406991821681, "tangential_field_ratio": 1.5668305500428308 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.475, "theta_Bn_degrees": 81.525, "compression": 1.5588446153754572, "u2x_km_s": -384.4394577269852, "u2y_km_s": -7.5915798754011465, "speed2_km_s": 384.5144064172668, "signed_deflection_degrees": 1.1312807595109715, "p2_over_p1": 2.513325756746977, "B2_over_B1": 1.5567332543235337, "entropy_over_cv": 0.18169868597512837, "upstream_fast_Mach": 1.4377963195957373, "downstream_fast_Mach": 0.7372736119428648, "downstream_alfven_margin": 0.5642221018612589, "state_global_normalized": { "rho": "1.55884461537545706646876481143319989002676153476917938295162000535304077542450512454474689", "p": "0.101940492693657395090961276678979020278393595887873701303879197095430896512744449483114667", "u": [ "-0.640732429544975342181378825169952458826418129057167659587302412762356888652128826265902021", "-0.0126526331256685774048636031429962328083698068738152001019349525316234195073215619766207169", "0E-91" ], "B": [ "0.0342795521943751656934324028227773576969777485595327315543410622393727395702390332252216542", "1.00302028957084348023602218451396538742077745952657617619718776066486500805526850282126323", "0E-91" ] }, "root_record": { "r": "1.55884461537545706646876481143319989002676153476917938295162000535304077542450512454474689", "b": "0.0407095644001583926146188622983238751832300373856723279603676093628582827933127961755097946", "h": "0.00906068405027100085825562318953131463681133573617123067619847909238281001014066831397452550", "A": "0.408093409120529247560982384444194538221277058660819958949228189813247982020752916927386208", "denominator": "0.985875801456616763167732767160124760093547314360694394723959307143334917125469072590670662", "polynomial_residual": "-1.214191937749272187027870E-65", "bracket_initial_signs": [ "1.44816611732565432186471207746207815701368637036107128524813312449264358921071771234312531", "-1.98448479614827589209087025984432236473203007396715353654714129333549444368566156918530117" ], "bracket_derivative_max": "-5.50004267269558430993710846431000131946029168306737830917692206949802561802819425852958461", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-3E-91", "0E-182", "-1E-90", "0E-182", "7.07342340939773139225855706775657015031217912663753312543382599965406307923175968709266835E-67", "3E-91" ], "diagnosis": { "case_id": "R95_phi_3.475", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.043410185281604105, 0.0 ], "rh_scaled_inf": 4.4166136524527664e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -4.4166136524527664e-16 }, "characteristics": { "left": { "slow": 0.02892723491316471, "alfven_n": 0.07609915338821378, "fast": 0.8684988108581517 }, "right": { "slow": 0.035583708583703764, "alfven_n": 0.09501260791217381, "fast": 0.6942300013236543 } }, "front_relative_normal_velocity": { "left": -0.6403212552494726, "right": -0.998161340856094 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5588446153754572, "pressure_ratio": 2.513325756746977, "entropy_over_cv": 0.18169868597512828, "tangential_field_ratio": 1.566850930461801 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.5, "theta_Bn_degrees": 81.5, "compression": 1.55881733237884, "u2x_km_s": -384.444889236697, "u2y_km_s": -7.558559799621627, "speed2_km_s": 384.51918636975796, "signed_deflection_degrees": 1.126345540548916, "p2_over_p1": 2.5132132922420993, "B2_over_B1": 1.5566936563675398, "entropy_over_cv": 0.1816831080487833, "upstream_fast_Mach": 1.4377691930930472, "downstream_fast_Mach": 0.7372813105743299, "downstream_alfven_margin": 0.5639927793386876, "state_global_normalized": { "rho": "1.55881733237883995889096619085277959746102725217777957535871660686715624632289139996814979", "p": "0.101935931133339548424675146432647518164171493823897199669867362939259132950863059749690267", "u": [ "-0.640741482061161682674035879486534874217306721609022625274166480805984792945971083762547457", "-0.0125975996660360446524179676097345667460921758829797973245928091322435703914602608037349509", "0E-91" ], "B": [ "0.0341227800718183852537055368319569916754154096256888282347259311497846791134908296004977250", "1.00300009213933707406254224788390891811168841256799555437376374358204986377436253750532744", "0E-91" ] }, "root_record": { "r": "1.55881733237883995889096619085277959746102725217777957535871660686715624632289139996814979", "b": "0.0407117295291649537159443526558619882666618550436232906299651798265788297198054504278855139", "h": "0.00911430966778411207336516204287987874660903003548804354178459714350796910415782484343516107", "A": "0.408061969749433606676435206520731298807824375298502301110116540209905907448980533637000237", "denominator": "0.985792456117190099365945061104671093502572357266921845331065384286650898982769506640742174", "polynomial_residual": "8.1957401445582579522668E-67", "bracket_initial_signs": [ "1.44792213005542955228853892513387755584563449944702126216196052766983827526908467421765836", "-1.98447107719040928773195714431087003227198854822292560431416132291097526958243287518000267" ], "bracket_derivative_max": "-5.49977254156990005345105598856479668069157344804325847156182038484726439669699299339287548", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "0E-91", "0E-182", "1E-90", "0E-182", "-4.77509053616060895517894668319114100940018971852118836742820536726280988674482387250939172E-68", "0E-91" ], "diagnosis": { "case_id": "R95_phi_3.5", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04379538431541611, 0.0 ], "rh_scaled_inf": 2.2085244806660655e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7971120719900689e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.2085244806660655e-16 }, "characteristics": { "left": { "slow": 0.029012365298439157, "alfven_n": 0.07632265576021457, "fast": 0.8684818479938236 }, "right": { "slow": 0.03568818091455659, "alfven_n": 0.09529082498701155, "fast": 0.6942246385698371 } }, "front_relative_normal_velocity": { "left": -0.6403154350989022, "right": -0.9981347984218669 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.55881733237884, "pressure_ratio": 2.5132132922420998, "entropy_over_cv": 0.18168310804878351, "tangential_field_ratio": 1.5668711795380266 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.525, "theta_Bn_degrees": 81.47500000000001, "compression": 1.558789777217682, "u2x_km_s": -384.45041671120714, "u2y_km_s": -7.5255433522755, "speed2_km_s": 384.52406519250235, "signed_deflection_degrees": 1.1214107050202367, "p2_over_p1": 2.513099612690175, "B2_over_B1": 1.5566537529333113, "entropy_over_cv": 0.18166733614499103, "upstream_fast_Mach": 1.4377418246167866, "downstream_fast_Mach": 0.7372890902262791, "downstream_alfven_margin": 0.5637634504319086, "state_global_normalized": { "rho": "1.55878977721768198550004193059094895450132150885376049712616330275857041581423624602013837", "p": "0.101931320290713490146308229421817678022178732299664573136132622584905351733437035391127195", "u": [ "-0.640750694518678592823321586903561226384433910882956414805219753581990670182147323388809130", "-0.0125425722537925013434143912384647018329718764925614378754124300745110901103146494074776544", "0E-91" ], "B": [ "0.0339660308882852053682623928943749033326632894571736322059706467743930294328972022527667631", "1.00297967261877110016897122950495529014710835106061387615696548947802754376438923497282203", "0E-91" ] }, "root_record": { "r": "1.55878977721768198550004193059094895450132150885376049712616330275857041581423624602013837", "b": "0.0407139103340223873800932898037772281341942659174492978889134332993062838007829132754719770", "h": "0.00916809638388981543697226513205308813071514713623751512764440821336583734730028586937502097", "A": "0.408030529911416377207347865015459645511508739430107733951630811724735294490947908348528735", "denominator": "0.985708865080246158778329955618374164945395147985984430711706496053098391415044854857542627", "polynomial_residual": "-2.41462309763762213221805E-66", "bracket_initial_signs": [ "1.44767655600386174216390796040176055119960202364694721833878226201279149850463079698672999", "-1.98445866763129103596779136970921694471300046008803487041690693727124531602947758171864232" ], "bracket_derivative_max": "-5.49950236591880780989766974276422998599005061864090632819271737176388261037932639827553052", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-4E-91", "0E-182", "-3E-90", "0E-182", "1.40699935035875959589712344619498712077969408035067360730469352451472574289592375242282117E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_3.525", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04418057938673866, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.029097494341408205, "alfven_n": 0.07654615420150684, "fast": 0.8684647760580588 }, "right": { "slow": 0.03579264886598918, "alfven_n": 0.09556902391982129, "fast": 0.6942192602784563 } }, "front_relative_normal_velocity": { "left": -0.6403096046334154, "right": -0.9981080659568636 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.558789777217682, "pressure_ratio": 2.513099612690175, "entropy_over_cv": 0.1816673361449911, "tangential_field_ratio": 1.566891297231248 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.55, "theta_Bn_degrees": 81.45, "compression": 1.5587619498619534, "u2x_km_s": -384.45604015704976, "u2y_km_s": -7.492530602776987, "speed2_km_s": 384.5290428928257, "signed_deflection_degrees": 1.116476267002218, "p2_over_p1": 2.512984718152124, "B2_over_B1": 1.556613544026387, "entropy_over_cv": 0.1816513702697593, "upstream_fast_Mach": 1.4377142141620818, "downstream_fast_Mach": 0.7372969509159981, "downstream_alfven_margin": 0.5635341151359448, "state_global_normalized": { "rho": "1.55876194986195342178650521986111071016654864387492985195485892694465128617178199225613463", "p": "0.101926660168250138447068800460817638329615860307130864819409487758762945148964251827250714", "u": [ "-0.640760066928416244175222939039476392684358488244176850948329362166418472929817818535277386", "-0.0124875510046283117604588692398615401284212281829630896340821010065654701288491592656320120", "0E-91" ], "B": [ "0.0338093048756765874990400563777242484695634943962965441997942654080995255714901448122143248", "1.00295903101724535906177616545687484232304702390896586242351356807221058985477334232664001", "0E-91" ] }, "root_record": { "r": "1.55876194986195342178650521986111071016654864387492985195485892694465128617178199225613463", "b": "0.0407161068180710224449764973377479393482010582630072613793993053913410182585106213787842659", "h": "0.00922204424472880283430881934274549814124023247507399746013132032668979912859293472493616971", "A": "0.407999089594565478352952473547953789741544929799155803535202744457691409733264907419837180", "denominator": "0.985625028331373325724945521936876827565862413495136054553935354789139696648429972041090832", "polynomial_residual": "8.36699300612578589460107E-66", "bracket_initial_signs": [ "1.44742939522705824659625163897997024986941924207791495263743370119947686558532639912106236", "-1.98444756701929316235775494577021595663119964568430092235593388043359424247479580119137377" ], "bracket_derivative_max": "-5.49923214517225081067511837177866600606983463474943404252794586103240153668667504108700689", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-5E-91", "0E-182", "0E-90", "0E-182", "-4.87601535891741815603946693520033043600615921579688330798827385246537910365263943636461296E-67", "2E-91" ], "diagnosis": { "case_id": "R95_phi_3.55", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.044565770459001994, 0.0 ], "rh_scaled_inf": 2.2089632677735228e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.7974225892536647e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.2089632677735228e-16 }, "characteristics": { "left": { "slow": 0.029182622040878892, "alfven_n": 0.07676964872906693, "fast": 0.8684475950558529 }, "right": { "slow": 0.03589711242495905, "alfven_n": 0.09584720465763791, "fast": 0.6942138664518024 } }, "front_relative_normal_velocity": { "left": -0.6403037638650118, "right": -0.9980811434661735 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5587619498619534, "pressure_ratio": 2.512984718152124, "entropy_over_cv": 0.18165137026975942, "tangential_field_ratio": 1.5669112835009036 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.575, "theta_Bn_degrees": 81.425, "compression": 1.5587338502814692, "u2x_km_s": -384.46175958076964, "u2y_km_s": -7.4595216205364485, "speed2_km_s": 384.53411947803636, "signed_deflection_degrees": 1.1115422405705946, "p2_over_p1": 2.5128686086903365, "B2_over_B1": 1.556573029652309, "entropy_over_cv": 0.18163521042929437, "upstream_fast_Mach": 1.437686361724065, "downstream_fast_Mach": 0.7373048926609049, "downstream_alfven_margin": 0.5633047734458786, "state_global_normalized": { "rho": "1.55873385028146907706460692481535338954303770831049055015910159942228397585085533939984996", "p": "0.101921950768480054719946622962672159851527389603497768671120113234623493649187009411215203", "u": [ "-0.640769599301282712107393002923323318591299753318393569944005150628642140764761629856141583", "-0.0124325360342274139352956706647981785308608055724181217093620471199191365883404235601966458", "0E-91" ], "B": [ "0.0336526022659044020480370517135396807010088121513481596429359229887711121899406332403378124", "1.00293816734297353652333033141094279054361792723557120061837505531169641225504809591621232", "0E-91" ] }, "root_record": { "r": "1.55873385028146907706460692481535338954303770831049055015910159942228397585085533939984996", "b": "0.0407183189846754742771701080187747408900714731953644555992751551451110494435578272806768294", "h": "0.00927615329669134456585094734360559827100974510019374557727963981107397314774013387748534245", "A": "0.407967648786968116857630342020732504068230280683954070095611622444304297067521134105857426", "denominator": "0.985540945856047157916065050673500310874893510577820756363182785291693005362444477465860199", "polynomial_residual": "1.316322634733244887818768E-65", "bracket_initial_signs": [ "1.44718064778051816428102201294686595839329352135099121752687571986435745827294878007135608", "-1.98443777490174652915173421203528452814111754663262421419218609558086486378621639517961039" ], "bracket_derivative_max": "-5.49896187875794535109841370528491776493459656157968116918691602471921910682328586359087422", "iterations": 216 }, "flux_residuals": [ "1E-90", "8.06100343806613272260168551149229728337204433735326214348253308215325266707961217213686283E-90", "0E-91", "0E-182", "1E-90", "0E-182", "-7.67200924566876247327920797548993398959361772716833099083296262395349844263020756523612389E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_3.575", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04495095749565432, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.029267748395665275, "alfven_n": 0.07699313935988879, "fast": 0.8684303049922223 }, "right": { "slow": 0.03600157157842226, "alfven_n": 0.09612536714749971, "fast": 0.6942084570921725 } }, "front_relative_normal_velocity": { "left": -0.6402979128057674, "right": -0.9980540309549222 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5587338502814692, "pressure_ratio": 2.512868608690337, "entropy_over_cv": 0.1816352104292943, "tangential_field_ratio": 1.5669311383061302 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.6, "theta_Bn_degrees": 81.4, "compression": 1.5587054784458882, "u2x_km_s": -384.4675749889224, "u2y_km_s": -7.426516474960337, "speed2_km_s": 384.5392949554253, "signed_deflection_degrees": 1.1066086397995076, "p2_over_p1": 2.512751284368675, "B2_over_B1": 1.5565322098166217, "entropy_over_cv": 0.18161885663000094, "upstream_fast_Mach": 1.4376582672978733, "downstream_fast_Mach": 0.7373129154785502, "downstream_alfven_margin": 0.5630754253568512, "state_global_normalized": { "rho": "1.55870547844588829807734128445144496413523813497255053455386007867752638055055041773973754", "p": "0.101917192093993450408160408164209728608130043970928155880404623458832439410295258955062781", "u": [ "-0.640779291648204049609215147338813959195353600944714129314113090749455404654294987592077003", "-0.0123775274582672290884654069831224280514497404428581268709548443902659511237658257170244375", "0E-91" ], "B": [ "0.0334959232908914636086631479792897951347122429565607377363953585664662735926854691380415187", "1.00291708160428316366892438777492586723888490155544779652772499937832481954867345032758480", "0E-91" ] }, "root_record": { "r": "1.55870547844588829807734128445144496413523813497255053455386007867752638055055041773973754", "b": "0.0407205468372246557460990697594971727972811465477626677699574959369219806613015360401639874", "h": "0.00933042358641741980683565269232770097321524723561516146189348633283013926084322368974865792", "A": "0.407936207476710769004712781204755807267631931127430565139893848037389694956461045450314244", "denominator": "0.985456617639630434659171220122892345028037853201318923379958286365134337573954281581056744", "polynomial_residual": "-1.311753760375943178580902E-65", "bracket_initial_signs": [ "1.44693031371913350783633029843305938566742265509357207200748303733635196284973071718134258", "-1.98442929082493818888711324564152363373275167168660098788725052629908347832756450670752341" ], "bracket_derivative_max": "-5.49869156610137821022403043074319341381680215740408975382126204693434323011784367906771298", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "-3E-91", "0E-182", "1E-90", "0E-182", "7.64627990640231098855581959222057968645263242076925285232726002171935897606387405241113420E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_3.6", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04533614046016199, 0.0 ], "rh_scaled_inf": 2.2094066952841247e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.7977362943281438e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -2.2094066952841247e-16 }, "characteristics": { "left": { "slow": 0.02935287340458855, "alfven_n": 0.07721662611098411, "fast": 0.8684129058722051 }, "right": { "slow": 0.03610602631333342, "alfven_n": 0.09640351133644846, "fast": 0.694203032201871 } }, "front_relative_normal_velocity": { "left": -0.6402920514678353, "right": -0.9980267284282716 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5587054784458882, "pressure_ratio": 2.512751284368675, "entropy_over_cv": 0.181618856630001, "tangential_field_ratio": 1.566950861605762 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.625, "theta_Bn_degrees": 81.375, "compression": 1.558676834324715, "u2x_km_s": -384.4734863880746, "u2y_km_s": -7.393515235451142, "speed2_km_s": 384.5445693322659, "signed_deflection_degrees": 1.1016754787614595, "p2_over_p1": 2.5126327452524704, "B2_over_B1": 1.5564910845248736, "entropy_over_cv": 0.1816023088784824, "upstream_fast_Mach": 1.4376299308786502, "downstream_fast_Mach": 0.7373210193866171, "downstream_alfven_margin": 0.5628460708640626, "state_global_normalized": { "rho": "1.55867683432471497276729495181606004898597661434977196009862875648552427843555491532236778", "p": "0.101912384147440193813775708300086546060105953354481266480740285900483714491182650217829034", "u": [ "-0.640789143980124361598829694786949035353063887134702260093135787519819910954926314457070059", "-0.0123225253924185710088728915512284225505861107671682326239757155738040814788576272054073288", "0E-91" ], "B": [ "0.0333392681825715663776550863068567630655175989015881107660482503720004148491280780763637379", "1.00289577380961557679567357797834375636606923149405503010970650075121624016220478640947204", "0E-91" ] }, "root_record": { "r": "1.55867683432471497276729495181606004898597661434977196009862875648552427843555491532236778", "b": "0.0407227903791317882786784347537297122139521589068335623873783095643576870068468885109650222", "h": "0.00938485516079684789352361615548558609448969777281537081388663943248748436875221816871850447", "A": "0.407904765651879162607992958249947720115318444569889312379063470088314951098871481197682621", "denominator": "0.985372043667373205220179884916698375044677295891566311921366974415428309065447518493699742", "polynomial_residual": "-1.494887206208962644288839E-65", "bracket_initial_signs": [ "1.44667839309719037953777409773694716053377547896974191498990893674953826877187721336722827", "-1.98442211433410872361089886735824120595535902096441713081029077580348832290891041296708640" ], "bracket_derivative_max": "-5.49842120662580405572355875235895204180478886542233486201873494119399261218692632819797868", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.06165108087186351703101984100540372928681827148880325542677132289795034013415542277893761E-90", "-1E-91", "0E-182", "0E-90", "0E-182", "8.71479954394881274946851416515882993204734876414467068825678410533399813563732960938440261E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_3.625", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.045721319316009534, 0.0 ], "rh_scaled_inf": 2.2096301502361598e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.7978943430204569e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.2096301502361598e-16 }, "characteristics": { "left": { "slow": 0.029437997066477123, "alfven_n": 0.07744010899938247, "fast": 0.8683953977008604 }, "right": { "slow": 0.03621047661664574, "alfven_n": 0.09668163717152947, "fast": 0.6941975917832086 } }, "front_relative_normal_velocity": { "left": -0.640286179863445, "right": -0.9979992358914197 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.558676834324715, "pressure_ratio": 2.5126327452524704, "entropy_over_cv": 0.18160230887848228, "tangential_field_ratio": 1.5669704533583304 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.65, "theta_Bn_degrees": 81.35000000000001, "compression": 1.5586479178872976, "u2x_km_s": -384.47949378480354, "u2y_km_s": -7.360517971407334, "speed2_km_s": 384.5499426158145, "signed_deflection_degrees": 1.0967427715272702, "p2_over_p1": 2.512512991408526, "B2_over_B1": 1.5564496537826162, "entropy_over_cv": 0.18158556718154084, "upstream_fast_Mach": 1.4376013524615443, "downstream_fast_Mach": 0.7373292044029214, "downstream_alfven_margin": 0.5626167099627717, "state_global_normalized": { "rho": "1.55864791788729753421370350810958360982893212754485077413174855828344722768263693707121375", "p": "0.101907526931529816866488849702258617506537969854492423606245689251917489054236610664466863", "u": [ "-0.640799156308005879777698730503764391659981679616949886534510851933534995479564666763329115", "-0.0122675299523455553730002984679264452308857150673403659440196212382381980212792765961312149", "0E-91" ], "B": [ "0.0331826371728895197284672754893313178154525004342501374346564186590613893489723218249265652", "1.00287424396752587702317291600850990064601345661745793128809290139669807436189691435772772", "0E-91" ] }, "root_record": { "r": "1.55864791788729753421370350810958360982893212754485077413174855828344722768263693707121375", "b": "0.0407250496138344129944744476700620158105942147633849884234528307079437580988477813654427518", "h": "0.00943944806696942043690128981255813741201111673002841170598304853756089419380368425393984575", "A": "0.407873323300558259000891138545825315501569697617484251076705192878516220086905642845605166", "denominator": "0.985287223924412837339166297925441628759203001734802331641820298616275637320195321567922963", "polynomial_residual": "-1.513463722998345707675105E-65", "bracket_initial_signs": [ "1.44642488596837015246749443892602937460688432159472513732615122243450586343469706494967894", "-1.98441624497344956970717108671190307637473403751775368488050490722766822098657280336468843" ], "bracket_derivative_max": "-5.49815079975224283378887333932814465982400338351352585548883940128259760381135213894038075", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "-1E-91", "0E-182", "0E-90", "0E-182", "8.82413394733157731874371836453532376368418516286372304367503121800582357220156372177921407E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_3.65", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04610649402669987, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -2.7755575615628914e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.029523119380166638, "alfven_n": 0.0776635880421314, "fast": 0.8683777804832685 }, "right": { "slow": 0.03631492247531096, "alfven_n": 0.09695974459979148, "fast": 0.6941921358385035 } }, "front_relative_normal_velocity": { "left": -0.6402802980049032, "right": -0.9979715533496006 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5586479178872976, "pressure_ratio": 2.5125129914085265, "entropy_over_cv": 0.18158556718154084, "tangential_field_ratio": 1.5669899135220642 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.675, "theta_Bn_degrees": 81.325, "compression": 1.558618729102829, "u2x_km_s": -384.48559718569743, "u2y_km_s": -7.327524752223305, "speed2_km_s": 384.5554148133099, "signed_deflection_degrees": 1.0918105321660314, "p2_over_p1": 2.512392022905116, "B2_over_B1": 1.5564079175954044, "entropy_over_cv": 0.18156863154617722, "upstream_fast_Mach": 1.4375725320417103, "downstream_fast_Mach": 0.7373374705454118, "downstream_alfven_margin": 0.562387342648296, "state_global_normalized": { "rho": "1.55861872910282896473608207265474532026604610609120539652347395799888996624603251543215690", "p": "0.101902620449031521852572324140547499091858209933812339023807556230053707419439621513008366", "u": [ "-0.640809328642829038023288356252713966849011024675517188752304973935685883941663809896712410", "-0.0122125412537055090035002785227967556788479082767903308548682786628009564150335722836047759", "0E-91" ], "B": [ "0.0330260304938011839470478106202326679791864057003458014672583498043817394565956180986438691", "1.00285249208668288972575170366648777436984683085249581494194234191378035789931432356062893", "0E-91" ] }, "root_record": { "r": "1.55861872910282896473608207265474532026604610609120539652347395799888996624603251543215690", "b": "0.0407273245447944019214479091934260080915496603292584332690491630320404022278974240861112762", "h": "0.00949420235232503426452016538519135276847947099024409686001581452739408400620530634427355665", "A": "0.407841880410832235023215636863010454468317352954042859549700542538843093864930168443111525", "denominator": "0.985202158395774065900867671622075177963791305623325511198598996915159236916509686920132032", "polynomial_residual": "-4.10672649244807918298568E-66", "bracket_initial_signs": [ "1.44616979238575065708958119459258232822133323750461225798433869427670423367833958609073304", "-1.98441168228610032830991777351939851486787976196787867060723106843259446066848707524694543" ], "bracket_derivative_max": "-5.49788034489947714405118095484798558101737462718543685894710638529993589549666849087409251", "iterations": 216 }, "flux_residuals": [ "2E-90", "8.06230496804198331037833320663011378636153455822914962599863600099053686431242959021751729E-90", "0E-91", "0E-182", "2E-90", "0E-182", "2.39467705151756518930103265146799845256112775775671699329200042739681203910924721302475474E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_3.675", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.046491664555754396, 0.0 ], "rh_scaled_inf": 2.2100805446444861e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7982128341805426e-16, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.2100805446444861e-16 }, "characteristics": { "left": { "slow": 0.029608240344500065, "alfven_n": 0.07788706325629649, "fast": 0.8683600542245314 }, "right": { "slow": 0.03641936387627937, "alfven_n": 0.09723783356828677, "fast": 0.69418666437008 } }, "front_relative_normal_velocity": { "left": -0.6402744059045926, "right": -0.9979436808080849 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.558618729102829, "pressure_ratio": 2.5123920229051167, "entropy_over_cv": 0.1815686315461772, "tangential_field_ratio": 1.5670092420548893 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.7, "theta_Bn_degrees": 81.30000000000001, "compression": 1.5585892679403468, "u2x_km_s": -384.4917965973555, "u2y_km_s": -7.294535647289328, "speed2_km_s": 384.5609859319739, "signed_deflection_degrees": 1.086878774745064, "p2_over_p1": 2.512269839811987, "B2_over_B1": 1.5563658759687955, "entropy_over_cv": 0.18155150197959136, "upstream_fast_Mach": 1.437543469614308, "downstream_fast_Mach": 0.7373458178321695, "downstream_alfven_margin": 0.5621579689160118, "state_global_normalized": { "rho": "1.55858926794034680016479913012429644682260809374697362382310375712241201178107511149558935", "p": "0.101897664702774188103976868719276749060525922941244771298011307374073218674981743714451741", "u": [ "-0.640819660995592548320451239870689938933102249313472287735020502435869775345319770588167399", "-0.0121575594121488790669028342150117143999658311298552081738617827984299810617903652579617835", "0E-91" ], "B": [ "0.0328694483772735061309114852368666934080340154083900611412914380586393117390338616594749320", "1.00283051817586912375617812041652844733484469428286837334384099238922742433439260121965264", "0E-91" ] }, "root_record": { "r": "1.55858926794034680016479913012429644682260809374697362382310375712241201178107511149558935", "b": "0.0407296151754979692923427520983062977140581675729540482665522887189720883049774871202463531", "h": "0.00954911806450382519117582891896592562864081016735243846601015072122374696654768837720330845", "A": "0.407810436970784465005461787896237987974786909881027590355707549886492794966932966603511879", "denominator": "0.985116847066369041760237077980305480896297871685500508314669515629088918317531760206175706", "polynomial_residual": "-1.003704205724614260609310E-65", "bracket_initial_signs": [ "1.44591311240180737326402198676025945043055873624865033209523591043161771136652316319996762", "-1.98440842581414606128117710843872682848511142151090058526800020335980860959674586767022772" ], "bracket_derivative_max": "-5.49760984148404959949618809241409574290578703567103440559304576888339805405712567515948836", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "2E-91", "0E-182", "-1E-90", "0E-182", "5.85339738656598135526095561212446671933602405959711929543070737237543473874561225132250160E-67", "0E-91" ], "diagnosis": { "case_id": "R95_phi_3.7", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04687683086671314, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.02969335995832778, "alfven_n": 0.07811053465896149, "fast": 0.8683422189297718 }, "right": { "slow": 0.0365238008064998, "alfven_n": 0.09751590402407112, "fast": 0.6941811773802702 } }, "front_relative_normal_velocity": { "left": -0.6402685035749733, "right": -0.997915618272179 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5585892679403468, "pressure_ratio": 2.512269839811987, "entropy_over_cv": 0.18155150197959136, "tangential_field_ratio": 1.5670284389144282 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.725, "theta_Bn_degrees": 81.275, "compression": 1.558559534368733, "u2x_km_s": -384.4980920263881, "u2y_km_s": -7.261550725991485, "speed2_km_s": 384.566655979011, "signed_deflection_degrees": 1.0819475133298702, "p2_over_p1": 2.5121464422003545, "B2_over_B1": 1.5563235289083508, "entropy_over_cv": 0.18153417848918213, "upstream_fast_Mach": 1.4375141651745031, "downstream_fast_Mach": 0.7373542462814089, "downstream_alfven_margin": 0.5619285887613537, "state_global_normalized": { "rho": "1.55855953436873313427896519794766238786698302824347769199883537487354238952053131247273304", "p": "0.101892659695646378647585276301866529756569307161265117519038615449447481564402268232989892", "u": [ "-0.640830153377313477232095881826761753902567189802487826737558038963727558316691750342805575", "-0.0121025845433191422101688951479146592570901205644739901465460029653778464610445214921660168", "0E-91" ], "B": [ "0.0327128910552845562524227902717474835620147422034168241125167652355497103754116471425249111", "1.00280832224398073046066402914148363948187265645054395940127017985345858321709819772738445", "0E-91" ] }, "root_record": { "r": "1.55855953436873313427896519794766238786698302824347769199883537487354238952053131247273304", "b": "0.0407319215094556829217832284778104506515755697321416345543078308948209907248833343244811617", "h": "0.00960419525139630261913415548839964146735037599034294807031519768435644770471576831130279629", "A": "0.407778992968497502750591233203349783067509746594496642910707022870074595919653810639581139", "denominator": "0.985031289920997380723324778368316798178501086177863585714253708422634731833953566720661338", "polynomial_residual": "1.39039861282328912906519E-66", "bracket_initial_signs": [ "1.44565484606841462771146637803266962825080058227846855475505757223162991736469525626587861", "-1.98440647509861457273427594783460790338516997987874041304942171557704470010058556147575320" ], "bracket_derivative_max": "-5.49733928892026017135750872663224812051264716502911327370987224099950623287188928057347133", "iterations": 216 }, "flux_residuals": [ "0E-90", "-8.06296510209212175926936789927157131129547348561707972029283858527882875241167622949308003E-90", "5E-91", "0E-182", "2E-90", "0E-182", "-8.10947391028938109819706519459563502162274761522690516014300691840876547406330780216349217E-68", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_3.725", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04726199292313485, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.0297784782205076, "alfven_n": 0.07833400226722848, "fast": 0.8683242746041339 }, "right": { "slow": 0.03662823325291965, "alfven_n": 0.09779395591420384, "fast": 0.6941756748714122 } }, "front_relative_normal_velocity": { "left": -0.6402625910285821, "right": -0.9978873657472256 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.558559534368733, "pressure_ratio": 2.5121464422003545, "entropy_over_cv": 0.18153417848918219, "tangential_field_ratio": 1.5670475040579996 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.75, "theta_Bn_degrees": 81.25000000000001, "compression": 1.5585295283567147, "u2x_km_s": -384.5044834794164, "u2y_km_s": -7.228570057711629, "speed2_km_s": 384.57242496160853, "signed_deflection_degrees": 1.0770167619840931, "p2_over_p1": 2.512021830142908, "B2_over_B1": 1.556280876419634, "entropy_over_cv": 0.18151666108254746, "upstream_fast_Mach": 1.437484618717467, "downstream_fast_Mach": 0.7373627559114769, "downstream_alfven_margin": 0.5616992021798146, "state_global_normalized": { "rho": "1.55852952835671462341201046144872194660496365314133693718397247763921693795955460339279953", "p": "0.101887605430596346814612789747119634922118860405521241411615950283182492530917504978068085", "u": [ "-0.640840805799027322909732597397545311693218584829502884114987020874562338375483277664946727", "-0.0120476167628527136358226694697443320651592472424682444325153328451190121190613890873617217", "0E-91" ], "B": [ "0.0325563587598235633872032231621310537161217400846155067837824454268948156863074161220218061", "1.00278590430002746248501953957877246699176033076962480362383748393954541222446136309419466", "0E-91" ] }, "root_record": { "r": "1.55852952835671462341201046144872194660496365314133693718397247763921693795955460339279953", "b": "0.0407342435502024756641435687381785670115966195058087684390602580195928506683989029471627191", "h": "0.00965943396114348496861674503828396079154999801757327100648202362077624570358191165762148720", "A": "0.407747548392053063513233808092572039056312017151604209602962790406149617574480014407029731", "denominator": "0.984945486944346212683764166809436484280543736488272905473201183452407532098882728219119064", "polynomial_residual": "1.362224435357284519307938E-65", "bracket_initial_signs": [ "1.44539499343684679694115399098676200521849850181317959654966554552944717945007121309892867", "-1.98440582967947367608181663693523486704780913904961986224222366385875532743674954800630873" ], "bracket_derivative_max": "-5.49706868662016351897031091096128965704343140029450612457641779406220159649352677828803043", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "7E-91", "0E-182", "3E-90", "0E-182", "-7.94608319927849606013806871228317947534089945480591311966070241424243140192027120850303238E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_3.75", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04764715068859715, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.029863595129904875, "alfven_n": 0.0785574660982179, "fast": 0.8683062212527827 }, "right": { "slow": 0.03673266120248483, "alfven_n": 0.09807198918574779, "fast": 0.6941701568458518 } }, "front_relative_normal_velocity": { "left": -0.6402566682780325, "right": -0.9978589232386035 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5585295283567147, "pressure_ratio": 2.512021830142908, "entropy_over_cv": 0.1815166610825475, "tangential_field_ratio": 1.5670664374426175 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.775, "theta_Bn_degrees": 81.225, "compression": 1.5584992498728625, "u2x_km_s": -384.51097096307285, "u2y_km_s": -7.195593711827313, "speed2_km_s": 384.57829288693705, "signed_deflection_degrees": 1.072086534769469, "p2_over_p1": 2.5118960037138076, "B2_over_B1": 1.5562379185082125, "entropy_over_cv": 0.18149894976748462, "upstream_fast_Mach": 1.4374548302383765, "downstream_fast_Mach": 0.737371346740854, "downstream_alfven_margin": 0.5614698091669463, "state_global_normalized": { "rho": "1.55849924987286249122532801202232859185535660903976457133153384562097155726596459773525182", "p": "0.101882501910632042810148744205064685496642961566128819732740223294761807520365494786255346", "u": [ "-0.640851618271788092644489797516975784444437710120103374670199557193126567306032991203305377", "-0.0119926561863788561153939764179810830117770878387357947520213377758816669499643133332423551", "0E-91" ], "B": [ "0.0323998517228909521085785677471691077473011300134407630034083374586527082806436014294365326", "1.00276326435313263237180626768533296544851799373775895784831458509626799486023257099313022", "0E-91" ] }, "root_record": { "r": "1.55849924987286249122532801202232859185535660903976457133153384562097155726596459773525182", "b": "0.0407365813012976569522544355025607386763840464237530667511040839913195926330962950293821222", "h": "0.00971483424213703593926245385748004312964673198108895638585925647209275945183101568925819282", "A": "0.407716103229532005976254298252005697399493253947163843685655641460819676627016580604305705", "denominator": "0.984859438120990230915140601409011866064643687153112169027990174445938298365506441082046557", "polynomial_residual": "9.0248704575465489237351E-67", "bracket_initial_signs": [ "1.44513355455777951565443218959597554446687118376911628272660137955321378430512059887021692", "-1.98440648909562844658792901851486810276220591647299022928887436756354502764507948543762376" ], "bracket_derivative_max": "-5.49679803399356630456707942328396367098460223124559947188785452556660359209464094272192078", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "5E-91", "0E-182", "-1E-90", "0E-182", "-5.26497728633082455878514066045214873658269416938988705706413086183882475318946691684444996E-68", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_3.775", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.048032304126696686, 0.0 ], "rh_scaled_inf": 2.2109952834404594e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.2109952834404594e-16 }, "characteristics": { "left": { "slow": 0.029948710685392527, "alfven_n": 0.07878092616906866, "fast": 0.8682880588809052 }, "right": { "slow": 0.0368370846421398, "alfven_n": 0.09835000378576934, "fast": 0.6941646233059409 } }, "front_relative_normal_velocity": { "left": -0.640250735336015, "right": -0.9978302907517279 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5584992498728625, "pressure_ratio": 2.5118960037138076, "entropy_over_cv": 0.18149894976748449, "tangential_field_ratio": 1.5670852390249934 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.8, "theta_Bn_degrees": 81.2, "compression": 1.5584686988855925, "u2x_km_s": -384.51755448400104, "u2y_km_s": -7.1626217577117535, "speed2_km_s": 384.5842597621498, "signed_deflection_degrees": 1.0671568457457843, "p2_over_p1": 2.5117689629886866, "B2_over_B1": 1.5561946551796564, "entropy_over_cv": 0.18148104455199007, "upstream_fast_Mach": 1.4374247997324145, "downstream_fast_Mach": 0.7373800187881532, "downstream_alfven_margin": 0.5612404097183584, "state_global_normalized": { "rho": "1.55846869888559253365036183455166523452012611056014355378076175836349830440797157151563847", "p": "0.101877349138821120242833932333987231478598765796600830683213243688883506134259142749119225", "u": [ "-0.640862590806668380959197742965563832612916173378345030690604973200499812469076259494663672", "-0.0119377029295195889409008894179564447909443549372532491612060346659548848882816522184143905", "0E-91" ], "B": [ "0.0322433701764983790489831501145276907456592523377508806039049296600015626410144519108252522", "1.00274040241253307094833762365418048241536556606782779801072133115799151066615926717974403", "0E-91" ] }, "root_record": { "r": "1.55846869888559253365036183455166523452012611056014355378076175836349830440797157151563847", "b": "0.0407389347663249244170109586550963536822896090835636331620015020065460255703795679068950188", "h": "0.00977039614301940160328663554679811542505663175025639474641365480490765795448224083137011731", "A": "0.407684657469014314224626321840605385900269083076889955322715134594924866374171180937903051", "denominator": "0.984773143435391741519522489684711538081832120942587359561802289931693032898483225711095737", "polynomial_residual": "-2.4660546038004042318557E-67", "bracket_initial_signs": [ "1.44487052948129089063636609917586176240567555858375517989213498371052704405761497823666209", "-1.98440845288491845940416841076295374366121942361119553252328163665810539380503586809567488" ], "bracket_derivative_max": "-5.49652733044802449299724997078373499560383077340520770584460021697767326037824876920077289", "iterations": 216 }, "flux_residuals": [ "1E-90", "0", "4E-91", "0E-182", "0E-90", "0E-182", "1.43882936953206862034659632895038922361276964829835332405722386328522000638257353917124252E-68", "-2E-91" ], "diagnosis": { "case_id": "R95_phi_3.8", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04841745320104919, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.030033824885851157, "alfven_n": 0.07900438249693832, "fast": 0.8682697874937089 }, "right": { "slow": 0.03694150355882753, "alfven_n": 0.09862799966133845, "fast": 0.6941590742540388 } }, "front_relative_normal_velocity": { "left": -0.6402447922152967, "right": -0.99780146829205 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5584686988855925, "pressure_ratio": 2.511768962988686, "entropy_over_cv": 0.18148104455199, "tangential_field_ratio": 1.567103908761533 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.825, "theta_Bn_degrees": 81.175, "compression": 1.5584378753631651, "u2x_km_s": -384.52423404885565, "u2y_km_s": -7.129654264733758, "speed2_km_s": 384.59032559438333, "signed_deflection_degrees": 1.0622277089708299, "p2_over_p1": 2.5116407080446486, "B2_over_B1": 1.5561510864395387, "entropy_over_cv": 0.18146294544425975, "upstream_fast_Mach": 1.4373945271947692, "downstream_fast_Mach": 0.7373887720721207, "downstream_alfven_margin": 0.5610110038297188, "state_global_normalized": { "rho": "1.55843787536316512399952120431779472333200389319931155229665563720647058715928688455651145", "p": "0.101872147118290942614667977561017544172910735134569399044653289610618082820733554124010220", "u": [ "-0.640873723414759448242140545369504895865268340209572194220886861786540524683013979208396618", "-0.0118827571078895968141021385696013576915188512709008508475852329645061246716131789032531402", "0E-91" ], "B": [ "0.0320869143526687696292394273631931342047124955538469383179181086798953480423826015015384968", "1.00271731848757908550537385376824908958895726487732673024331423853052810976867183898306464", "0E-91" ] }, "root_record": { "r": "1.55843787536316512399952120431779472333200389319931155229665563720647058715928688455651145", "b": "0.0407413039488923755879476014005676623566817582928347806732892086685404813200691927834275116", "h": "0.00982611971268394833106447073244438196117918432642919221789171281746247040508569781538520764", "A": "0.407653211098579079716555578368867704386415126100861023399039557128542939232423432313312071", "denominator": "0.984686602871900713032435083978960327483394620084309675851090440548950983111620513238012207", "polynomial_residual": "-1.51142613506339715327432E-66", "bracket_initial_signs": [ "1.44460591825686272014802103603577500182786117497776068906674720943006772149058789424135497", "-1.98441172058411501306830416617994888543435858802643709084448866984502359538174395617856238" ], "bracket_derivative_max": "-5.49625657538884063635234861709631234410946777662751811706691912038603784353972179106866944", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.06430412101764144966913531745796498766666926665077287498255009369113230502398505978926447E-90", "-2E-91", "0E-182", "0E-90", "0E-182", "8.81951311612735453019942483832838984068730603706057728090625387424661648622284221002825802E-68", "0E-91" ], "diagnosis": { "case_id": "R95_phi_3.825", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04880259787528968, 0.0 ], "rh_scaled_inf": 1.799187479267125e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 1.799187479267125e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.030118937730169066, "alfven_n": 0.07922783509900311, "fast": 0.8682514070964225 }, "right": { "slow": 0.03704591793948955, "alfven_n": 0.09890597675952863, "fast": 0.6941535096925114 } }, "front_relative_normal_velocity": { "left": -0.6402388389287219, "right": -0.9977724558650571 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5584378753631651, "pressure_ratio": 2.5116407080446486, "entropy_over_cv": 0.18146294544425978, "tangential_field_ratio": 1.567122446608338 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.85, "theta_Bn_degrees": 81.15, "compression": 1.5584067792736853, "u2x_km_s": -384.53100966430276, "u2y_km_s": -7.096691302257684, "speed2_km_s": 384.596490390757, "signed_deflection_degrees": 1.0572991385003578, "p2_over_p1": 2.5115112389602707, "B2_over_B1": 1.5561072122934358, "entropy_over_cv": 0.18144465245268915, "upstream_fast_Mach": 1.4373640126206344, "downstream_fast_Mach": 0.7373976066116362, "downstream_alfven_margin": 0.5607815914967537, "state_global_normalized": { "rho": "1.55840677927368521824630567087263211191346937211920799396106793820749074587480615346346156", "p": "0.101866895852228589770940810413690120322254102461783681112558341326712883758685204010559594", "u": [ "-0.640885016107171299923080794527953225346408403567020011615013421575424879984829949968452193", "-0.0118278188370961386732478357133998610413686526640928592105039981474663220709895287417964914", "0E-91" ], "B": [ "0.0319304844834363549566326253463889095358751065421592088059680114219350686866298176799521531", "1.00269401258773441776635895171758960162645785939079075683249183840686657603998678908495422", "0E-91" ] }, "root_record": { "r": "1.55840677927368521824630567087263211191346937211920799396106793820749074587480615346346156", "b": "0.0407436888526325196748455714202551387888264812102420597324814584129905176935380861645006382", "h": "0.00988200500027510154986953623270288047237829065568120713086486915586152243902059787630898913", "A": "0.407621764106304483251794690989878548129792014929593933425858375448241881796302103146444320", "denominator": "0.984599816414754826184558533070562063718724582134975901592384431047629056826736018181239979", "polynomial_residual": "5.24327788921932855391101E-66", "bracket_initial_signs": [ "1.44433972093338171883207486575402184900845387572667107098256878957010084528555730603771229", "-1.98441629172891833844510707185732286277356388392321986402057666404876208446121926631937212" ], "bracket_derivative_max": "-5.49598576821906114347814808591090314541290252006594488409442507708092498148577713357256209", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "6E-91", "0E-182", "1E-90", "0E-182", "-3.05993099436091728644987370300053858560562389032504321793179773017616297495152310260398563E-67", "-3E-91" ], "diagnosis": { "case_id": "R95_phi_3.85", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.04918773811307256, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.030204049217242342, "alfven_n": 0.07945128399245809, "fast": 0.8682329176942962 }, "right": { "slow": 0.03715032777106588, "alfven_n": 0.09918393502741694, "fast": 0.6941479296237317 } }, "front_relative_normal_velocity": { "left": -0.6402328754892118, "right": -0.9977432534762729 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5584067792736853, "pressure_ratio": 2.511511238960271, "entropy_over_cv": 0.18144465245268904, "tangential_field_ratio": 1.5671408525212043 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.875, "theta_Bn_degrees": 81.125, "compression": 1.5583754105851024, "u2x_km_s": -384.5378813370196, "u2y_km_s": -7.063732939643375, "speed2_km_s": 384.6027541583736, "signed_deflection_degrees": 1.0523711483880362, "p2_over_p1": 2.5113805558156033, "B2_over_B1": 1.556063032746927, "entropy_over_cv": 0.1814261655858733, "upstream_fast_Mach": 1.4373332560052097, "downstream_fast_Mach": 0.7374065224257126, "downstream_alfven_margin": 0.560552172715247, "state_global_normalized": { "rho": "1.55837541058510236047502732675283706373368008772544235286845574735928459515950180888688718", "p": "0.101861595343880864310282152496574066211331160453103660263166119920008559765240409161248318", "u": [ "-0.640896468895032766192164804922164625958284489003004310745398488346428974420276183285312588", "-0.0117728882327389564570561945815526797417826714406376852893646691558948634941360492095019457", "0E-91" ], "B": [ "0.0317740808008467088927015078679558335197706871742148082715246229026651182852924498368495503", "1.00267048472257620164704594341217403811363213245826703212790042887251287165900047330645537", "0E-91" ] }, "root_record": { "r": "1.55837541058510236047502732675283706373368008772544235286845574735928459515950180888688718", "b": "0.0407460894812022894304389559751844267363451351114475259692246425139191154472704836505564746", "h": "0.00993805205518848533650354195005999777765452662758727428647874248757310933708574332032716204", "A": "0.407590316480267776937091853797162730363004005735841107385555619684358090007154843195467832", "denominator": "0.984512784048079523820432825531002710351459379549188925244947173227800265900284475396843537", "polynomial_residual": "-7.81954140481427861991818E-66", "bracket_initial_signs": [ "1.44407193755914074814449541083262264851780522447220011957916687211073424035585039614097252", "-1.98442216585395479308810730893679731557260352645856673398225264211020738138938658367523130" ], "bracket_derivative_max": "-5.49571490833947353435523042492339706524333915814879775717166422475973992960843044836515998", "iterations": 216 }, "flux_residuals": [ "2E-90", "0", "3E-91", "0E-182", "0E-90", "0E-182", "4.56395246001518445564830501610026941457722760785731088764055870409809904168824632242561303E-67", "-1E-91" ], "diagnosis": { "case_id": "R95_phi_3.875", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.049572873878071716, 0.0 ], "rh_scaled_inf": 2.211928645325155e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": -1.7995187595371546e-16, "t1_momentum": -1.3877787807814457e-17, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.211928645325155e-16 }, "characteristics": { "left": { "slow": 0.030289159345974943, "alfven_n": 0.07967472919451722, "fast": 0.8682143192926012 }, "right": { "slow": 0.037254733040495064, "alfven_n": 0.09946187441208408, "fast": 0.6941423340500796 } }, "front_relative_normal_velocity": { "left": -0.6402269019097643, "right": -0.9977138611312569 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5583754105851024, "pressure_ratio": 2.5113805558156033, "entropy_over_cv": 0.1814261655858732, "tangential_field_ratio": 1.5671591264556233 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.9, "theta_Bn_degrees": 81.10000000000001, "compression": 1.5583437692652107, "u2x_km_s": -384.54484907369493, "u2y_km_s": -7.0307792462461105, "speed2_km_s": 384.60911690431925, "signed_deflection_degrees": 1.047443752685405, "p2_over_p1": 2.511248658692167, "B2_over_B1": 1.556018547805594, "entropy_over_cv": 0.18140748485260708, "upstream_fast_Mach": 1.4373022573437004, "downstream_fast_Mach": 0.7374155195334958, "downstream_alfven_margin": 0.5603227474810408, "state_global_normalized": { "rho": "1.55834376926521068850051958252063740915044484166214152759767106133332994490087421373775562", "p": "0.101856245596554297954822721872719855424038276321573640823275820518758298435535978050145869", "u": [ "-0.640908081789491582262320094927983356289388815646318166596695790101128564922886531704690453", "-0.0117179654104101838056430227967253586957450956365397851880660753490177923368404919569520454", "0E-91" ], "B": [ "0.0316177035369567852916677335472298377277512437038062342080366656642235557874286470457924940", "1.00264673490179492080535643568290167067005915078826612581919969511846707108816381912836864", "0E-91" ] }, "root_record": { "r": "1.55834376926521068850051958252063740915044484166214152759767106133332994490087421373775562", "b": "0.0407485058382830530942862251478214288900575230020371654010458652390653018097230699731585051", "h": "0.00999426092707106284455794747598440152080476655913713907880846115398401677944337099593019952", "A": "0.407558868208545266148715480384815919180744045271866073389709597153356454356434474568630102", "denominator": "0.984425505755888060974453349282654053468188405596040369792445228832529447550831596379824066", "polynomial_residual": "-1.056659937689072390352464E-65", "bracket_initial_signs": [ "1.44380256818184005232509578549591080617493062873523201863407647207889594175748950951756607", "-1.98442934249277404100115795398253631106824158010822169920445780278137262368719750217636746" ], "bracket_derivative_max": "-5.49544399514860367932922318109525217585102053195120210588121420482690682077205933846529145", "iterations": 216 }, "flux_residuals": [ "0E-90", "8.06532480234290796568921704176066380634058645288124417127703454260754873430586434602942734E-90", "-3E-91", "0E-182", "1E-90", "0E-182", "6.16802518815507230253601961029426138796407755364636412010454389748600738516114504865071166E-67", "1E-91" ], "diagnosis": { "case_id": "R95_phi_3.9", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.049958005133980715, 0.0 ], "rh_scaled_inf": 4.4243297979025937e-16, "rh_components": { "mass": 0.0, "normal_momentum": 1.799685600780443e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": -4.4243297979025937e-16 }, "characteristics": { "left": { "slow": 0.030374268115278727, "alfven_n": 0.07989817072241355, "fast": 0.8681956118966295 }, "right": { "slow": 0.03735913373471415, "alfven_n": 0.09973979486061431, "fast": 0.6941367229739418 } }, "front_relative_normal_velocity": { "left": -0.6402209182034544, "right": -0.9976842788356053 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5583437692652107, "pressure_ratio": 2.511248658692167, "entropy_over_cv": 0.18140748485260716, "tangential_field_ratio": 1.5671772683667802 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.925, "theta_Bn_degrees": 81.075, "compression": 1.5583118552816488, "u2x_km_s": -384.55191288102867, "u2y_km_s": -6.997830291416553, "speed2_km_s": 384.6155786356628, "signed_deflection_degrees": 1.0425169654418307, "p2_over_p1": 2.5111155476729574, "B2_over_B1": 1.5559737574750219, "entropy_over_cv": 0.18138861026188513, "upstream_fast_Mach": 1.4372710166313174, "downstream_fast_Mach": 0.7374245979542655, "downstream_alfven_margin": 0.560093315790035, "state_global_normalized": { "rho": "1.55831185528164893965822419644419634175877134776748088082447357183464676393295963257885879", "p": "0.101850846613615157880460682431595248187228650083350786490327563188536314690539297041243518", "u": [ "-0.640919854801714469175760340298359642418447079550724841037175101727407961226110947492412554", "-0.0116630504856942546981298616621428410935624189572664114402412265164970601118427330936265599", "0E-91" ], "B": [ "0.0314613529238349554104276376615333874770379332195452999821564019216281023844928034334861177", "1.00262276313519436598131970356626091661475943560397301706483277322748934944066902490634852", "0E-90" ] }, "root_record": { "r": "1.55831185528164893965822419644419634175877134776748088082447357183464676393295963257885879", "b": "0.0407509379275806264178742133265477211910929115946607353731322428117587463979150180071672625", "h": "0.0100506316658212775670529603032265311381068336286026679791509656612379384114998580478950063", "A": "0.407527419279212291491997034267554717625052252425726190136639886428339006100129454561028331", "denominator": "0.984337981522081555104441880204260929226159659653106304174613367005318625082559819948013969", "polynomial_residual": "1.73044564595569220900637E-66", "bracket_initial_signs": [ "1.44353161284858849991985844864123845762216051503805650159845903408174704748048465469239464", "-1.98443782117784621777850207601866607187437753719175643233703790135385589936194012154682338" ], "bracket_derivative_max": "-5.49517302804271302317185374134996140631769066253060213820695593571269752950462061647320490", "iterations": 216 }, "flux_residuals": [ "-2E-90", "0", "5E-91", "0E-181", "-1E-90", "0E-181", "-1.01022921679789732412691807548182647475318568870576000609307629807359936785990787772850838E-67", "0E-90" ], "diagnosis": { "case_id": "R95_phi_3.925", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.05034313184451286, 0.0 ], "rh_scaled_inf": 4.4248046374600887e-16, "rh_components": { "mass": -1.1102230246251565e-16, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -4.4248046374600887e-16 }, "characteristics": { "left": { "slow": 0.03045937552407354, "alfven_n": 0.08012160859339916, "fast": 0.8681767955116949 }, "right": { "slow": 0.037463529840658726, "alfven_n": 0.10001769632009547, "fast": 0.6941310963977115 } }, "front_relative_normal_velocity": { "left": -0.6402149243834342, "right": -0.9976545065949499 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5583118552816488, "pressure_ratio": 2.5111155476729574, "entropy_over_cv": 0.18138861026188513, "tangential_field_ratio": 1.567195278209555 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.95, "theta_Bn_degrees": 81.05000000000001, "compression": 1.5582796686019005, "u2x_km_s": -384.5590727657323, "u2y_km_s": -6.964886144500687, "speed2_km_s": 384.62213935945715, "signed_deflection_degrees": 1.037590800704462, "p2_over_p1": 2.510981222842442, "B2_over_B1": 1.5559286617607988, "entropy_over_cv": 0.18136954182290205, "upstream_fast_Mach": 1.4372395338632775, "downstream_fast_Mach": 0.7374337577074348, "downstream_alfven_margin": 0.5598638776381871, "state_global_normalized": { "rho": "1.55827966860190045676505083719069120956758643100041438925816801937374887756347817708600240", "p": "0.101845398398489453007226668280704702312359901306843217148305536822681504741398490204704968", "u": [ "-0.640931787942887215155216678950427501497246324925273925805747751636594555467300928367123446", "-0.0116081435741678120266557437766785106171259191727776281285434603430415866159254463407783572", "0E-91" ], "B": [ "0.0313050291935610454910316647421480958102581103305262784144399817357206151274213440477392533", "1.00259856943269159212693597310177324795877915244895012223508633423562324054732782965056884", "0E-90" ] }, "root_record": { "r": "1.55827966860190045676505083719069120956758643100041438925816801937374887756347817708600240", "b": "0.0407533857528252847710221555280443012219636095522759756838378384392732108974359428536285245", "h": "0.0101071643215891954352042136830556354726000465235694326572434033317169029345793546542343371", "A": "0.407495969680343210757834205783468816129856127450760590134146993190244650856769435120793916", "denominator": "0.984250211330449036483078900486788773933633389194289451505214500275353055540600156107841361", "polynomial_residual": "9.24481665203623484845525E-66", "bracket_initial_signs": [ "1.44325907160590483086799683649905746467137851799085301157684423789959618718517922909650961", "-1.98444760144055908110190435866035726629068816866900202940937292096626843116904565198826020" ], "bracket_derivative_max": "-5.49490200641579579395384383094421593821016883687600284252198172392847437190574554023148316", "iterations": 216 }, "flux_residuals": [ "2E-90", "-8.06601307914229209050313838447202439747957499468478223242292637933144298079656851741665449E-90", "-5E-91", "0E-181", "-1E-90", "0E-181", "-5.39773211438678340719742841835154286827987067605351004778099933750927796712628929555934009E-67", "0E-90" ], "diagnosis": { "case_id": "R95_phi_3.95", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.05072825397340138, 0.0 ], "rh_scaled_inf": 1.1102230246251565e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.1102230246251565e-16, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.03054448157128729, "alfven_n": 0.08034504282474544, "fast": 0.8681578701431313 }, "right": { "slow": 0.03756792134526284, "alfven_n": 0.10029557873761907, "fast": 0.6941254543237896 } }, "front_relative_normal_velocity": { "left": -0.6402089204629325, "right": -0.997624544414959 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5582796686019005, "pressure_ratio": 2.5109812228424424, "entropy_over_cv": 0.1813695418229021, "tangential_field_ratio": 1.5672131559385212 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 3.975, "theta_Bn_degrees": 81.02499999999999, "compression": 1.5582472091932933, "u2x_km_s": -384.56632873452884, "u2y_km_s": -6.93194687483977, "speed2_km_s": 384.6287990827381, "signed_deflection_degrees": 1.032665272518187, "p2_over_p1": 2.510845684286562, "B2_over_B1": 1.5558832606685153, "entropy_over_cv": 0.18135027954505253, "upstream_fast_Mach": 1.4372078090348028, "downstream_fast_Mach": 0.7374429988125502, "downstream_alfven_margin": 0.5596344330215124, "state_global_normalized": { "rho": "1.55824720919329319425140599121566321956827249662339522494744526415585984385512535423403622", "p": "0.101839900954662940249740522284510133635903704886500741194440448589257999886818648766767238", "u": [ "-0.640943881224214757500517887027473956622538589677744241874489552415425294472072687415705554", "-0.0115532447913996161065166274903496117765916081239207400344360851992931019978573583002702912", "0E-91" ], "B": [ "0.0311487325782263745165780735594494034563761698061368248278686960190403915349518220611882018", "1.00257415380431687532580793672408287084573823747480201699007077172852455525388227710516844", "0E-90" ] }, "root_record": { "r": "1.55824720919329319425140599121566321956827249662339522494744526415585984385512535423403622", "b": "0.0407558493177717753296538222251461278801222798796686183923577955206338793387975278056755677", "h": "0.0101638589447766477540722245846397983765876891405617852152628592160524779156051171856391146", "A": "0.407464519400011380876096583810270116117889561493545064152480766897432324500628178376199302", "denominator": "0.984162195164667498747484234762978545167170383989408819124947747738055830736423422051541675", "polynomial_residual": "-1.537430511736235318261560E-65", "bracket_initial_signs": [ "1.44298494449971890916680166548493565250243668214841246953807602595215057055024218367195853", "-1.98445868281121514657327085567509261185787553485821847995157111118946983216185953659653433" ], "bracket_derivative_max": "-5.49463092965957619671054333358235407130178262600616789593560779125573875758823965078343239", "iterations": 216 }, "flux_residuals": [ "0E-90", "0", "-1.3E-90", "0E-181", "1E-90", "0E-181", "8.97758612240014685962356855842582220203123697108219370275884248256272571106368889822780938E-67", "1E-90" ], "diagnosis": { "case_id": "R95_phi_3.975", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.05111337148439952, 0.0 ], "rh_scaled_inf": 2.212880658544745e-16, "rh_components": { "mass": 0.0, "normal_momentum": -1.8001909326668413e-16, "t1_momentum": 2.7755575615628914e-17, "t2_momentum": 0.0, "t1_induction": 1.1102230246251565e-16, "t2_induction": 0.0, "energy": 2.212880658544745e-16 }, "characteristics": { "left": { "slow": 0.030629586255855996, "alfven_n": 0.08056847343374315, "fast": 0.8681388357962947 }, "right": { "slow": 0.037672308235459084, "alfven_n": 0.10057344206028022, "fast": 0.6941197967545829 } }, "front_relative_normal_velocity": { "left": -0.6402029064552556, "right": -0.997594392301337 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5582472091932933, "pressure_ratio": 2.510845684286562, "entropy_over_cv": 0.18135027954505245, "tangential_field_ratio": 1.567230901507946 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } }, { "phi_degrees": 4.0, "theta_Bn_degrees": 81.0, "compression": 1.5582144770229998, "u2x_km_s": -384.5736807941528, "u2y_km_s": -6.899012551770272, "speed2_km_s": 384.6355578125251, "signed_deflection_degrees": 1.0277403949255857, "p2_over_p1": 2.51070893209273, "B2_over_B1": 1.5558375542037652, "entropy_over_cv": 0.18133082343793142, "upstream_fast_Mach": 1.4371758421411216, "downstream_fast_Mach": 0.7374523212892918, "downstream_alfven_margin": 0.5594049819360838, "state_global_normalized": { "rho": "1.55821447702299972446479056310832331355787950590556964668794966167660390979631018018601487", "p": "0.101834354285681130727752695588898563620809228160442656590547102156132507611196987831965093", "u": [ "-0.640956134656921265031145596655350252063000945666980209200521217013241131688266086652097090", "-0.0114983542529504531221556510725481140305218945050908804787913819629458019040823905626890986", "0E-91" ], "B": [ "0.0309924633099337921414489394062749481360803583314656288369176720576178817886917861357534191", "1.00254951626021366950238391639156570346520667220959932763808549821180336001568465576838173", "0E-90" ] }, "root_record": { "r": "1.55821447702299972446479056310832331355787950590556964668794966167660390979631018018601487", "b": "0.0407583286261993293450062640059285114452396814918781484749496743528741521715304825277677253", "h": "0.0102207155860373749758545409532021793213753690131092219977175031488787922555041585465994638", "A": "0.407433068426289139865875954016575498404987614211474959188297628158441868105343283200850293", "denominator": "0.984073933008301949607234078809797495334130741155872724786321003140338767288284044615001042", "polynomial_residual": "-1.571415496011631492802072E-65", "bracket_initial_signs": [ "1.44270923157537298112739738410134568641556447487338360495652806287057969019444738243303667", "-1.98447106481902880886104296902519096679342594528101345785778680842507214467581571463863407" ], "bracket_derivative_max": "-5.49435979716350559188107960169796196871953183698358276877140209846872821582848518286005198", "iterations": 216 }, "flux_residuals": [ "-1E-90", "0", "1E-91", "0E-181", "1E-90", "0E-181", "9.17711496942211151408090995415769611266078100343871032753431481008898174861562265937429119E-67", "0E-90" ], "diagnosis": { "case_id": "R95_phi_4", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.05149848434128067, 0.0 ], "rh_scaled_inf": 2.2131215794860735e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 2.2131215794860735e-16 }, "characteristics": { "left": { "slow": 0.03071468957672387, "alfven_n": 0.08079190043770244, "fast": 0.8681196924765614 }, "right": { "slow": 0.03777669049817849, "alfven_n": 0.10085128623517767, "fast": 0.6941141236925062 } }, "front_relative_normal_velocity": { "left": -0.6401968823737862, "right": -0.9975640502598242 }, "upstream_side": "right", "characteristic_transition": [ 1, 2 ], "compression": 1.5582144770229998, "pressure_ratio": 2.5107089320927303, "entropy_over_cv": 0.1813308234379314, "tangential_field_ratio": 1.567248514871789 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." } } ], "sources": [ "https://farside.ph.utexas.edu/teaching/plasma/Plasma/node102.html", "https://farside.ph.utexas.edu/teaching/plasma/Plasma/node105.html" ] }