{ "summary": { "status": "PASS", "scientific_checkpoint": "R99", "reference": "Saved R98 alpha=120 degree slow state", "source_R98_json_sha256": "d2da6fef60769c1a13af2bc90ee11b007cecd545e5aeb2d447fbb2874695a23b", "compression": "2.16777372674628571456846035289235997091915771158507132962527462913711634348321147559045940", "normal_acoustic_Mach_squared": "3", "fast_upper_compression": "2", "partial_input_result": "FAST_EXCLUDED", "control_families": [ "fast_shock", "fast_shock" ], "max_control_flux_residual": "8.18415491307700787542425096395862311168090696206612707245428474838490411785960931164692178E-90", "saved_reference_compression_difference": "3.22700935109805660564E-69", "exact_reduction_identity": "PASS", "fast_limits_covered_by_analytic_proof": [ "perpendicular", "parallel/gas", "switch-on" ], "full_state_API_with_B_missing": "INSUFFICIENT_DATA", "unique_slow_identification": false, "solar_identification": false, "measurement_error_propagation": false, "native_browser_tested": false, "historical_benchmark_rerun": false }, "partial_input_request": { "rho1": "1", "p1": "3/20", "upstream_normal_speed_squared": "3/4", "gamma": "5/3", "upstream_acoustic_speed_squared": "1/4", "normal_acoustic_Mach_squared": "3", "compression": "2.16777372674628571456846035289235997091915771158507132962527462913711634348321147559045940", "magnetic_components": "WITHHELD", "downstream_pressure": "WITHHELD", "tangential_velocities": "WITHHELD", "front_geometry": "one fixed local normal", "pressure_meaning": "total scalar thermal pressure under the declared ideal-MHD equation of state" }, "compression_enclosure": { "polynomial_coefficients_ascending": [ "8", "-638/27", "5270/243", "-1400/243" ], "initial_bracket": [ "21677/10000", "10839/5000" ], "initial_sign_values": [ "969581369/1215000000000", "-4799587/16875000000" ], "derivative_max_on_initial_bracket": "-1314959909/121500000", "lower": "71341630932043758904042097882781131012672981763894774086362255349593/32910091146424120843099383651147010099654717312671597266972180480000", "upper": "285366523728175035616168391531124524050691927055579096345449021398373/131640364585696483372397534604588040398618869250686389067888721920000", "width": "1/131640364585696483372397534604588040398618869250686389067888721920000", "bisections": 213, "meaning": "numerical enclosure of one exact input, not measurement uncertainty" }, "reduction_identity": { "status": "PASS", "residual_coefficients": [], "identity": "(1+2rh)r\u00b2(1-h)\u00b2-(5+2rh-4r)(1-rh)\u00b2=(r-1)[r+5-2rh(4-r)]", "scope": "Exact coefficient identity; endpoint proof separately uses undivided energy relation" }, "full_scalar_input_screen": { "status": "FAST_EXCLUDED", "normal_acoustic_Mach_squared": "3", "upper_fast_compression": "2", "compression_minus_bound_lower": "5521448639195517217843330580487110813363547138551579552417894389593/32910091146424120843099383651147010099654717312671597266972180480000", "other_families": "NOT_EXCLUDED_BY_THIS_SCREEN", "unique_slow_identification": false }, "omission_controls": [ { "case": "normal_flow_withheld", "upstream": { "rho": "1", "p": "0.15", "u": [ "0.980187202149079329599520768149991800322404376432337433978465356325027847833715831926105124", "0.565911345016997076616225706172230730796150742441281093865033857338775760981473758668381700", "0E-89" ], "B": [ "0.183420785544263847684735775502483356866456450562760132619499105718000429757708709808705244", "0.398133401866375928304971860736833082134500735115968427486876424693681040044500644457006376", "0E-90" ] }, "downstream": { "rho": "2.16777372674628571456846035289235997091915771158507132962527462913711634348321147559045940", "p": "0.673389965399065905467706581525696178208386579361967202244224737788532340130139982851584830", "u": [ 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"0.539470005340369610929171403769155176478609259021358609315176514433858203516499616681201377", "0.773908929237376163249780155385565369983849132211773342594895336479949404532957792205137630", "0.829710645938391360823706634787255951820481235438865494785711131422089452940961583732144815", "1.13182269003399415323245141234446146159230148488256218773006771467755152196294751733676340", "1.43393473412959694564119618990166697136412173432625888067442429793301359098493345094138198", "1.48973645083061214321512266930335755320075383755335103286524009287515363939293724246838917", "1.72417537472761869553573142091976774670599371074376576614495891492124484040939541799232542" ] }, "downstream": { "normal_velocity": "0.522112929070692469900107012396480645713104953746414729228091071911614570557592329579006007", "fast": "0.847066492391819367005388315521065401435397432707078068921068388083183218610640344437869263", "alfven_normal": 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}, "request_without_family": { "schema_version": "rmo-local-discontinuity-0.1", "case_id": "R99_normal_flow_withheld", "model": "ideal_mhd_single_planar_discontinuity", "units": "normalized_mu0_1", "frame": "common_inertial_local_basis", "gamma": 1.6666666666666667, "front_speed": 0.0, "basis": { "normal": [ 0.8660254037844386, 0.5, 0.0 ], "t1": [ -0.5, 0.8660254037844386, 0.0 ], "t2": [ 0.0, 0.0, 1.0 ] }, "left": { "rho": 1.0, "p": 0.15, "u": [ 1.131822690033994, 0.0, 0.0 ], "B": [ 0.35791376079661796, 0.25308324733926846, 0.0 ] }, "right": { "rho": 2.1677737267462858, "p": 0.6733899653990659, "u": [ 0.5221129290706925, 0.11932649180321588, 0.0 ], "B": [ 0.35791376079661796, 0.6304267466348432, 0.0 ] }, "uncertainty": { "mode": "exact_synthetic" } }, "diagnosis": { "case_id": "R99_normal_flow_withheld", "status": "SUPPORTED_LOCAL_CLASS", "family": "fast_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, 0.05966324590160794, 0.0 ], "rh_scaled_inf": 1.961832068575708e-16, "rh_components": { "mass": 1.961832068575708e-16, "normal_momentum": 1.5871699446861577e-16, "t1_momentum": 2.7755575615628914e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 1.806280189060908e-16 }, "characteristics": { "left": { "slow": 0.30211204409560277, "alfven_n": 0.35791376079661796, "fast": 0.5923526846936246 }, "right": { "slow": 0.20649267016496503, "alfven_n": 0.24309242272895284, "fast": 0.8470664923918193 } }, "front_relative_normal_velocity": { "left": 1.131822690033994, "right": 0.5221129290706925 }, "upstream_side": "left", "characteristic_transition": [ 1, 2 ], "compression": 2.1677737267462858, "pressure_ratio": 4.489266435993773, "entropy_over_cv": 0.2121881302081623, "tangential_field_ratio": 2.4909856865781808 }, "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "partial_screen": { "status": "FAST_NOT_EXCLUDED", "normal_acoustic_Mach_squared": "5.12409040670314723165122523232802617171240712871372491915357070801608016816797596593774304", "upper_fast_compression": "2.52291156310879323384330240137348166025111524922610830682785390793276618753255101862652721", "compression_minus_bound_lower": "-0.35513783636250751927484204848112168933195753764103697720257927879564984404933954303606781", "other_families": "NOT_EXCLUDED_BY_THIS_SCREEN", "unique_slow_identification": false } }, { "case": "thermal_constraint_withheld", "upstream": { "rho": "1", "p": "0.0878204645670042230432470757935007265210837539139773715461502865048541875423312904860940378", "u": [ "0.750000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", "0.433012701892219323381861585376468091735701313452595157013951744862983254227200009270286546", "0E-90" ], "B": [ 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rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0.0, "evaluation_boost": [ 0.0, -0.26971960727105615, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 1.1102230246251565e-16, "normal_momentum": 2.220446049250313e-16, "t1_momentum": -5.551115123125783e-17, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 1.1102230246251565e-16 }, "characteristics": { "left": { "slow": 0.41923270369853305, "alfven_n": 0.9128709291752769, "fast": 1.088740121085252 }, "right": { "slow": 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"normal": [ 0.8660254037844386, 0.5, 0.0 ], "t1": [ -0.5, 0.8660254037844386, 0.0 ], "t2": [ 0.0, 0.0, 1.0 ] }, "left": { "rho": 1.0, "p": 0.15, "u": [ 0.8660254037844386, -0.5, 0.0 ], "B": null }, "right": { "rho": 2.1677737267462858, "p": 0.6888510171415839, "u": [ 0.3994999077160591, -0.039439214542112286, 0.0 ], "B": null }, "uncertainty": { "mode": "exact_synthetic" } }, "result": { "case_id": "R99_full_state_API_without_B", "status": "INSUFFICIENT_DATA", "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": {}, "missing": [ "left.B", "right.B" ], "result_sentence": "Supply or constrain: left.B, right.B. Missing values were not replaced by zero.", "next_action": "Supply or constrain: left.B, right.B. Missing values were not replaced by zero." } }, "necessary_Mach_boundary": { "M2_lower": "214024892796131276712126293648343393038018945291684322259086766048779/60298733653652724468355436721806909385945887486791614981526466570407", "M2_upper": "285366523728175035616168391531124524050691927055579096345449021398373/80398311538203632624473915629075879181261183315722153308701955427209", "value_decimal": "3.54940941256676394733262491737897271955489180652595627643226466126265393717469734315427740", "meaning": "Boundary for this necessary fast condition, not a sufficient fast criterion or instrument requirement" } }