{ "status": "PASS", "scope": "Conditional single-jump regular evolutionary family selection; not an observed shock classification.", "frozen_G0_Vn_km_s": 705.5353411601552, "central": { "scenario": "R110_C0", "fL_MHz": 132, "fU_MHz": 165, "T_MK": 1.8, "compression": 1.5625, "wcrit_km_s": 308.61476631452746, "ucrit_km_s": 396.92057484562775 }, "whole_radio_temperature_domain": { "maximum_wcrit_km_s": 428.0217806904416, "sufficient_upper_u1n_km_s": 277.51356046971364, "conditional_onset_threshold_range_km_s": [ 277.51356046971364, 483.1509740090886 ], "extrema_proof": "wcrit^2=10*kB*T*r/(mp*(4-r)) increases with T and r; r=(fU/fL)^2 increases with fU and decreases with fL. Extrema therefore occur at the stated paired source corners." }, "thresholds": [ { "scenario": "R110_C0", "fL_MHz": 132, "fU_MHz": 165, "T_MK": 1.8, "compression": 1.5625, "wcrit_km_s": 308.61476631452746, "ucrit_km_s": 396.92057484562775 }, { "scenario": "R109_corner_0", "fL_MHz": 127, "fU_MHz": 150, "T_MK": 1.4, "compression": 1.3950027900055797, "wcrit_km_s": 248.76579964592608, "ucrit_km_s": 456.7695415142291 }, { "scenario": "R109_corner_1", "fL_MHz": 127, "fU_MHz": 150, "T_MK": 2.2, "compression": 1.3950027900055797, "wcrit_km_s": 311.84443324201794, "ucrit_km_s": 393.69090791813727 }, { "scenario": "R109_corner_2", "fL_MHz": 127, "fU_MHz": 180, "T_MK": 1.4, "compression": 2.008804017608035, "wcrit_km_s": 341.44326205334414, "ucrit_km_s": 364.09207910681107 }, { "scenario": "R109_corner_3", "fL_MHz": 127, "fU_MHz": 180, "T_MK": 2.2, "compression": 2.008804017608035, "wcrit_km_s": 428.0217806904416, "ucrit_km_s": 277.51356046971364 }, { "scenario": "R109_corner_4", "fL_MHz": 137, "fU_MHz": 150, "T_MK": 1.4, "compression": 1.1987852309659546, "wcrit_km_s": 222.3843671510666, "ucrit_km_s": 483.1509740090886 }, { "scenario": "R109_corner_5", "fL_MHz": 137, "fU_MHz": 150, "T_MK": 2.2, "compression": 1.1987852309659546, "wcrit_km_s": 278.7735574376206, "ucrit_km_s": 426.76178372253463 }, { "scenario": "R109_corner_6", "fL_MHz": 137, "fU_MHz": 180, "T_MK": 1.4, "compression": 1.7262507325909744, "wcrit_km_s": 296.2016123815303, "ucrit_km_s": 409.3337287786249 }, { "scenario": "R109_corner_7", "fL_MHz": 137, "fU_MHz": 180, "T_MK": 2.2, "compression": 1.7262507325909744, "wcrit_km_s": 371.30837144800773, "ucrit_km_s": 334.2269697121475 } ], "regular_FAST_certificate": { "tests": { "W": { "status": "PASS", "minimum_exact": "11193/18769", "maximum_exact": "113045/16129", "covering_cells": 256 }, "pressure_numerator": { "status": "PASS", "minimum_exact": "51936866891/6611856250609", "maximum_exact": "2565465839/260144641", "covering_cells": 256 }, "upstream_characteristic_numerator_times_r": { "status": "PASS", "minimum_exact": "623242402692/6611856250609", "maximum_exact": "255311358998400/4195872914689", "covering_cells": 256 }, "negative_downstream_characteristic_numerator": { "status": "PASS", "minimum_exact": "0", "maximum_exact": "135598765487020/4195872914689", "covering_cells": 256, "strict_positive_anchor_exact": "5512043080453/13223712501218", "boundary_handling": "The closed box includes the excluded eta=1,t=1 degeneracy. All coefficients are nonnegative; every r-index coefficient at local eta-index=0,t-index=0 is strictly positive. Their Bernstein weights are positive for local eta<1,t<1, proving strict positivity on the declared open domain. At interior cell boundaries choose the next cell with local coordinate zero. No guard or domain was changed." } }, "domain": "r in saved radio enclosure; 0wcrit and a nondegenerate angle 00; M=(4-r)*(1-eta)>0 in the open domain.", "excluded_endpoints": "eta=1 is the gas/zero-tangential-field boundary; t=1 is switch-on; eta=0 has zero upstream pressure. No endpoint is forced into an ordinary class." }, "regular_SLOW_onset_certificate": { "tests": { "negative_W": { "status": "PASS", "minimum_exact": "2548160695/352275361", "maximum_exact": "3325321415965925605/366570189281961604", "covering_cells": 32 }, "negative_pressure_numerator": { "status": "PASS", "minimum_exact": "36301606893109/6611856250609", "maximum_exact": "1327147550788021/104896822867225", "covering_cells": 32 }, "upstream_characteristic_numerator": { "status": "PASS", "minimum_exact": "38028750212180/6611856250609", "maximum_exact": "380662768141390879/10489682286722500", "covering_cells": 32 }, "negative_downstream_characteristic_numerator": { "status": "PASS", "minimum_exact": "997532146815693580/124097929967680321", "maximum_exact": "37050546222099758096/338376171205094405", "covering_cells": 32 } }, "domain": "h=2, b=bcrit*(1+zeta), 01 and r*h>1. With W<0, the certified numerator signs give upstream cslow<10.", "entropy": "At zeta=0 the gas-Hugoniot entropy is positive for r>1. For W<0, d(p2/b)/db=-(r-1)^3/(b^2*r*W)>0, so entropy remains positive as zeta increases.", "meaning": "Checked regular SLOW solutions exist arbitrarily close above ucrit as theta approaches zero. ucrit is the infimum of onset when geometry and field strength are unbounded, not proof of SLOW at every larger flow or fixed angle.", "not_an_observation": "h=2 and its resulting small theta are explicit model coordinates. No solar normal/field/flow is inferred." }, "finite_controls": [ { "source": "R110_C0", "zeta": 0.0001, "w1_km_s": 308.5993367334207, "u1n_km_s": 396.9360044267345, "u_minus_threshold_km_s": 0.015429581106729984, "theta_deg": 0.5163873588644539, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.3120312, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.012746170596101804, 0.0 ] }, "right": { "rho": 1.5625, "p": 0.6720685135135136, "u": [ 0.64, 0.004771537233175146, 0.0 ], "B": [ 1.4142135623730951, -0.009372184261839563, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 3.468795293054091e-16, "entropy_over_cv": 0.02344526943548564, "characteristics": { "left": { "fast": 1.4142911816033086, "alfven_n": 1.4142135623730951, "slow": 0.7211067317006427 }, "right": { "fast": 1.131427312943917, "alfven_n": 1.1313708498984762, "slow": 0.8466413247779757 } }, "baseline_diagnosis": { "case_id": "R135_onset_R110_C00.0001", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.002385768616587573, 0.0 ], "rh_scaled_inf": 3.468904108013248e-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": -3.468904108013248e-16 }, "characteristics": { "left": { "slow": 0.7211067317006427, "alfven_n": 1.4142135623730951, "fast": 1.4142911816033086 }, "right": { "slow": 0.8466413247779757, "alfven_n": 1.1313708498984762, "fast": 1.131427312943917 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.64 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.5625, "pressure_ratio": 2.153850363404408, "entropy_over_cv": 0.02344526943548564, "tangential_field_ratio": 0.7352941176470589 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 5.551115123125783e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R110_C0", "zeta": 1e-05, "w1_km_s": 308.6132232522688, "u1n_km_s": 396.9221179078864, "u_minus_threshold_km_s": 0.001543062258633654, "theta_deg": 0.16330000026793673, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.31200312, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.004030693052889468, 0.0 ] }, "right": { "rho": 1.5625, "p": 0.6720068513513513, "u": [ 0.64, 0.0015088925597186384, 0.0 ], "B": [ 1.4142135623730951, -0.0029637448918304913, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 5.204072662568735e-16, "entropy_over_cv": 0.023443510460981254, "characteristics": { "left": { "fast": 1.4142213245118072, "alfven_n": 1.4142135623730951, "slow": 0.7211099027073177 }, "right": { "fast": 1.1313764963159942, "alfven_n": 1.1313708498984762, "slow": 0.8466405100829248 } }, "baseline_diagnosis": { "case_id": "R135_onset_R110_C01e-05", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0007544462798593192, 0.0 ], "rh_scaled_inf": 5.204088989871443e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 8.673617379884035e-19, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -5.204088989871443e-16 }, "characteristics": { "left": { "slow": 0.7211099027073177, "alfven_n": 1.4142135623730951, "fast": 1.4142213245118072 }, "right": { "slow": 0.8466405100829248, "alfven_n": 1.1313708498984762, "fast": 1.1313764963159942 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.64 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.5625, "pressure_ratio": 2.1538465748398647, "entropy_over_cv": 0.023443510460981254, "tangential_field_ratio": 0.7352941176470589 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 5.551115123125783e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R110_C0", "zeta": 1e-06, "w1_km_s": 308.61461200726, "u1n_km_s": 396.9207291528952, "u_minus_threshold_km_s": 0.00015430726745080392, "theta_deg": 0.051640120115981354, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.31200031199999995, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0012746170595103244, 0.0 ] }, "right": { "rho": 1.5625, "p": 0.672000685135135, "u": [ 0.64, 0.00047715372328013345, 0.0 ], "B": [ 1.4142135623730951, -0.0009372184261105327, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 1.7347202170763189e-16, "entropy_over_cv": 0.023443334545946826, "characteristics": { "left": { "fast": 1.4142143385891233, "alfven_n": 1.4142135623730951, "slow": 0.7211102198537872 }, "right": { "fast": 1.1313714145413576, "alfven_n": 1.1313708498984762, "slow": 0.8466404285950799 } }, "baseline_diagnosis": { "case_id": "R135_onset_R110_C01e-06", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.00023857686164006672, 0.0 ], "rh_scaled_inf": 5.204162284009827e-16, "rh_components": { "mass": 0.0, "normal_momentum": -4.440892098500626e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -2.168404344971009e-19, "t2_induction": 0.0, "energy": -5.204162284009827e-16 }, "characteristics": { "left": { "slow": 0.7211102198537872, "alfven_n": 1.4142135623730951, "fast": 1.4142143385891233 }, "right": { "slow": 0.8466404285950799, "alfven_n": 1.1313708498984762, "fast": 1.1313714145413576 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.64 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.5625, "pressure_ratio": 2.1538461959459037, "entropy_over_cv": 0.023443334545946826, "tangential_field_ratio": 0.7352941176470589 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 5.551115123125783e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R110_C0", "zeta": 1e-07, "w1_km_s": 308.6147508837903, "u1n_km_s": 396.9205902763649, "u_minus_threshold_km_s": 1.543073716447907e-05, "theta_deg": 0.016330043808141417, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.3120000312, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.00040306930543948933, 0.0 ] }, "right": { "rho": 1.5625, "p": 0.6720000685135135, "u": [ 0.64, 0.00015088925602821954, 0.0 ], "B": [ 1.4142135623730951, -0.00029637448929374215, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 1.7347231500862069e-16, "entropy_over_cv": 0.02344331695426749, "characteristics": { "left": { "fast": 1.4142136399947198, "alfven_n": 1.4142135623730951, "slow": 0.7211102515688922 }, "right": { "fast": 1.1313709063627757, "alfven_n": 1.1313708498984762, "slow": 0.8466404204461119 } }, "baseline_diagnosis": { "case_id": "R135_onset_R110_C01e-07", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 7.544462801410977e-05, 0.0 ], "rh_scaled_inf": 5.204169613537213e-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": -5.204169613537213e-16 }, "characteristics": { "left": { "slow": 0.7211102515688921, "alfven_n": 1.4142135623730951, "fast": 1.4142136399947198 }, "right": { "slow": 0.8466404204461119, "alfven_n": 1.1313708498984762, "fast": 1.1313709063627757 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.64 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.5625, "pressure_ratio": 2.1538461580561323, "entropy_over_cv": 0.02344331695426749, "tangential_field_ratio": 0.7352941176470588 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 5.551115123125783e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R110_C0", "zeta": 1e-08, "w1_km_s": 308.6147647714536, "u1n_km_s": 396.9205763887016, "u_minus_threshold_km_s": 1.5430738358190865e-06, "theta_deg": 0.005164013374730414, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.31200000312, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0001274617054285306, 0.0 ] }, "right": { "rho": 1.5625, "p": 0.6720000068513514, "u": [ 0.64, 4.7715372132414456e-05, 0.0 ], "B": [ 1.4142135623730951, -9.372184222686073e-05, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 2.710505431213761e-20, "entropy_over_cv": 0.023443315195098124, "characteristics": { "left": { "fast": 1.4142135701352578, "alfven_n": 1.4142135623730951, "slow": 0.7211102547404072 }, "right": { "fast": 1.131370855544906, "alfven_n": 1.1313708498984762, "slow": 0.8466404196312134 } }, "baseline_diagnosis": { "case_id": "R135_onset_R110_C01e-08", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 2.3857686066207228e-05, 0.0 ], "rh_scaled_inf": 1.3552527156068805e-20, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.3552527156068805e-20, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.7211102547404072, "alfven_n": 1.4142135623730951, "fast": 1.4142135701352578 }, "right": { "slow": 0.8466404196312132, "alfven_n": 1.1313708498984762, "fast": 1.1313708555449065 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.64 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.5625, "pressure_ratio": 2.153846154267152, "entropy_over_cv": 0.023443315195098124, "tangential_field_ratio": 0.7352941176470588 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 5.551115123125783e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_0", "zeta": 0.0001, "w1_km_s": 248.75336228873783, "u1n_km_s": 456.7819788714174, "u_minus_threshold_km_s": 0.012437357188247233, "theta_deg": 0.4911859947053081, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.3735129031111112, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.012124085210064105, 0.0 ] }, "right": { "rho": 1.3950027900055797, "p": 0.6566973169129751, "u": [ 0.7168444444444446, 0.003783639547659811, 0.0 ], "B": [ 1.4142135623730951, -0.009448648028348251, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 4.64551381602935e-16, "entropy_over_cv": 0.00944329822605372, "characteristics": { "left": { "fast": 1.414289013478894, "alfven_n": 1.4142135623730951, "slow": 0.7889582276523034 }, "right": { "fast": 1.1974265007107296, "alfven_n": 1.1973674828092207, "slow": 0.8857232642428012 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_00.0001", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0018918197738299054, 0.0 ], "rh_scaled_inf": 6.194150810545017e-16, "rh_components": { "mass": 0.0, "normal_momentum": -4.440892098500626e-16, "t1_momentum": -1.734723475976807e-18, "t2_momentum": 0.0, "t1_induction": -1.734723475976807e-18, "t2_induction": 0.0, "energy": -6.194150810545017e-16 }, "characteristics": { "left": { "slow": 0.7889582276523034, "alfven_n": 1.4142135623730951, "fast": 1.414289013478894 }, "right": { "slow": 0.8857232642428011, "alfven_n": 1.1973674828092207, "fast": 1.1974265007107299 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.7168444444444446 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.3950027900055797, "pressure_ratio": 1.7581650096773853, "entropy_over_cv": 0.00944329822605372, "tangential_field_ratio": 0.7793287381801808 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.4432899320127035e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_0", "zeta": 1e-05, "w1_km_s": 248.7645558262565, "u1n_km_s": 456.77078533389874, "u_minus_threshold_km_s": 0.0012438196695825354, "theta_deg": 0.15533007452190045, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.3734792903111112, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.003833972380973089, 0.0 ] }, "right": { "rho": 1.3950027900055797, "p": 0.6566377316912975, "u": [ 0.7168444444444446, 0.0011964918815684012, 0.0 ], "B": [ 1.4142135623730951, -0.002987924857881421, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.009442554478572895, "characteristics": { "left": { "fast": 1.4142211076853974, "alfven_n": 1.4142135623730951, "slow": 0.7889606085053665 }, "right": { "fast": 1.1973733847158685, "alfven_n": 1.1973674828092207, "slow": 0.8857223697020788 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_01e-05", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0005982459407842006, 0.0 ], "rh_scaled_inf": 7.74370781237057e-16, "rh_components": { "mass": 0.0, "normal_momentum": -4.440892098500626e-16, "t1_momentum": -8.673617379884035e-19, "t2_momentum": 0.0, "t1_induction": -4.336808689942018e-19, "t2_induction": 0.0, "energy": -7.74370781237057e-16 }, "characteristics": { "left": { "slow": 0.7889606085053665, "alfven_n": 1.4142135623730951, "fast": 1.4142211076853974 }, "right": { "slow": 0.8857223697020788, "alfven_n": 1.1973674828092207, "fast": 1.1973733847158685 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.7168444444444446 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.3950027900055797, "pressure_ratio": 1.7581637020470748, "entropy_over_cv": 0.009442554478572895, "tangential_field_ratio": 0.7793287381801809 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.4432899320127035e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_0", "zeta": 1e-06, "w1_km_s": 248.76567526311953, "u1n_km_s": 456.7696658970357, "u_minus_threshold_km_s": 0.0001243828065469188, "theta_deg": 0.04911979076049201, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.37347592903111115, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0012124085208916995, 0.0 ] }, "right": { "rho": 1.3950027900055797, "p": 0.6566317731691296, "u": [ 0.7168444444444446, 0.00037836395473018233, 0.0 ], "B": [ 1.4142135623730951, -0.0009448648027454277, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 1.5487616203342594e-16, "entropy_over_cv": 0.009442480096431227, "characteristics": { "left": { "fast": 1.4142143169063426, "alfven_n": 1.4142135623730951, "slow": 0.7889608466267938 }, "right": { "fast": 1.1973680730010505, "alfven_n": 1.1973674828092207, "slow": 0.8857222802286763 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_01e-06", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.00018918197736509117, 0.0 ], "rh_scaled_inf": 1.5487619514100618e-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": -1.5487619514100618e-16 }, "characteristics": { "left": { "slow": 0.7889608466267937, "alfven_n": 1.4142135623730951, "fast": 1.4142143169063428 }, "right": { "slow": 0.8857222802286763, "alfven_n": 1.1973674828092207, "fast": 1.1973680730010505 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.7168444444444446 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.3950027900055797, "pressure_ratio": 1.7581635712710981, "entropy_over_cv": 0.009442480096431227, "tangential_field_ratio": 0.7793287381801809 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.4432899320127035e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_0", "zeta": 1e-07, "w1_km_s": 248.765787207637, "u1n_km_s": 456.7695539525182, "u_minus_threshold_km_s": 1.2438289076044384e-05, "theta_deg": 0.015533045136203025, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.3734755929031112, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0003833972383554808, 0.0 ] }, "right": { "rho": 1.3950027900055797, "p": 0.656631177316913, "u": [ 0.7168444444444446, 0.00011964918823740939, 0.0 ], "B": [ 1.4142135623730951, -0.00029879248598934293, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 3.0975279144510157e-16, "entropy_over_cv": 0.009442472658143242, "characteristics": { "left": { "fast": 1.4142136378264403, "alfven_n": 1.4142135623730951, "slow": 0.7889608704392976 }, "right": { "fast": 1.1973675418284155, "alfven_n": 1.1973674828092207, "slow": 0.8857222712811428 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_01e-07", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 5.9824594118704695e-05, 0.0 ], "rh_scaled_inf": 1.5487639903331818e-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": 1.5487639903331818e-16 }, "characteristics": { "left": { "slow": 0.7889608704392977, "alfven_n": 1.4142135623730951, "fast": 1.41421363782644 }, "right": { "slow": 0.8857222712811424, "alfven_n": 1.1973674828092207, "fast": 1.1973675418284158 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.7168444444444446 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.3950027900055797, "pressure_ratio": 1.7581635581933712, "entropy_over_cv": 0.009442472658143242, "tangential_field_ratio": 0.779328738180181 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.4432899320127035e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_0", "zeta": 1e-08, "w1_km_s": 248.7657984020971, "u1n_km_s": 456.76954275805815, "u_minus_threshold_km_s": 1.2438289900273958e-06, "theta_deg": 0.004911980254417038, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.3734755592903112, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.000121240851768806, 0.0 ] }, "right": { "rho": 1.3950027900055797, "p": 0.6566311177316911, "u": [ 0.7168444444444446, 3.783639537304026e-05, 0.0 ], "B": [ 1.4142135623730951, -9.448648002487392e-05, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 1.5487641909150217e-16, "entropy_over_cv": 0.009442471914313466, "characteristics": { "left": { "fast": 1.4142135699184297, "alfven_n": 1.4142135623730951, "slow": 0.7889608728205518 }, "right": { "fast": 1.1973674887111403, "alfven_n": 1.1973674828092207, "slow": 0.8857222703863875 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_01e-08", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 1.891819768652013e-05, 0.0 ], "rh_scaled_inf": 1.5487641942257898e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 2.710505431213761e-20, "t2_momentum": 0.0, "t1_induction": -2.710505431213761e-20, "t2_induction": 0.0, "energy": 1.5487641942257898e-16 }, "characteristics": { "left": { "slow": 0.7889608728205518, "alfven_n": 1.4142135623730951, "fast": 1.4142135699184297 }, "right": { "slow": 0.8857222703863873, "alfven_n": 1.1973674828092207, "fast": 1.1973674887111403 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.7168444444444446 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.3950027900055797, "pressure_ratio": 1.758163556885597, "entropy_over_cv": 0.009442471914313466, "tangential_field_ratio": 0.7793287381801809 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.4432899320127035e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_1", "zeta": 0.0001, "w1_km_s": 311.8288421896751, "u1n_km_s": 393.70649897048014, "u_minus_threshold_km_s": 0.01559105234287017, "theta_deg": 0.4911859947053081, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.3735129031111112, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.012124085210064105, 0.0 ] }, "right": { "rho": 1.3950027900055797, "p": 0.6566973169129751, "u": [ 0.7168444444444446, 0.003783639547659811, 0.0 ], "B": [ 1.4142135623730951, -0.009448648028348251, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 4.64551381602935e-16, "entropy_over_cv": 0.00944329822605372, "characteristics": { "left": { "fast": 1.414289013478894, "alfven_n": 1.4142135623730951, "slow": 0.7889582276523034 }, "right": { "fast": 1.1974265007107296, "alfven_n": 1.1973674828092207, "slow": 0.8857232642428012 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_10.0001", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0018918197738299054, 0.0 ], "rh_scaled_inf": 6.194150810545017e-16, "rh_components": { "mass": 0.0, "normal_momentum": -4.440892098500626e-16, "t1_momentum": -1.734723475976807e-18, "t2_momentum": 0.0, "t1_induction": -1.734723475976807e-18, "t2_induction": 0.0, "energy": -6.194150810545017e-16 }, "characteristics": { "left": { "slow": 0.7889582276523034, "alfven_n": 1.4142135623730951, "fast": 1.414289013478894 }, "right": { "slow": 0.8857232642428011, "alfven_n": 1.1973674828092207, "fast": 1.1974265007107299 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.7168444444444446 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.3950027900055797, "pressure_ratio": 1.7581650096773853, "entropy_over_cv": 0.00944329822605372, "tangential_field_ratio": 0.7793287381801808 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.4432899320127035e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_1", "zeta": 1e-05, "w1_km_s": 311.8428740315458, "u1n_km_s": 393.6924671286094, "u_minus_threshold_km_s": 0.0015592104721235955, "theta_deg": 0.15533007452190045, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.3734792903111112, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.003833972380973089, 0.0 ] }, "right": { "rho": 1.3950027900055797, "p": 0.6566377316912975, "u": [ 0.7168444444444446, 0.0011964918815684012, 0.0 ], "B": [ 1.4142135623730951, -0.002987924857881421, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.009442554478572895, "characteristics": { "left": { "fast": 1.4142211076853974, "alfven_n": 1.4142135623730951, "slow": 0.7889606085053665 }, "right": { "fast": 1.1973733847158685, "alfven_n": 1.1973674828092207, "slow": 0.8857223697020788 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_11e-05", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0005982459407842006, 0.0 ], "rh_scaled_inf": 7.74370781237057e-16, "rh_components": { "mass": 0.0, "normal_momentum": -4.440892098500626e-16, "t1_momentum": -8.673617379884035e-19, "t2_momentum": 0.0, "t1_induction": -4.336808689942018e-19, "t2_induction": 0.0, "energy": -7.74370781237057e-16 }, "characteristics": { "left": { "slow": 0.7889606085053665, "alfven_n": 1.4142135623730951, "fast": 1.4142211076853974 }, "right": { "slow": 0.8857223697020788, "alfven_n": 1.1973674828092207, "fast": 1.1973733847158685 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.7168444444444446 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.3950027900055797, "pressure_ratio": 1.7581637020470748, "entropy_over_cv": 0.009442554478572895, "tangential_field_ratio": 0.7793287381801809 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.4432899320127035e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_1", "zeta": 1e-06, "w1_km_s": 311.84427731991826, "u1n_km_s": 393.69106384023695, "u_minus_threshold_km_s": 0.00015592209967962845, "theta_deg": 0.04911979076049201, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.37347592903111115, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0012124085208916995, 0.0 ] }, "right": { "rho": 1.3950027900055797, "p": 0.6566317731691296, "u": [ 0.7168444444444446, 0.00037836395473018233, 0.0 ], "B": [ 1.4142135623730951, -0.0009448648027454277, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 1.5487616203342594e-16, "entropy_over_cv": 0.009442480096431227, "characteristics": { "left": { "fast": 1.4142143169063426, "alfven_n": 1.4142135623730951, "slow": 0.7889608466267938 }, "right": { "fast": 1.1973680730010505, "alfven_n": 1.1973674828092207, "slow": 0.8857222802286763 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_11e-06", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.00018918197736509117, 0.0 ], "rh_scaled_inf": 1.5487619514100618e-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": -1.5487619514100618e-16 }, "characteristics": { "left": { "slow": 0.7889608466267937, "alfven_n": 1.4142135623730951, "fast": 1.4142143169063428 }, "right": { "slow": 0.8857222802286763, "alfven_n": 1.1973674828092207, "fast": 1.1973680730010505 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.7168444444444446 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.3950027900055797, "pressure_ratio": 1.7581635712710981, "entropy_over_cv": 0.009442480096431227, "tangential_field_ratio": 0.7793287381801809 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.4432899320127035e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_1", "zeta": 1e-07, "w1_km_s": 311.84441764979744, "u1n_km_s": 393.6909235103578, "u_minus_threshold_km_s": 1.55922205067327e-05, "theta_deg": 0.015533045136203025, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.3734755929031112, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0003833972383554808, 0.0 ] }, "right": { "rho": 1.3950027900055797, "p": 0.656631177316913, "u": [ 0.7168444444444446, 0.00011964918823740939, 0.0 ], "B": [ 1.4142135623730951, -0.00029879248598934293, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 3.0975279144510157e-16, "entropy_over_cv": 0.009442472658143242, "characteristics": { "left": { "fast": 1.4142136378264403, "alfven_n": 1.4142135623730951, "slow": 0.7889608704392976 }, "right": { "fast": 1.1973675418284155, "alfven_n": 1.1973674828092207, "slow": 0.8857222712811428 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_11e-07", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 5.9824594118704695e-05, 0.0 ], "rh_scaled_inf": 1.5487639903331818e-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": 1.5487639903331818e-16 }, "characteristics": { "left": { "slow": 0.7889608704392977, "alfven_n": 1.4142135623730951, "fast": 1.41421363782644 }, "right": { "slow": 0.8857222712811424, "alfven_n": 1.1973674828092207, "fast": 1.1973675418284158 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.7168444444444446 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.3950027900055797, "pressure_ratio": 1.7581635581933712, "entropy_over_cv": 0.009442472658143242, "tangential_field_ratio": 0.779328738180181 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.4432899320127035e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_1", "zeta": 1e-08, "w1_km_s": 311.8444316827958, "u1n_km_s": 393.6909094773594, "u_minus_threshold_km_s": 1.5592221416227403e-06, "theta_deg": 0.004911980254417038, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.3734755592903112, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.000121240851768806, 0.0 ] }, "right": { "rho": 1.3950027900055797, "p": 0.6566311177316911, "u": [ 0.7168444444444446, 3.783639537304026e-05, 0.0 ], "B": [ 1.4142135623730951, -9.448648002487392e-05, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 1.5487641909150217e-16, "entropy_over_cv": 0.009442471914313466, "characteristics": { "left": { "fast": 1.4142135699184297, "alfven_n": 1.4142135623730951, "slow": 0.7889608728205518 }, "right": { "fast": 1.1973674887111403, "alfven_n": 1.1973674828092207, "slow": 0.8857222703863875 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_11e-08", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 1.891819768652013e-05, 0.0 ], "rh_scaled_inf": 1.5487641942257898e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 2.710505431213761e-20, "t2_momentum": 0.0, "t1_induction": -2.710505431213761e-20, "t2_induction": 0.0, "energy": 1.5487641942257898e-16 }, "characteristics": { "left": { "slow": 0.7889608728205518, "alfven_n": 1.4142135623730951, "fast": 1.4142135699184297 }, "right": { "slow": 0.8857222703863873, "alfven_n": 1.1973674828092207, "fast": 1.1973674887111403 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.7168444444444446 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.3950027900055797, "pressure_ratio": 1.758163556885597, "entropy_over_cv": 0.009442471914313466, "tangential_field_ratio": 0.7793287381801809 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.4432899320127035e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_2", "zeta": 0.0001, "w1_km_s": 341.42619117054704, "u1n_km_s": 364.10914998960817, "u_minus_threshold_km_s": 0.017070882797099785, "theta_deg": 0.5740608143361468, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.19826673827160496, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.01416983524845949, 0.0 ] }, "right": { "rho": 2.008804017608035, "p": 0.7005139997761088, "u": [ 0.49780864197530866, 0.006699212814459227, 0.0 ], "B": [ 1.4142135623730951, -0.009432776438743554, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.09963518247096825, "characteristics": { "left": { "fast": 1.4142985959342633, "alfven_n": 1.4142135623730951, "slow": 0.5748085155557011 }, "right": { "fast": 0.9978595503228131, "alfven_n": 0.9978062356743506, "slow": 0.7623261115101456 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_20.0001", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0033496064072296135, 0.0 ], "rh_scaled_inf": 4.440892098500626e-16, "rh_components": { "mass": 0.0, "normal_momentum": -4.440892098500626e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -4.440892098500626e-16 }, "characteristics": { "left": { "slow": 0.574808515555701, "alfven_n": 1.4142135623730951, "fast": 1.4142985959342635 }, "right": { "slow": 0.7623261115101457, "alfven_n": 0.9978062356743506, "fast": 0.9978595503228129 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.49780864197530866 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 2.008804017608035, "pressure_ratio": 3.533189711410277, "entropy_over_cv": 0.09963518247096825, "tangential_field_ratio": 0.6656941505208441 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.5543122344752192e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_2", "zeta": 1e-05, "w1_km_s": 341.4415548498379, "u1n_km_s": 364.0937863103173, "u_minus_threshold_km_s": 0.0017072035062142277, "theta_deg": 0.1815394360705945, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.19824889604938276, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0044808953454669774, 0.0 ] }, "right": { "rho": 2.008804017608035, "p": 0.7004458444220553, "u": [ 0.49780864197530866, 0.002118477102397265, 0.0 ], "B": [ 1.4142135623730951, -0.0029829058205734435, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.09962787943757712, "characteristics": { "left": { "fast": 1.4142220659899702, "alfven_n": 1.4142135623730951, "slow": 0.574813755262632 }, "right": { "fast": 0.9978115672589869, "alfven_n": 0.9978062356743506, "slow": 0.7623256831621003 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_21e-05", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0010592385511986324, 0.0 ], "rh_scaled_inf": 7.771561172376096e-16, "rh_components": { "mass": 0.0, "normal_momentum": -4.440892098500626e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -7.771561172376096e-16 }, "characteristics": { "left": { "slow": 0.574813755262632, "alfven_n": 1.4142135623730951, "fast": 1.4142220659899702 }, "right": { "slow": 0.7623256831621004, "alfven_n": 0.9978062356743506, "fast": 0.9978115672589867 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.49780864197530866 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 2.008804017608035, "pressure_ratio": 3.533163908502057, "entropy_over_cv": 0.09962787943757712, "tangential_field_ratio": 0.665694150520844 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.5543122344752192e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_2", "zeta": 1e-06, "w1_km_s": 341.4430913318411, "u1n_km_s": 364.0922498283141, "u_minus_threshold_km_s": 0.00017072150302510636, "theta_deg": 0.05740798320305723, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.19824711182716048, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0014169835246626546, 0.0 ] }, "right": { "rho": 2.008804017608035, "p": 0.7004390288866498, "u": [ 0.49780864197530866, 0.0006699212813592649, 0.0 ], "B": [ 1.4142135623730951, -0.0009432776437523374, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 2.220446049250313e-16, "entropy_over_cv": 0.09962714905900438, "characteristics": { "left": { "fast": 1.4142144127373903, "alfven_n": 1.4142135623730951, "slow": 0.5748142793054253 }, "right": { "fast": 0.997806768834012, "alfven_n": 0.9978062356743506, "slow": 0.7623256403163966 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_21e-06", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0003349606406796324, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 2.168404344971009e-19, "t2_momentum": 0.0, "t1_induction": -1.0842021724855044e-19, "t2_induction": 0.0, "energy": -2.220446049250313e-16 }, "characteristics": { "left": { "slow": 0.5748142793054253, "alfven_n": 1.4142135623730951, "fast": 1.4142144127373903 }, "right": { "slow": 0.7623256403163966, "alfven_n": 0.9978062356743506, "fast": 0.9978067688340121 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.49780864197530866 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 2.008804017608035, "pressure_ratio": 3.533161327955787, "entropy_over_cv": 0.09962714905900438, "tangential_field_ratio": 0.6656941505208441 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.5543122344752192e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_2", "zeta": 1e-07, "w1_km_s": 341.4432449811823, "u1n_km_s": 364.0920961789729, "u_minus_threshold_km_s": 1.707216182467164e-05, "theta_deg": 0.018154003745363616, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.1982469334049383, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.00044808953443676837, 0.0 ] }, "right": { "rho": 2.008804017608035, "p": 0.7004383473331094, "u": [ 0.49780864197530866, 0.0002118477101877541, 0.0 ], "B": [ 1.4142135623730951, -0.000298290581984165, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.09962707602039478, "characteristics": { "left": { "fast": 1.4142136474095508, "alfven_n": 1.4142135623730951, "slow": 0.5748143317104256 }, "right": { "fast": 0.9978062889903286, "alfven_n": 0.9978062356743506, "slow": 0.7623256360317172 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_21e-07", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.00010592385509387705, 0.0 ], "rh_scaled_inf": 4.440892098500626e-16, "rh_components": { "mass": 0.0, "normal_momentum": -4.440892098500626e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.0842021724855044e-19, "t2_induction": 0.0, "energy": -3.3306690738754696e-16 }, "characteristics": { "left": { "slow": 0.5748143317104256, "alfven_n": 1.4142135623730951, "fast": 1.4142136474095508 }, "right": { "slow": 0.7623256360317172, "alfven_n": 0.9978062356743506, "fast": 0.9978062889903287 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.49780864197530866 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 2.008804017608035, "pressure_ratio": 3.533161069898606, "entropy_over_cv": 0.09962707602039478, "tangential_field_ratio": 0.665694150520844 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.5543122344752192e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_2", "zeta": 1e-08, "w1_km_s": 341.44326034612783, "u1n_km_s": 364.0920808140274, "u_minus_threshold_km_s": 1.7072163132070273e-06, "theta_deg": 0.005740800195949961, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.19824691556271606, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.00014169835181841484, 0.0 ] }, "right": { "rho": 2.008804017608035, "p": 0.7004382791777553, "u": [ 0.49780864197530866, 6.699212782963576e-05, 0.0 ], "B": [ 1.4142135623730951, -9.432776394396337e-05, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 0.0, "entropy_over_cv": 0.09962706871652616, "characteristics": { "left": { "fast": 1.414213570876741, "alfven_n": 1.4142135623730951, "slow": 0.5748143369509329 }, "right": { "fast": 0.9978062410059484, "alfven_n": 0.9978062356743506, "slow": 0.7623256356032482 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_21e-08", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 3.349606391481788e-05, 0.0 ], "rh_scaled_inf": 3.3306690738754696e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -2.710505431213761e-20, "t2_momentum": 0.0, "t1_induction": -1.3552527156068805e-20, "t2_induction": 0.0, "energy": -3.3306690738754696e-16 }, "characteristics": { "left": { "slow": 0.5748143369509329, "alfven_n": 1.4142135623730951, "fast": 1.414213570876741 }, "right": { "slow": 0.7623256356032482, "alfven_n": 0.9978062356743506, "fast": 0.9978062410059484 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.49780864197530866 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 2.008804017608035, "pressure_ratio": 3.5331610440928616, "entropy_over_cv": 0.09962706871652616, "tangential_field_ratio": 0.665694150520844 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.5543122344752192e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_3", "zeta": 0.0001, "w1_km_s": 428.00038120635503, "u1n_km_s": 277.5349599538002, "u_minus_threshold_km_s": 0.021399484086543907, "theta_deg": 0.5740608143361468, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.19826673827160496, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.01416983524845949, 0.0 ] }, "right": { "rho": 2.008804017608035, "p": 0.7005139997761088, "u": [ 0.49780864197530866, 0.006699212814459227, 0.0 ], "B": [ 1.4142135623730951, -0.009432776438743554, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.09963518247096825, "characteristics": { "left": { "fast": 1.4142985959342633, "alfven_n": 1.4142135623730951, "slow": 0.5748085155557011 }, "right": { "fast": 0.9978595503228131, "alfven_n": 0.9978062356743506, "slow": 0.7623261115101456 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_30.0001", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0033496064072296135, 0.0 ], "rh_scaled_inf": 4.440892098500626e-16, "rh_components": { "mass": 0.0, "normal_momentum": -4.440892098500626e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -4.440892098500626e-16 }, "characteristics": { "left": { "slow": 0.574808515555701, "alfven_n": 1.4142135623730951, "fast": 1.4142985959342635 }, "right": { "slow": 0.7623261115101457, "alfven_n": 0.9978062356743506, "fast": 0.9978595503228129 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.49780864197530866 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 2.008804017608035, "pressure_ratio": 3.533189711410277, "entropy_over_cv": 0.09963518247096825, "tangential_field_ratio": 0.6656941505208441 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.5543122344752192e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_3", "zeta": 1e-05, "w1_km_s": 428.0196405975888, "u1n_km_s": 277.5157005625664, "u_minus_threshold_km_s": 0.002140092852755515, "theta_deg": 0.1815394360705945, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.19824889604938276, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0044808953454669774, 0.0 ] }, "right": { "rho": 2.008804017608035, "p": 0.7004458444220553, "u": [ 0.49780864197530866, 0.002118477102397265, 0.0 ], "B": [ 1.4142135623730951, -0.0029829058205734435, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.09962787943757712, "characteristics": { "left": { "fast": 1.4142220659899702, "alfven_n": 1.4142135623730951, "slow": 0.574813755262632 }, "right": { "fast": 0.9978115672589869, "alfven_n": 0.9978062356743506, "slow": 0.7623256831621003 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_31e-05", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0010592385511986324, 0.0 ], "rh_scaled_inf": 7.771561172376096e-16, "rh_components": { "mass": 0.0, "normal_momentum": -4.440892098500626e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -7.771561172376096e-16 }, "characteristics": { "left": { "slow": 0.574813755262632, "alfven_n": 1.4142135623730951, "fast": 1.4142220659899702 }, "right": { "slow": 0.7623256831621004, "alfven_n": 0.9978062356743506, "fast": 0.9978115672589867 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.49780864197530866 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 2.008804017608035, "pressure_ratio": 3.533163908502057, "entropy_over_cv": 0.09962787943757712, "tangential_field_ratio": 0.665694150520844 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.5543122344752192e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_3", "zeta": 1e-06, "w1_km_s": 428.0215666797117, "u1n_km_s": 277.5137744804435, "u_minus_threshold_km_s": 0.0002140107298487237, "theta_deg": 0.05740798320305723, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.19824711182716048, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0014169835246626546, 0.0 ] }, "right": { "rho": 2.008804017608035, "p": 0.7004390288866498, "u": [ 0.49780864197530866, 0.0006699212813592649, 0.0 ], "B": [ 1.4142135623730951, -0.0009432776437523374, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 2.220446049250313e-16, "entropy_over_cv": 0.09962714905900438, "characteristics": { "left": { "fast": 1.4142144127373903, "alfven_n": 1.4142135623730951, "slow": 0.5748142793054253 }, "right": { "fast": 0.997806768834012, "alfven_n": 0.9978062356743506, "slow": 0.7623256403163966 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_31e-06", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0003349606406796324, 0.0 ], "rh_scaled_inf": 2.220446049250313e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 2.168404344971009e-19, "t2_momentum": 0.0, "t1_induction": -1.0842021724855044e-19, "t2_induction": 0.0, "energy": -2.220446049250313e-16 }, "characteristics": { "left": { "slow": 0.5748142793054253, "alfven_n": 1.4142135623730951, "fast": 1.4142144127373903 }, "right": { "slow": 0.7623256403163966, "alfven_n": 0.9978062356743506, "fast": 0.9978067688340121 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.49780864197530866 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 2.008804017608035, "pressure_ratio": 3.533161327955787, "entropy_over_cv": 0.09962714905900438, "tangential_field_ratio": 0.6656941505208441 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.5543122344752192e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_3", "zeta": 1e-07, "w1_km_s": 428.0217592893541, "u1n_km_s": 277.5135818708011, "u_minus_threshold_km_s": 2.140108745152247e-05, "theta_deg": 0.018154003745363616, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.1982469334049383, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.00044808953443676837, 0.0 ] }, "right": { "rho": 2.008804017608035, "p": 0.7004383473331094, "u": [ 0.49780864197530866, 0.0002118477101877541, 0.0 ], "B": [ 1.4142135623730951, -0.000298290581984165, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.09962707602039478, "characteristics": { "left": { "fast": 1.4142136474095508, "alfven_n": 1.4142135623730951, "slow": 0.5748143317104256 }, "right": { "fast": 0.9978062889903286, "alfven_n": 0.9978062356743506, "slow": 0.7623256360317172 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_31e-07", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.00010592385509387705, 0.0 ], "rh_scaled_inf": 4.440892098500626e-16, "rh_components": { "mass": 0.0, "normal_momentum": -4.440892098500626e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -1.0842021724855044e-19, "t2_induction": 0.0, "energy": -3.3306690738754696e-16 }, "characteristics": { "left": { "slow": 0.5748143317104256, "alfven_n": 1.4142135623730951, "fast": 1.4142136474095508 }, "right": { "slow": 0.7623256360317172, "alfven_n": 0.9978062356743506, "fast": 0.9978062889903287 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.49780864197530866 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 2.008804017608035, "pressure_ratio": 3.533161069898606, "entropy_over_cv": 0.09962707602039478, "tangential_field_ratio": 0.665694150520844 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.5543122344752192e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_3", "zeta": 1e-08, "w1_km_s": 428.02177855033267, "u1n_km_s": 277.51356260982254, "u_minus_threshold_km_s": 2.14010890431382e-06, "theta_deg": 0.005740800195949961, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.19824691556271606, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.00014169835181841484, 0.0 ] }, "right": { "rho": 2.008804017608035, "p": 0.7004382791777553, "u": [ 0.49780864197530866, 6.699212782963576e-05, 0.0 ], "B": [ 1.4142135623730951, -9.432776394396337e-05, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 0.0, "entropy_over_cv": 0.09962706871652616, "characteristics": { "left": { "fast": 1.414213570876741, "alfven_n": 1.4142135623730951, "slow": 0.5748143369509329 }, "right": { "fast": 0.9978062410059484, "alfven_n": 0.9978062356743506, "slow": 0.7623256356032482 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_31e-08", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 3.349606391481788e-05, 0.0 ], "rh_scaled_inf": 3.3306690738754696e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -2.710505431213761e-20, "t2_momentum": 0.0, "t1_induction": -1.3552527156068805e-20, "t2_induction": 0.0, "energy": -3.3306690738754696e-16 }, "characteristics": { "left": { "slow": 0.5748143369509329, "alfven_n": 1.4142135623730951, "fast": 1.414213570876741 }, "right": { "slow": 0.7623256356032482, "alfven_n": 0.9978062356743506, "fast": 0.9978062410059484 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.49780864197530866 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 2.008804017608035, "pressure_ratio": 3.5331610440928616, "entropy_over_cv": 0.09962706871652616, "tangential_field_ratio": 0.665694150520844 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 1.5543122344752192e-15, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_4", "zeta": 0.0001, "w1_km_s": 222.37324876658096, "u1n_km_s": 483.16209239357426, "u_minus_threshold_km_s": 0.011118384485655497, "theta_deg": 0.4551111246662356, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.46738895644444434, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.011233599874688778, 0.0 ] }, "right": { "rho": 1.1987852309659546, "p": 0.6332278514760012, "u": [ 0.8341777777777777, 0.0022596665162335334, 0.0 ], "B": [ 1.4142135623730951, -0.009635774357839865, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.0014872905610408549, "characteristics": { "left": { "fast": 1.4142866360302822, "alfven_n": 1.4142135623730951, "slow": 0.8825537371663934 }, "right": { "fast": 1.2917118574722544, "alfven_n": 1.291648386967427, "slow": 0.9382365486918592 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_40.0001", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0011298332581167667, 0.0 ], "rh_scaled_inf": 2.661477848406015e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -1.734723475976807e-18, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -2.661477848406015e-16 }, "characteristics": { "left": { "slow": 0.8825537371663936, "alfven_n": 1.4142135623730951, "fast": 1.414286636030282 }, "right": { "slow": 0.9382365486918592, "alfven_n": 1.291648386967427, "fast": 1.2917118574722544 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.8341777777777777 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.1987852309659546, "pressure_ratio": 1.3548198834074703, "entropy_over_cv": 0.0014872905610408549, "tangential_field_ratio": 0.857763714688727 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 7.771561172376096e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_4", "zeta": 1e-05, "w1_km_s": 222.3832552375702, "u1n_km_s": 483.152085922585, "u_minus_threshold_km_s": 0.0011119134964019395, "theta_deg": 0.14392149843428595, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.46734689564444437, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0035523761926998625, 0.0 ] }, "right": { "rho": 1.1987852309659546, "p": 0.6331707851476002, "u": [ 0.8341777777777777, 0.000714569294371581, 0.0 ], "B": [ 1.4142135623730951, -0.0030470993990220313, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 0.0, "entropy_over_cv": 0.0014871618118221797, "characteristics": { "left": { "fast": 1.4142208699227519, "alfven_n": 1.4142135623730951, "slow": 0.8825550652465209 }, "right": { "fast": 1.2916547341463769, "alfven_n": 1.291648386967427, "slow": 0.9382357624886551 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_41e-05", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0003572846471857905, 0.0 ], "rh_scaled_inf": 1.3309009587271627e-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": 1.3309009587271627e-16 }, "characteristics": { "left": { "slow": 0.882555065246521, "alfven_n": 1.4142135623730951, "fast": 1.4142208699227516 }, "right": { "slow": 0.938235762488655, "alfven_n": 1.291648386967427, "fast": 1.2916547341463769 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.8341777777777777 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.1987852309659546, "pressure_ratio": 1.35481970897548, "entropy_over_cv": 0.0014871618118221797, "tangential_field_ratio": 0.857763714688727 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 7.771561172376096e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_4", "zeta": 1e-06, "w1_km_s": 222.3842559589664, "u1n_km_s": 483.15108520118883, "u_minus_threshold_km_s": 0.00011119210020638093, "theta_deg": 0.04551206007779582, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.4673426895644443, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.001123359987379832, 0.0 ] }, "right": { "rho": 1.1987852309659546, "p": 0.63316507851476, "u": [ 0.8341777777777777, 0.00022596665160544164, 0.0 ], "B": [ 1.4142135623730951, -0.0009635774357076061, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 3.992751078757239e-16, "entropy_over_cv": 0.001487148935624738, "characteristics": { "left": { "fast": 1.4142142931299002, "alfven_n": 1.4142135623730951, "slow": 0.8825551980766787 }, "right": { "fast": 1.2916490216866066, "alfven_n": 1.291648386967427, "slow": 0.9382356838521042 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_41e-06", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.00011298332580272082, 0.0 ], "rh_scaled_inf": 2.6618343286997625e-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": 2.6618343286997625e-16 }, "characteristics": { "left": { "slow": 0.8825551980766787, "alfven_n": 1.4142135623730951, "fast": 1.4142142931299002 }, "right": { "slow": 0.9382356838521041, "alfven_n": 1.291648386967427, "fast": 1.2916490216866068 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.8341777777777777 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.1987852309659546, "pressure_ratio": 1.3548196915305541, "entropy_over_cv": 0.001487148935624738, "tangential_field_ratio": 0.857763714688727 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 7.771561172376096e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_4", "zeta": 1e-07, "w1_km_s": 222.38435603184908, "u1n_km_s": 483.15098512830616, "u_minus_threshold_km_s": 1.1119217532495895e-05, "theta_deg": 0.014392179804966156, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.4673422689564444, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0003552376191291927, 0.0 ] }, "right": { "rho": 1.1987852309659546, "p": 0.633164507851476, "u": [ 0.8341777777777777, 7.145692940883712e-05, 0.0 ], "B": [ 1.4142135623730951, -0.0003047099397814355, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 1.3309187711240773e-16, "entropy_over_cv": 0.0014871476479922374, "characteristics": { "left": { "fast": 1.414213635448794, "alfven_n": 1.4142135623730951, "slow": 0.882555211359916 }, "right": { "fast": 1.2916484504393577, "alfven_n": 1.291648386967427, "slow": 0.9382356759882868 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_41e-07", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 3.572846470441856e-05, 0.0 ], "rh_scaled_inf": 1.3309187849338586e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -5.421010862427522e-20, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -1.3309187849338586e-16 }, "characteristics": { "left": { "slow": 0.882555211359916, "alfven_n": 1.4142135623730951, "fast": 1.414213635448794 }, "right": { "slow": 0.9382356759882868, "alfven_n": 1.291648386967427, "fast": 1.2916484504393577 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.8341777777777777 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.1987852309659546, "pressure_ratio": 1.3548196897860443, "entropy_over_cv": 0.0014871476479922374, "tangential_field_ratio": 0.857763714688727 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 7.771561172376096e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_4", "zeta": 1e-08, "w1_km_s": 222.3843660391448, "u1n_km_s": 483.15097512101045, "u_minus_threshold_km_s": 1.1119218186195212e-06, "theta_deg": 0.004551206921518635, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.4673422268956443, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.00011233599790095397, 0.0 ] }, "right": { "rho": 1.1987852309659546, "p": 0.6331644507851476, "u": [ 0.8341777777777777, 2.2596664992173657e-05, 0.0 ], "B": [ 1.4142135623730951, -9.635774285278731e-05, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 2.661837891222991e-16, "entropy_over_cv": 0.001487147519228904, "characteristics": { "left": { "fast": 1.4142135696806653, "alfven_n": 1.4142135623730951, "slow": 0.8825552126882419 }, "right": { "fast": 1.2916483933146201, "alfven_n": 1.291648386967427, "slow": 0.9382356752019035 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_41e-08", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 1.1298332496086829e-05, 0.0 ], "rh_scaled_inf": 1.3309189469924738e-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": 1.3309189469924738e-16 }, "characteristics": { "left": { "slow": 0.882555212688242, "alfven_n": 1.4142135623730951, "fast": 1.4142135696806648 }, "right": { "slow": 0.9382356752019032, "alfven_n": 1.291648386967427, "fast": 1.2916483933146203 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.8341777777777777 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.1987852309659546, "pressure_ratio": 1.3548196896115932, "entropy_over_cv": 0.001487147519228904, "tangential_field_ratio": 0.8577637146887269 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 7.771561172376096e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_5", "zeta": 0.0001, "w1_km_s": 278.75961980506247, "u1n_km_s": 426.77572135509274, "u_minus_threshold_km_s": 0.01393763255811109, "theta_deg": 0.4551111246662356, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.46738895644444434, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.011233599874688778, 0.0 ] }, "right": { "rho": 1.1987852309659546, "p": 0.6332278514760012, "u": [ 0.8341777777777777, 0.0022596665162335334, 0.0 ], "B": [ 1.4142135623730951, -0.009635774357839865, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.0014872905610408549, "characteristics": { "left": { "fast": 1.4142866360302822, "alfven_n": 1.4142135623730951, "slow": 0.8825537371663934 }, "right": { "fast": 1.2917118574722544, "alfven_n": 1.291648386967427, "slow": 0.9382365486918592 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_50.0001", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0011298332581167667, 0.0 ], "rh_scaled_inf": 2.661477848406015e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -1.734723475976807e-18, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -2.661477848406015e-16 }, "characteristics": { "left": { "slow": 0.8825537371663936, "alfven_n": 1.4142135623730951, "fast": 1.414286636030282 }, "right": { "slow": 0.9382365486918592, "alfven_n": 1.291648386967427, "fast": 1.2917118574722544 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.8341777777777777 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.1987852309659546, "pressure_ratio": 1.3548198834074703, "entropy_over_cv": 0.0014872905610408549, "tangential_field_ratio": 0.857763714688727 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 7.771561172376096e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_5", "zeta": 1e-05, "w1_km_s": 278.7721635802873, "u1n_km_s": 426.7631775798679, "u_minus_threshold_km_s": 0.001393857333255255, "theta_deg": 0.14392149843428595, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.46734689564444437, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0035523761926998625, 0.0 ] }, "right": { "rho": 1.1987852309659546, "p": 0.6331707851476002, "u": [ 0.8341777777777777, 0.000714569294371581, 0.0 ], "B": [ 1.4142135623730951, -0.0030470993990220313, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 0.0, "entropy_over_cv": 0.0014871618118221797, "characteristics": { "left": { "fast": 1.4142208699227519, "alfven_n": 1.4142135623730951, "slow": 0.8825550652465209 }, "right": { "fast": 1.2916547341463769, "alfven_n": 1.291648386967427, "slow": 0.9382357624886551 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_51e-05", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0003572846471857905, 0.0 ], "rh_scaled_inf": 1.3309009587271627e-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": 1.3309009587271627e-16 }, "characteristics": { "left": { "slow": 0.882555065246521, "alfven_n": 1.4142135623730951, "fast": 1.4142208699227516 }, "right": { "slow": 0.938235762488655, "alfven_n": 1.291648386967427, "fast": 1.2916547341463769 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.8341777777777777 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.1987852309659546, "pressure_ratio": 1.35481970897548, "entropy_over_cv": 0.0014871618118221797, "tangential_field_ratio": 0.857763714688727 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 7.771561172376096e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_5", "zeta": 1e-06, "w1_km_s": 278.77341805094636, "u1n_km_s": 426.76192310920885, "u_minus_threshold_km_s": 0.00013938667422053186, "theta_deg": 0.04551206007779582, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.4673426895644443, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.001123359987379832, 0.0 ] }, "right": { "rho": 1.1987852309659546, "p": 0.63316507851476, "u": [ 0.8341777777777777, 0.00022596665160544164, 0.0 ], "B": [ 1.4142135623730951, -0.0009635774357076061, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 3.992751078757239e-16, "entropy_over_cv": 0.001487148935624738, "characteristics": { "left": { "fast": 1.4142142931299002, "alfven_n": 1.4142135623730951, "slow": 0.8825551980766787 }, "right": { "fast": 1.2916490216866066, "alfven_n": 1.291648386967427, "slow": 0.9382356838521042 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_51e-06", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.00011298332580272082, 0.0 ], "rh_scaled_inf": 2.6618343286997625e-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": 2.6618343286997625e-16 }, "characteristics": { "left": { "slow": 0.8825551980766787, "alfven_n": 1.4142135623730951, "fast": 1.4142142931299002 }, "right": { "slow": 0.9382356838521041, "alfven_n": 1.291648386967427, "fast": 1.2916490216866068 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.8341777777777777 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.1987852309659546, "pressure_ratio": 1.3548196915305541, "entropy_over_cv": 0.001487148935624738, "tangential_field_ratio": 0.857763714688727 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 7.771561172376096e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_5", "zeta": 1e-07, "w1_km_s": 278.77354349894375, "u1n_km_s": 426.76179766121146, "u_minus_threshold_km_s": 1.3938676829639007e-05, "theta_deg": 0.014392179804966156, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.4673422689564444, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0003552376191291927, 0.0 ] }, "right": { "rho": 1.1987852309659546, "p": 0.633164507851476, "u": [ 0.8341777777777777, 7.145692940883712e-05, 0.0 ], "B": [ 1.4142135623730951, -0.0003047099397814355, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 1.3309187711240773e-16, "entropy_over_cv": 0.0014871476479922374, "characteristics": { "left": { "fast": 1.414213635448794, "alfven_n": 1.4142135623730951, "slow": 0.882555211359916 }, "right": { "fast": 1.2916484504393577, "alfven_n": 1.291648386967427, "slow": 0.9382356759882868 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_51e-07", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 3.572846470441856e-05, 0.0 ], "rh_scaled_inf": 1.3309187849338586e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": -5.421010862427522e-20, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -1.3309187849338586e-16 }, "characteristics": { "left": { "slow": 0.882555211359916, "alfven_n": 1.4142135623730951, "fast": 1.414213635448794 }, "right": { "slow": 0.9382356759882868, "alfven_n": 1.291648386967427, "fast": 1.2916484504393577 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.8341777777777777 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.1987852309659546, "pressure_ratio": 1.3548196897860443, "entropy_over_cv": 0.0014871476479922374, "tangential_field_ratio": 0.857763714688727 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 7.771561172376096e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_5", "zeta": 1e-08, "w1_km_s": 278.7735560437528, "u1n_km_s": 426.7617851164024, "u_minus_threshold_km_s": 1.3938677625446871e-06, "theta_deg": 0.004551206921518635, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.4673422268956443, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.00011233599790095397, 0.0 ] }, "right": { "rho": 1.1987852309659546, "p": 0.6331644507851476, "u": [ 0.8341777777777777, 2.2596664992173657e-05, 0.0 ], "B": [ 1.4142135623730951, -9.635774285278731e-05, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 2.661837891222991e-16, "entropy_over_cv": 0.001487147519228904, "characteristics": { "left": { "fast": 1.4142135696806653, "alfven_n": 1.4142135623730951, "slow": 0.8825552126882419 }, "right": { "fast": 1.2916483933146201, "alfven_n": 1.291648386967427, "slow": 0.9382356752019035 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_51e-08", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 1.1298332496086829e-05, 0.0 ], "rh_scaled_inf": 1.3309189469924738e-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": 1.3309189469924738e-16 }, "characteristics": { "left": { "slow": 0.882555212688242, "alfven_n": 1.4142135623730951, "fast": 1.4142135696806648 }, "right": { "slow": 0.9382356752019032, "alfven_n": 1.291648386967427, "fast": 1.2916483933146203 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.8341777777777777 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.1987852309659546, "pressure_ratio": 1.3548196896115932, "entropy_over_cv": 0.001487147519228904, "tangential_field_ratio": 0.8577637146887269 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 7.771561172376096e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_6", "zeta": 0.0001, "w1_km_s": 296.1868034115748, "u1n_km_s": 409.34853774858044, "u_minus_threshold_km_s": 0.014808969955538487, "theta_deg": 0.5383262703994265, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.26345844197530865, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.013287727678365209, 0.0 ] }, "right": { "rho": 1.7262507325909744, "p": 0.6842128621984341, "u": [ 0.5792901234567902, 0.00556471625837649, 0.0 ], "B": [ 1.4142135623730951, -0.00935287907668816, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 3.469446951953614e-18, "entropy_over_cv": 0.044453680967479814, "characteristics": { "left": { "fast": 1.4142935429512458, "alfven_n": 1.4142135623730951, "slow": 0.6626067773313584 }, "right": { "fast": 1.076428412194259, "alfven_n": 1.0763736558061892, "slow": 0.8127293831330437 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_60.0001", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.002782358129188245, 0.0 ], "rh_scaled_inf": 4.440892098500626e-16, "rh_components": { "mass": 0.0, "normal_momentum": 4.440892098500626e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -3.469446951953614e-18, "t2_induction": 0.0, "energy": 3.83240487297534e-16 }, "characteristics": { "left": { "slow": 0.6626067773313584, "alfven_n": 1.4142135623730951, "fast": 1.414293542951246 }, "right": { "slow": 0.8127293831330437, "alfven_n": 1.0763736558061892, "fast": 1.076428412194259 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.5792901234567902 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.7262507325909744, "pressure_ratio": 2.5970428469419047, "entropy_over_cv": 0.044453680967479814, "tangential_field_ratio": 0.7038734765701374 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 6.661338147750939e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_6", "zeta": 1e-05, "w1_km_s": 296.20013138457585, "u1n_km_s": 409.33520977557936, "u_minus_threshold_km_s": 0.0014809969544558044, "theta_deg": 0.17023822231057195, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.2634347330864198, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.004201948439161327, 0.0 ] }, "right": { "rho": 1.7262507325909744, "p": 0.6841490639976211, "u": [ 0.5792901234567902, 0.0017597177909005363, 0.0 ], "B": [ 1.4142135623730951, -0.0029576400562409465, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 1.9164832090375988e-16, "entropy_over_cv": 0.04445042846446012, "characteristics": { "left": { "fast": 1.4142215606610036, "alfven_n": 1.4142135623730951, "slow": 0.6626106867607916 }, "right": { "fast": 1.0763791315581277, "alfven_n": 1.0763736558061892, "slow": 0.8127286995393074 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_61e-05", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0008798588954502682, 0.0 ], "rh_scaled_inf": 1.9164912174517433e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 8.673617379884035e-19, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -1.9164912174517433e-16 }, "characteristics": { "left": { "slow": 0.6626106867607916, "alfven_n": 1.4142135623730951, "fast": 1.4142215606610036 }, "right": { "slow": 0.8127286995393074, "alfven_n": 1.0763736558061892, "fast": 1.0763791315581277 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.5792901234567902 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.7262507325909744, "pressure_ratio": 2.5970344000659393, "entropy_over_cv": 0.04445042846446012, "tangential_field_ratio": 0.7038734765701377 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 6.661338147750939e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_6", "zeta": 1e-06, "w1_km_s": 296.2014642808352, "u1n_km_s": 409.33387687932003, "u_minus_threshold_km_s": 0.00014810069512805057, "theta_deg": 0.05383419531021456, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.26343236219753086, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0013287727678728543, 0.0 ] }, "right": { "rho": 1.7262507325909744, "p": 0.68414268417754, "u": [ 0.5792901234567902, 0.0005564716258528648, 0.0 ], "B": [ 1.4142135623730951, -0.0009352879076943903, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 5.7495578984008e-16, "entropy_over_cv": 0.04445010318137699, "characteristics": { "left": { "fast": 1.4142143622041872, "alfven_n": 1.4142135623730951, "slow": 0.6626110777585581 }, "right": { "fast": 1.0763742033825145, "alfven_n": 1.0763736558061892, "slow": 0.8127286311638847 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_61e-06", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0002782358129264324, 0.0 ], "rh_scaled_inf": 7.666080401341991e-16, "rh_components": { "mass": 0.0, "normal_momentum": 4.440892098500626e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 7.666080401341991e-16 }, "characteristics": { "left": { "slow": 0.6626110777585582, "alfven_n": 1.4142135623730951, "fast": 1.4142143622041872 }, "right": { "slow": 0.8127286311638849, "alfven_n": 1.0763736558061892, "fast": 1.076374203382514 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.5792901234567902 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.7262507325909744, "pressure_ratio": 2.59703355529472, "entropy_over_cv": 0.04445010318137699, "tangential_field_ratio": 0.7038734765701375 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 6.661338147750939e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_6", "zeta": 1e-07, "w1_km_s": 296.2015975714508, "u1n_km_s": 409.3337435887044, "u_minus_threshold_km_s": 1.4810079505878093e-05, "theta_deg": 0.017023871831945096, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.263432125108642, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0004201948440515463, 0.0 ] }, "right": { "rho": 1.7262507325909744, "p": 0.6841420461955318, "u": [ 0.5792901234567902, 0.00017597177914676303, 0.0 ], "B": [ 1.4142135623730951, -0.0002957640057194087, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.044450070652740425, "characteristics": { "left": { "fast": 1.4142136423562275, "alfven_n": 1.4142135623730951, "slow": 0.6626111168588831 }, "right": { "fast": 1.0763737105638331, "alfven_n": 1.0763736558061892, "slow": 0.8127286243261819 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_61e-07", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 8.798588957338152e-05, 0.0 ], "rh_scaled_inf": 4.440892098500626e-16, "rh_components": { "mass": 0.0, "normal_momentum": 4.440892098500626e-16, "t1_momentum": -1.0842021724855044e-19, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 3.833045977343511e-16 }, "characteristics": { "left": { "slow": 0.6626111168588832, "alfven_n": 1.4142135623730951, "fast": 1.4142136423562273 }, "right": { "slow": 0.812728624326182, "alfven_n": 1.0763736558061892, "fast": 1.076373710563833 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.5792901234567902 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.7262507325909744, "pressure_ratio": 2.597033470816761, "entropy_over_cv": 0.044450070652740425, "tangential_field_ratio": 0.7038734765701375 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 6.661338147750939e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_6", "zeta": 1e-08, "w1_km_s": 296.20161090052227, "u1n_km_s": 409.33373025963294, "u_minus_threshold_km_s": 1.4810080415372795e-06, "theta_deg": 0.005383421111464918, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.2634321013997531, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0001328772770857386, 0.0 ] }, "right": { "rho": 1.7262507325909744, "p": 0.6841419823973309, "u": [ 0.5792901234567902, 5.5647162710274546e-05, 0.0 ], "B": [ 1.4142135623730951, -9.352879097951229e-05, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 1.916523269497145e-16, "entropy_over_cv": 0.04445006739987367, "characteristics": { "left": { "fast": 1.4142135703714087, "alfven_n": 1.4142135623730951, "slow": 0.662611120768921 }, "right": { "fast": 1.0763736612819537, "alfven_n": 1.0763736558061892, "slow": 0.81272862364241 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_61e-08", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 2.7823581355137273e-05, 0.0 ], "rh_scaled_inf": 2.710505431213761e-20, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -2.710505431213761e-20, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.6626111207689211, "alfven_n": 1.4142135623730951, "fast": 1.4142135703714085 }, "right": { "slow": 0.81272862364241, "alfven_n": 1.0763736558061892, "fast": 1.0763736612819537 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.5792901234567902 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.7262507325909744, "pressure_ratio": 2.597033462368957, "entropy_over_cv": 0.04445006739987367, "tangential_field_ratio": 0.7038734765701374 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 6.661338147750939e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_7", "zeta": 0.0001, "w1_km_s": 371.28980742172575, "u1n_km_s": 334.24553373842946, "u_minus_threshold_km_s": 0.01856402628197884, "theta_deg": 0.5383262703994265, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.26345844197530865, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.013287727678365209, 0.0 ] }, "right": { "rho": 1.7262507325909744, "p": 0.6842128621984341, "u": [ 0.5792901234567902, 0.00556471625837649, 0.0 ], "B": [ 1.4142135623730951, -0.00935287907668816, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 3.469446951953614e-18, "entropy_over_cv": 0.044453680967479814, "characteristics": { "left": { "fast": 1.4142935429512458, "alfven_n": 1.4142135623730951, "slow": 0.6626067773313584 }, "right": { "fast": 1.076428412194259, "alfven_n": 1.0763736558061892, "slow": 0.8127293831330437 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_70.0001", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.002782358129188245, 0.0 ], "rh_scaled_inf": 4.440892098500626e-16, "rh_components": { "mass": 0.0, "normal_momentum": 4.440892098500626e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -3.469446951953614e-18, "t2_induction": 0.0, "energy": 3.83240487297534e-16 }, "characteristics": { "left": { "slow": 0.6626067773313584, "alfven_n": 1.4142135623730951, "fast": 1.414293542951246 }, "right": { "slow": 0.8127293831330437, "alfven_n": 1.0763736558061892, "fast": 1.076428412194259 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.5792901234567902 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.7262507325909744, "pressure_ratio": 2.5970428469419047, "entropy_over_cv": 0.044453680967479814, "tangential_field_ratio": 0.7038734765701374 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 6.661338147750939e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_7", "zeta": 1e-05, "w1_km_s": 371.30651492007445, "u1n_km_s": 334.22882624008076, "u_minus_threshold_km_s": 0.001856527933284724, "theta_deg": 0.17023822231057195, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.2634347330864198, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.004201948439161327, 0.0 ] }, "right": { "rho": 1.7262507325909744, "p": 0.6841490639976211, "u": [ 0.5792901234567902, 0.0017597177909005363, 0.0 ], "B": [ 1.4142135623730951, -0.0029576400562409465, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 1.9164832090375988e-16, "entropy_over_cv": 0.04445042846446012, "characteristics": { "left": { "fast": 1.4142215606610036, "alfven_n": 1.4142135623730951, "slow": 0.6626106867607916 }, "right": { "fast": 1.0763791315581277, "alfven_n": 1.0763736558061892, "slow": 0.8127286995393074 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_71e-05", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0008798588954502682, 0.0 ], "rh_scaled_inf": 1.9164912174517433e-16, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 8.673617379884035e-19, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": -1.9164912174517433e-16 }, "characteristics": { "left": { "slow": 0.6626106867607916, "alfven_n": 1.4142135623730951, "fast": 1.4142215606610036 }, "right": { "slow": 0.8127286995393074, "alfven_n": 1.0763736558061892, "fast": 1.0763791315581277 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.5792901234567902 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.7262507325909744, "pressure_ratio": 2.5970344000659393, "entropy_over_cv": 0.04445042846446012, "tangential_field_ratio": 0.7038734765701377 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 6.661338147750939e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_7", "zeta": 1e-06, "w1_km_s": 371.30818579396123, "u1n_km_s": 334.227155366194, "u_minus_threshold_km_s": 0.00018565404650416895, "theta_deg": 0.05383419531021456, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.26343236219753086, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0013287727678728543, 0.0 ] }, "right": { "rho": 1.7262507325909744, "p": 0.68414268417754, "u": [ 0.5792901234567902, 0.0005564716258528648, 0.0 ], "B": [ 1.4142135623730951, -0.0009352879076943903, 0.0 ] }, "status": "ACCEPTED", "family": "slow_shock", "guards": [], "scaled_flux_residual": 5.7495578984008e-16, "entropy_over_cv": 0.04445010318137699, "characteristics": { "left": { "fast": 1.4142143622041872, "alfven_n": 1.4142135623730951, "slow": 0.6626110777585581 }, "right": { "fast": 1.0763742033825145, "alfven_n": 1.0763736558061892, "slow": 0.8127286311638847 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_71e-06", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 0.0002782358129264324, 0.0 ], "rh_scaled_inf": 7.666080401341991e-16, "rh_components": { "mass": 0.0, "normal_momentum": 4.440892098500626e-16, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 7.666080401341991e-16 }, "characteristics": { "left": { "slow": 0.6626110777585582, "alfven_n": 1.4142135623730951, "fast": 1.4142143622041872 }, "right": { "slow": 0.8127286311638849, "alfven_n": 1.0763736558061892, "fast": 1.076374203382514 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.5792901234567902 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.7262507325909744, "pressure_ratio": 2.59703355529472, "entropy_over_cv": 0.04445010318137699, "tangential_field_ratio": 0.7038734765701375 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 6.661338147750939e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_7", "zeta": 1e-07, "w1_km_s": 371.30835288259055, "u1n_km_s": 334.22698827756466, "u_minus_threshold_km_s": 1.856541717870641e-05, "theta_deg": 0.017023871831945096, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.263432125108642, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0004201948440515463, 0.0 ] }, "right": { "rho": 1.7262507325909744, "p": 0.6841420461955318, "u": [ 0.5792901234567902, 0.00017597177914676303, 0.0 ], "B": [ 1.4142135623730951, -0.0002957640057194087, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 4.440892098500626e-16, "entropy_over_cv": 0.044450070652740425, "characteristics": { "left": { "fast": 1.4142136423562275, "alfven_n": 1.4142135623730951, "slow": 0.6626111168588831 }, "right": { "fast": 1.0763737105638331, "alfven_n": 1.0763736558061892, "slow": 0.8127286243261819 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_71e-07", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 8.798588957338152e-05, 0.0 ], "rh_scaled_inf": 4.440892098500626e-16, "rh_components": { "mass": 0.0, "normal_momentum": 4.440892098500626e-16, "t1_momentum": -1.0842021724855044e-19, "t2_momentum": 0.0, "t1_induction": 0.0, "t2_induction": 0.0, "energy": 3.833045977343511e-16 }, "characteristics": { "left": { "slow": 0.6626111168588832, "alfven_n": 1.4142135623730951, "fast": 1.4142136423562273 }, "right": { "slow": 0.812728624326182, "alfven_n": 1.0763736558061892, "fast": 1.076373710563833 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.5792901234567902 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.7262507325909744, "pressure_ratio": 2.597033470816761, "entropy_over_cv": 0.044450070652740425, "tangential_field_ratio": 0.7038734765701375 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 6.661338147750939e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } }, { "source": "R109_corner_7", "zeta": 1e-08, "w1_km_s": 371.3083695914659, "u1n_km_s": 334.2269715686893, "u_minus_threshold_km_s": 1.8565418145044532e-06, "theta_deg": 0.005383421111464918, "h_ASSUMED": 2.0, "check": { "left": { "rho": 1.0, "p": 0.2634321013997531, "u": [ 1.0, 0.0, 0.0 ], "B": [ 1.4142135623730951, -0.0001328772770857386, 0.0 ] }, "right": { "rho": 1.7262507325909744, "p": 0.6841419823973309, "u": [ 0.5792901234567902, 5.5647162710274546e-05, 0.0 ], "B": [ 1.4142135623730951, -9.352879097951229e-05, 0.0 ] }, "status": "UNRESOLVED", "family": null, "guards": [ "left_characteristic_coincidence", "right_characteristic_coincidence" ], "scaled_flux_residual": 1.916523269497145e-16, "entropy_over_cv": 0.04445006739987367, "characteristics": { "left": { "fast": 1.4142135703714087, "alfven_n": 1.4142135623730951, "slow": 0.662611120768921 }, "right": { "fast": 1.0763736612819537, "alfven_n": 1.0763736558061892, "slow": 0.81272862364241 } }, "baseline_diagnosis": { "case_id": "R135_onset_R109_corner_71e-08", "status": "SUPPORTED_LOCAL_CLASS", "family": "slow_shock", "scope": "one planar discontinuity, ideal MHD, exact supplied states", "candidates": { "fast_shock": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition." }, "slow_shock": { "status": "SUPPORTED", "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition." }, "rotational_discontinuity": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation." }, "contact": { "status": "INCOMPATIBLE_FOR_EXACT_PAIR", "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump." } }, "coverage": { "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded", "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check", "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model" }, "global_uniqueness": false, "uncertainty_propagated": false, "checks": { "front_speed": 0, "evaluation_boost": [ 0, 2.7823581355137273e-05, 0.0 ], "rh_scaled_inf": 2.710505431213761e-20, "rh_components": { "mass": 0.0, "normal_momentum": 0.0, "t1_momentum": 0.0, "t2_momentum": 0.0, "t1_induction": -2.710505431213761e-20, "t2_induction": 0.0, "energy": 0.0 }, "characteristics": { "left": { "slow": 0.6626111207689211, "alfven_n": 1.4142135623730951, "fast": 1.4142135703714085 }, "right": { "slow": 0.81272862364241, "alfven_n": 1.0763736558061892, "fast": 1.0763736612819537 } }, "front_relative_normal_velocity": { "left": 1.0, "right": 0.5792901234567902 }, "upstream_side": "left", "characteristic_transition": [ 3, 4 ], "compression": 1.7262507325909744, "pressure_ratio": 2.597033462368957, "entropy_over_cv": 0.04445006739987367, "tangential_field_ratio": 0.7038734765701374 }, "result_sentence": "For these supplied states and front speed, a slow shock passes the local ideal-MHD checks.", "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness." }, "normal_field_jump": 0.0, "transverse_evolutionary": { "status": "PASS_NECESSARY_TRANSVERSE_TEST", "incoming_alfven": 2, "outgoing_alfven": 2, "jump_equations": 2, "outgoing_flux_rank": 2, "generic_incoming_residual": 6.661338147750939e-16, "scope": "Coplanar base states, unrestricted out-of-plane ideal-MHD perturbations; not a dissipative or restricted coplanar stability claim." } } } ], "finite_control_statuses": { "ACCEPTED": 27, "UNRESOLVED": 18 }, "guard_vs_theorem": "Guard-limited finite controls stay UNRESOLVED even though the exact theorem certifies an open mathematical domain. No observational precision is inferred from numerical tolerances.", "observational_test": { "same_local_patch_required": true, "inequality": "min_supported(Vn-u1n) > max_supported(wcrit)", "fixed_G0_sufficient_rule": "An independently supported upper bound on u1n strictly below the listed whole-domain threshold, including uncertainty, excludes regular SLOW for every retained radio/T tuple.", "not_sufficient_alone": "Radio/EUV association, a physical discontinuity, pressure closure and nondegenerate local geometry remain necessary. Unknown Vn must not be silently fixed by a projected image speed." }, "specification_sha256": "2b5f14ed3bdee6ba7f0006fc7501317cac24f371abf7fea6ff5e8157092900b5" }