{
  "title": "Quadratic Dielectric Corrections Preserve Conditional Three/Four Flux Guides Above Derived Thresholds",
  "sources": {
    "experiments/mixed-dielectric-tube-checks.py": "3e36076f207ab13bcd009cd1e3ea525ede79a909ef3d2e48c681415291d62eb1",
    "experiments/hodge-flux-tube-checks.py": "24ef86b4855274c5c8ca74890aa5e6bfa5f15bcccf2bc6ae566c02d998adb38b"
  },
  "checks_passed": 374,
  "dependency_checks_passed": 26,
  "case_count": 50,
  "occupied_depths": [
    2,
    3,
    4,
    5,
    6,
    10
  ],
  "scope": "complete fixed commuting flux energy, sharp interpolation reduction, global threshold and local branch stability; not full non-Abelian confinement",
  "cases": [
    {
      "case": "mixed-dielectric-occupied-depth-2",
      "real_depth": 2,
      "transverse_dimension": 1,
      "hodge_coefficient": 0.0,
      "quadratic_dielectric_is_an_ordinary_positive_vacuum_floor": false,
      "independent_connection_zero_source_constraint_retained": true,
      "independent_connection_present": true
    },
    {
      "case": "mixed-dielectric-occupied-depth-3",
      "real_depth": 3,
      "transverse_dimension": 2,
      "hodge_coefficient": 1.0,
      "quadratic_dielectric_is_an_ordinary_positive_vacuum_floor": false,
      "independent_connection_zero_source_constraint_retained": false,
      "independent_connection_present": true
    },
    {
      "case": "mixed-dielectric-occupied-depth-4",
      "real_depth": 4,
      "transverse_dimension": 3,
      "hodge_coefficient": 1.0,
      "quadratic_dielectric_is_an_ordinary_positive_vacuum_floor": false,
      "independent_connection_zero_source_constraint_retained": false,
      "independent_connection_present": true
    },
    {
      "case": "mixed-dielectric-occupied-depth-5",
      "real_depth": 5,
      "transverse_dimension": 4,
      "hodge_coefficient": 0.0,
      "quadratic_dielectric_is_an_ordinary_positive_vacuum_floor": false,
      "independent_connection_zero_source_constraint_retained": true,
      "independent_connection_present": true
    },
    {
      "case": "mixed-dielectric-occupied-depth-6",
      "real_depth": 6,
      "transverse_dimension": 5,
      "hodge_coefficient": 0.0,
      "quadratic_dielectric_is_an_ordinary_positive_vacuum_floor": false,
      "independent_connection_zero_source_constraint_retained": true,
      "independent_connection_present": true
    },
    {
      "case": "mixed-dielectric-occupied-depth-10",
      "real_depth": 10,
      "transverse_dimension": 9,
      "hodge_coefficient": 0.0,
      "quadratic_dielectric_is_an_ordinary_positive_vacuum_floor": false,
      "independent_connection_zero_source_constraint_retained": false,
      "independent_connection_present": false
    },
    {
      "case": "mixed-profile-n1-k21.0-t0.2",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 1.0,
      "quartic_coefficient": 1.0,
      "neutral_restoring_frequency": 1.0,
      "t": 0.2,
      "commuting_flux_Q": 14.666666666733738,
      "width": 1.118033988749895,
      "amplitude": 1.4142135623730951,
      "complete_tension": 8.944271910037315,
      "diffuse_threshold": 14.666666666733738,
      "tension_to_diffuse_ratio": 0.6098367211361191,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
        1.230199615539839,
        10.64128855593981
      ],
      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n1-k21.0-t0.5",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 1.0,
      "quartic_coefficient": 1.0,
      "neutral_restoring_frequency": 1.0,
      "t": 0.5,
      "commuting_flux_Q": 3.3333333333703004,
      "width": 1.414213562373095,
      "amplitude": 0.7071067811865476,
      "complete_tension": 2.8284271247739428,
      "diffuse_threshold": 3.3333333333703004,
      "tension_to_diffuse_ratio": 0.8485281374227726,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
        0.19631063210865932,
        3.0563805613745947
      ],
      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n1-k21.0-t0.8",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 1.0,
      "quartic_coefficient": 1.0,
      "neutral_restoring_frequency": 1.0,
      "t": 0.8,
      "commuting_flux_Q": 1.166666666685579,
      "width": 2.2360679774997902,
      "amplitude": 0.35355339059327373,
      "complete_tension": 1.1180339887670656,
      "diffuse_threshold": 1.166666666685579,
      "tension_to_diffuse_ratio": 0.9583148474990929,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
        0.02344472375230119,
        1.1425050073895366
      ],
      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n1-k21.0-t0.95",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 1.0,
      "quartic_coefficient": 1.0,
      "neutral_restoring_frequency": 1.0,
      "t": 0.95,
      "commuting_flux_Q": 0.4749308174951558,
      "width": 4.472135954999577,
      "amplitude": 0.16222142113076263,
      "complete_tension": 0.47075115316638594,
      "diffuse_threshold": 0.4749308174951558,
      "tension_to_diffuse_ratio": 0.9911994248955797,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
        0.0020851253746765447,
        0.472854915171495
      ],
      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n1-k21.2-t0.2",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 1.2,
      "quartic_coefficient": 0.7,
      "neutral_restoring_frequency": 0.9,
      "t": 0.2,
      "commuting_flux_Q": 27.54262003467145,
      "width": 1.2422599874998832,
      "amplitude": 1.851640199545103,
      "complete_tension": 13.799733804057574,
      "diffuse_threshold": 22.628571428674913,
      "tension_to_diffuse_ratio": 0.6098367211361191,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
        1.8980222639757511,
        16.417988057735712
      ],
      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n1-k21.2-t0.5",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 1.2,
      "quartic_coefficient": 0.7,
      "neutral_restoring_frequency": 0.9,
      "t": 0.5,
      "commuting_flux_Q": 6.259686371557034,
      "width": 1.5713484026367721,
      "amplitude": 0.9258200997725515,
      "complete_tension": 4.36385899250837,
      "diffuse_threshold": 5.1428571429141785,
      "tension_to_diffuse_ratio": 0.8485281374227727,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
        0.3028792609676459,
        4.715558580406517
      ],
      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n1-k21.2-t0.8",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 1.2,
      "quartic_coefficient": 0.7,
      "neutral_restoring_frequency": 0.9,
      "t": 0.8,
      "commuting_flux_Q": 2.1908902300561803,
      "width": 2.484519974999767,
      "amplitude": 0.4629100498862757,
      "complete_tension": 1.7249667255263303,
      "diffuse_threshold": 1.8000000000291794,
      "tension_to_diffuse_ratio": 0.9583148474990929,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
        0.036171859503550424,
        1.762722011401
      ],
      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n1-k21.2-t0.95",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 1.2,
      "quartic_coefficient": 0.7,
      "neutral_restoring_frequency": 0.9,
      "t": 0.95,
      "commuting_flux_Q": 0.891875389702169,
      "width": 4.96903994999953,
      "amplitude": 0.2123976976214367,
      "complete_tension": 0.7263017791709954,
      "diffuse_threshold": 0.7327504041353831,
      "tension_to_diffuse_ratio": 0.9911994248955798,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
        0.0032170505780723824,
        0.7295475834074494
      ],
      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n1-k20.4-t0.2",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 0.4,
      "quartic_coefficient": 2.3,
      "neutral_restoring_frequency": 1.6,
      "t": 0.2,
      "commuting_flux_Q": 1.613219907803421,
      "width": 0.6987712429686843,
      "amplitude": 0.5897678246195887,
      "complete_tension": 2.4888408793147327,
      "diffuse_threshold": 4.081159420308521,
      "tension_to_diffuse_ratio": 0.6098367211361191,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
        0.34231641475891184,
        2.9610542068702124
      ],
      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n1-k20.4-t0.5",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 0.4,
      "quartic_coefficient": 2.3,
      "neutral_restoring_frequency": 1.6,
      "t": 0.5,
      "commuting_flux_Q": 0.3666408881395302,
      "width": 0.8838834764831842,
      "amplitude": 0.29488391230979427,
      "complete_tension": 0.7870405912414449,
      "diffuse_threshold": 0.9275362318943441,
      "tension_to_diffuse_ratio": 0.8485281374227728,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
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        0.8504711127303223
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      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n1-k20.4-t0.8",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 0.4,
      "quartic_coefficient": 2.3,
      "neutral_restoring_frequency": 1.6,
      "t": 0.8,
      "commuting_flux_Q": 0.12832431084949278,
      "width": 1.3975424859373689,
      "amplitude": 0.14744195615489714,
      "complete_tension": 0.31110510991779233,
      "diffuse_threshold": 0.32463768116468306,
      "tension_to_diffuse_ratio": 0.9583148474990927,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
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      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n1-k20.4-t0.95",
      "transverse_dimension": 1,
      "real_depth": 2,
      "actual_hodge_active": false,
      "quadratic_coefficient": 0.4,
      "quartic_coefficient": 2.3,
      "neutral_restoring_frequency": 1.6,
      "t": 0.95,
      "commuting_flux_Q": 0.05223871701879783,
      "width": 2.795084971874736,
      "amplitude": 0.06765100914917388,
      "complete_tension": 0.13099162522890745,
      "diffuse_threshold": 0.1321546622595217,
      "tension_to_diffuse_ratio": 0.9911994248955796,
      "bound_below_diffuse_threshold": true,
      "moment_hessian_eigenvalues": [
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      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n2-k21.0-t0.2",
      "transverse_dimension": 2,
      "real_depth": 3,
      "actual_hodge_active": true,
      "quadratic_coefficient": 1.0,
      "quartic_coefficient": 1.0,
      "neutral_restoring_frequency": 1.0,
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      "moment_hessian_eigenvalues": [
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      "stable_moment_branch": true
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    {
      "case": "mixed-profile-n2-k21.0-t0.5",
      "transverse_dimension": 2,
      "real_depth": 3,
      "actual_hodge_active": true,
      "quadratic_coefficient": 1.0,
      "quartic_coefficient": 1.0,
      "neutral_restoring_frequency": 1.0,
      "t": 0.5,
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      "moment_hessian_eigenvalues": [
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      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n2-k21.0-t0.8",
      "transverse_dimension": 2,
      "real_depth": 3,
      "actual_hodge_active": true,
      "quadratic_coefficient": 1.0,
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      "neutral_restoring_frequency": 1.0,
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      "moment_hessian_eigenvalues": [
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      "stable_moment_branch": true
    },
    {
      "case": "mixed-profile-n2-k21.0-t0.95",
      "transverse_dimension": 2,
      "real_depth": 3,
      "actual_hodge_active": true,
      "quadratic_coefficient": 1.0,
      "quartic_coefficient": 1.0,
      "neutral_restoring_frequency": 1.0,
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      "moment_hessian_eigenvalues": [
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      "stable_moment_branch": true
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    {
      "case": "mixed-profile-n2-k21.2-t0.2",
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      "actual_hodge_active": true,
      "quadratic_coefficient": 1.2,
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      "stable_moment_branch": true
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    {
      "case": "mixed-profile-n2-k21.2-t0.5",
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      "actual_hodge_active": true,
      "quadratic_coefficient": 1.2,
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    {
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      "real_depth": 3,
      "actual_hodge_active": true,
      "quadratic_coefficient": 1.2,
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    {
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      "stable_moment_branch": true
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    {
      "case": "mixed-profile-n2-k20.4-t0.8",
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    {
      "case": "mixed-profile-n2-k20.4-t0.95",
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}