{
  "experiment_key": "shell-preserving-curvature-locking",
  "created_utc": "2026-10-12T04:44:24.575317+00:00",
  "sources": {
    "experiments/shell-curvature-locking.py": "b6461249405e98dbd094dffe043e996c61d9668599d244c916282b172de29018",
    "experiments/inverse-current-radial.py": "52d9f1c981635192e06d96b11f0b1e4e5e2d1bf3d5ed420b59411fd45ef7be80"
  },
  "conditions": {
    "all assigned shell potential values are preserved": 14,
    "all assigned shell complete first sources are preserved": 14,
    "one common correction removes every assigned shell scalar curvature": 14,
    "one common flat patch equals the exact shell tangent at finite neighboring ratios": 42,
    "flat patch retains a constant source throughout its open neighborhood": 42,
    "flat patch curvature vanishes throughout its open neighborhood": 42,
    "flat patch returns to the original law away from its support": 28,
    "independent full matrix action variation retains the same stationary source": 14,
    "independent full matrix scalar-source derivative vanishes": 14,
    "independent full matrix identity-source derivative vanishes": 14,
    "the assigned shell is the zero mode of the full self-adjoint linearization": 14,
    "the retained background source has its original clock identity": 14
  },
  "evaluations": 266,
  "maximum_errors": {
    "all assigned shell potential values are preserved": "0.0",
    "all assigned shell complete first sources are preserved": "3.06752685169455596279879346862e-141",
    "one common correction removes every assigned shell scalar curvature": "1.37819140210291611941176709082e-137",
    "one common flat patch equals the exact shell tangent at finite neighboring ratios": "0.0",
    "flat patch retains a constant source throughout its open neighborhood": "2.49899409669227254841003626101e-141",
    "flat patch curvature vanishes throughout its open neighborhood": "1.481666431813142395883399021e-137",
    "flat patch returns to the original law away from its support": "0.0",
    "independent full matrix action variation retains the same stationary source": "2.9714121963300195132207943139e-67",
    "independent full matrix scalar-source derivative vanishes": "2.2177701339828832937059923248e-59",
    "independent full matrix identity-source derivative vanishes": "2.11562213305047517174571978637e-59",
    "the assigned shell is the zero mode of the full self-adjoint linearization": "8.59888141768587360229243595386e-137",
    "the retained background source has its original clock identity": "6.59227540857411215383206816504e-137"
  },
  "cases": [
    {
      "particle_assignment": "W",
      "depth": 2,
      "mode_index": 76,
      "spatial_shell_degree": 75,
      "epsilon": "0.003141361256544502617801047120418848167539",
      "c": "0.2403141361256544502617801047120418848168",
      "x": "0.9706951715024549470192639219246464997319",
      "frequency": "9.19162303664921465968586387434554973822",
      "original_scalar_curvature": "282.3060056650609080446551482354984555272",
      "corrected_scalar_curvature": "0.0",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "Z",
      "depth": 2,
      "mode_index": 81,
      "spatial_shell_degree": 80,
      "epsilon": "0.003141361256544502617801047120418848167539",
      "c": "0.2560209424083769633507853403141361256545",
      "x": "0.9666712352440857263521011543606793603828",
      "frequency": "10.4324607329842931937172774869109947644",
      "original_scalar_curvature": "288.5383238007635138199449621936319958624",
      "corrected_scalar_curvature": "3.75999740623169e-145",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "Higgs",
      "depth": 2,
      "mode_index": 95,
      "spatial_shell_degree": 94,
      "epsilon": "0.003141361256544502617801047120418848167539",
      "c": "0.3",
      "x": "0.9539392014169456491526215860232265402546",
      "frequency": "14.32460732984293193717277486910994764398",
      "original_scalar_curvature": "299.8148148148148148148148148148148148148",
      "corrected_scalar_curvature": "0.0",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "down",
      "depth": 3,
      "mode_index": 1,
      "spatial_shell_degree": 0,
      "epsilon": "0.02432432432432432432432432432432432432432",
      "c": "0.04459459459459459459459459459459459459459",
      "x": "0.9990051662193463124280096977106335493469",
      "frequency": "0.02432432432432432432432432432432432432432",
      "original_scalar_curvature": "6598.196056061069835174518370110656612034",
      "corrected_scalar_curvature": "0.0",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "strange",
      "depth": 3,
      "mode_index": 4,
      "spatial_shell_degree": 3,
      "epsilon": "0.02432432432432432432432432432432432432432",
      "c": "0.3",
      "x": "0.9539392014169456491526215860232265402546",
      "frequency": "0.4864864864864864864864864864864864864865",
      "original_scalar_curvature": "83.53086419753086419753086419753086419753",
      "corrected_scalar_curvature": "-5.11176398384009e-148",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "up",
      "depth": 4,
      "mode_index": 3,
      "spatial_shell_degree": 2,
      "epsilon": "0.000004534307705678086824435384225899209896882",
      "c": "0.00006461388480591273724820422521906374103057",
      "x": "0.9999999979125229429653393247513389650767",
      "frequency": "0.00006801461558517130236653076338848814845323",
      "original_scalar_curvature": "9501131297773.856387613383891670359746113",
      "corrected_scalar_curvature": "-1.37819140210292e-137",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "charm",
      "depth": 4,
      "mode_index": 20,
      "spatial_shell_degree": 19,
      "epsilon": "0.000004534307705678086824435384225899209896882",
      "c": "0.007490298470804726260065218459166669815491",
      "x": "0.9999719473209327287640162496317903779518",
      "frequency": "0.04015129473377945883037532732033750363689",
      "original_scalar_curvature": "32949425.99401575530114611680114640692757",
      "corrected_scalar_curvature": "0.0",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "top",
      "depth": 4,
      "mode_index": 72,
      "spatial_shell_degree": 71,
      "epsilon": "0.000004534307705678086824435384225899209896882",
      "c": "0.3",
      "x": "0.9539392014169456491526215860232265402546",
      "frequency": "5.511224300866430630759987757369194669166",
      "original_scalar_curvature": "1878.09034884132844701787344717214205968",
      "corrected_scalar_curvature": "0.0",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "nu1",
      "depth": 5,
      "mode_index": 10,
      "spatial_shell_degree": 9,
      "epsilon": "0.00002181495584895324570184772676040633991095",
      "c": "0.01845617981340941097195323843019577710932",
      "x": "0.9998296702072283966713328560549188622033",
      "frequency": "0.04367354160960439789509914897433349250171",
      "original_scalar_curvature": "1357217.631056063098028230215511424478635",
      "corrected_scalar_curvature": "0.0",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "nu2",
      "depth": 5,
      "mode_index": 15,
      "spatial_shell_degree": 14,
      "epsilon": "0.00002181495584895324570184772676040633991095",
      "c": "0.0751296171960025305348784785765014143363",
      "x": "0.9971737765404694600438646715423786305145",
      "frequency": "0.2536643066116283410210853667700049204845",
      "original_scalar_curvature": "28995.47455766234564923117684945988368784",
      "corrected_scalar_curvature": "-1.16826655408052e-145",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "nu3",
      "depth": 5,
      "mode_index": 22,
      "spatial_shell_degree": 21,
      "epsilon": "0.00002181495584895324570184772676040633991095",
      "c": "0.3",
      "x": "0.9539392014169456491526215860232265402546",
      "frequency": "1.434987795744144502267543466299529039342",
      "original_scalar_curvature": "668.6756546218397103224489357358518948307",
      "corrected_scalar_curvature": "0.0",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "electron",
      "depth": 6,
      "mode_index": 13,
      "spatial_shell_degree": 12,
      "epsilon": "0.0000004874726304429365892894138547846115723294",
      "c": "0.003546452756454611558788522186098093034152",
      "x": "0.9999937113166493486014362711014892551853",
      "frequency": "0.009049441911542674843568678800221529228724",
      "original_scalar_curvature": "267467392.8800959063615189217323154304358",
      "corrected_scalar_curvature": "0.0",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "muon",
      "depth": 6,
      "mode_index": 35,
      "spatial_shell_degree": 34,
      "epsilon": "0.0000004874726304429365892894138547846115723294",
      "c": "0.3",
      "x": "0.9539392014169456491526215860232265402546",
      "frequency": "1.871105195239558945596700351928157366998",
      "original_scalar_curvature": "1118.012509583083433594263971514863172428",
      "corrected_scalar_curvature": "6.20668249056858e-147",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    },
    {
      "particle_assignment": "tau",
      "depth": 10,
      "mode_index": 23,
      "spatial_shell_degree": 22,
      "epsilon": "0.00000001264756232761091072286220148266713351955",
      "c": "0.3",
      "x": "0.9539392014169456491526215860232265402546",
      "frequency": "0.8159225762937936991718598289781779577255",
      "original_scalar_curvature": "898.0227482502795873374285032320983622525",
      "corrected_scalar_curvature": "0.0",
      "flat_patch_inner_half_width": "1/8",
      "flat_patch_outer_half_width": "1/4",
      "full_linearized_spectral_formula": "+/-sqrt((m+d/2)^2+(h*x/c)^2)-h/c, divided by R",
      "classification": "full spin and angular linearization for the preferred-time density action"
    }
  ],
  "limits": [
    "inverse constitutive construction on the supplied ordinary sphere and balanced carrier",
    "the density rho action selects a preferred time frame; no Lorentz completion is claimed",
    "the sine correction alone establishes linear norm persistence, not nonlinear stability",
    "the alternative flat-patch nonlinear persistence uses the separately stated Sobolev bootstrap proof",
    "no Euclidean spatial localization, complete boost inertia or charge selection is established",
    "no field amplitude was chosen to fit mass; one formula applies to every admissible integer shell"
  ]
}