Recorded data and provenance for the associated calculation.

Download recorded JSON

titleClassical Zero Color Currents and Complete Spatial Dynamics
checks_passed328
dependency_checks_passed192
case_count32
scopeactual finite-parent Clifford and source algebra; free-mode controls, not localized particles or derived occupation
View complete data
{
  "title": "Classical Zero Color Currents and Complete Spatial Dynamics",
  "sources": {
    "experiments/classical-color-source-checks.py": "27cc4d6c2d3afa8b7245d5abadf1fdc53472d2e07a174e5c0c6754ef616daf95",
    "experiments/hodge-gated-gauss-checks.py": "d24406f940aea7e81ee65cb9596a57a3dc88e0f5d03c07106db93cc948ff1faa"
  },
  "checks_passed": 328,
  "dependency_checks_passed": 192,
  "case_count": 32,
  "occupied_depths": [
    2,
    3,
    4,
    5,
    6,
    10
  ],
  "scope": "actual finite-parent Clifford and source algebra; free-mode controls, not localized particles or derived occupation",
  "cases": [
    {
      "case": "complex-paired-normal-line-depth-2",
      "real_depth": 2,
      "linear_branch_rank": 4,
      "normal_casimir": "4/3",
      "normal_number_variance": "1/4",
      "complex_symplectic_norm": "I_4",
      "maximum_packet_source": 0.0,
      "full_free_spatial_dynamics_preserved": true,
      "fibre_singlet": false,
      "physical_particle_identified": false
    },
    {
      "case": "complex-paired-normal-line-depth-3",
      "real_depth": 3,
      "linear_branch_rank": 4,
      "normal_casimir": "4/3",
      "normal_number_variance": "1/4",
      "complex_symplectic_norm": "I_4",
      "maximum_packet_source": 0.0,
      "full_free_spatial_dynamics_preserved": true,
      "fibre_singlet": false,
      "physical_particle_identified": false
    },
    {
      "case": "complex-paired-normal-line-depth-4",
      "real_depth": 4,
      "linear_branch_rank": 4,
      "normal_casimir": "4/3",
      "normal_number_variance": "1/4",
      "complex_symplectic_norm": "I_4",
      "maximum_packet_source": 0.0,
      "full_free_spatial_dynamics_preserved": true,
      "fibre_singlet": false,
      "physical_particle_identified": false
    },
    {
      "case": "positive-pure-triplet-floor-depth-2",
      "real_depth": 2,
      "positive_spin_multiplicity": 2,
      "exact_density_norm_floor": "1/12",
      "sample_density_norms": [
        0.08333333333333326,
        0.29692028583770097,
        0.1352641224094439,
        0.24959007185575893,
        0.14753821434013276
      ],
      "zero_source_allowed": false
    },
    {
      "case": "positive-pure-triplet-floor-depth-3",
      "real_depth": 3,
      "positive_spin_multiplicity": 2,
      "exact_density_norm_floor": "1/12",
      "sample_density_norms": [
        0.08333333333333333,
        0.20649629199592553,
        0.21320078576481258,
        0.10787104388154073,
        0.160759332660435
      ],
      "zero_source_allowed": false
    },
    {
      "case": "positive-pure-triplet-floor-depth-4",
      "real_depth": 4,
      "positive_spin_multiplicity": 2,
      "exact_density_norm_floor": "1/12",
      "sample_density_norms": [
        0.08333333333333329,
        0.15619064044472683,
        0.2528710702738031,
        0.19271699945152532,
        0.2377728294379432
      ],
      "zero_source_allowed": false
    },
    {
      "case": "positive-symbol-depth-2-sample-0",
      "real_depth": 2,
      "momentum": [
        1.6302400683004754,
        1.3093604073423093
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 2.7755575615628914e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-2-sample-1",
      "real_depth": 2,
      "momentum": [
        1.1981329552542803,
        0.6416841050196881
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 2.7755575615628914e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-2-sample-2",
      "real_depth": 2,
      "momentum": [
        -0.8185494684088607,
        -1.6345531419288057
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 2.7755575615628914e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-2-sample-3",
      "real_depth": 2,
      "momentum": [
        -0.11304745886789722,
        0.26709736713908155
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 2.7755575615628914e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-3-sample-0",
      "real_depth": 3,
      "momentum": [
        0.056992492233426,
        0.9280066873722447,
        0.1546595791575885
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": true,
      "maximum_symbol_identity_error": 3.642919299551295e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-3-sample-1",
      "real_depth": 3,
      "momentum": [
        1.6546417043970008,
        0.5094613587628836,
        0.9469642656033326
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": true,
      "maximum_symbol_identity_error": 2.7755575615628914e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-3-sample-2",
      "real_depth": 3,
      "momentum": [
        0.0746400622692435,
        -0.24831785035269835,
        -0.028059641028748503
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": true,
      "maximum_symbol_identity_error": 2.7755575615628914e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-3-sample-3",
      "real_depth": 3,
      "momentum": [
        -0.41977458930674505,
        0.04237545700686721,
        0.26234680127299526
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": true,
      "maximum_symbol_identity_error": 1.3877787807814457e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-4-sample-0",
      "real_depth": 4,
      "momentum": [
        -0.24168272979103075,
        0.4469530567907538,
        0.9160769422054245,
        -0.22639391263254718
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": true,
      "maximum_symbol_identity_error": 2.0816681711721685e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-4-sample-1",
      "real_depth": 4,
      "momentum": [
        0.9111772908486233,
        -0.9278070058937258,
        -0.42166737764110773,
        -0.44651829113859665
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": true,
      "maximum_symbol_identity_error": 2.0816681711721685e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-4-sample-2",
      "real_depth": 4,
      "momentum": [
        -1.3738454630796335,
        0.12400547441542425,
        -0.03783890129141011,
        0.16781735966573436
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": true,
      "maximum_symbol_identity_error": 5.551115123125783e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-4-sample-3",
      "real_depth": 4,
      "momentum": [
        0.4075585876299132,
        -1.3335556586352026,
        1.3985639553353064,
        0.7733517271346563
      ],
      "algebra_dimension": 8,
      "hodge_coefficient_active": true,
      "maximum_symbol_identity_error": 3.122502256758253e-17,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-5-sample-0",
      "real_depth": 5,
      "momentum": [
        -0.5275805380280357,
        0.5850851566990001,
        0.5949097260165285,
        -0.058536277549531834,
        0.08236799626116093
      ],
      "algebra_dimension": 3,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 4.163336342344337e-17,
      "residual_canceled_nonsinglet_exists": true,
      "residual_casimir": "3/4"
    },
    {
      "case": "positive-symbol-depth-5-sample-1",
      "real_depth": 5,
      "momentum": [
        0.2996053622873091,
        -0.08223395370679913,
        -1.6111080128338122,
        0.2454655646226214,
        1.3507178967749294
      ],
      "algebra_dimension": 3,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 1.3877787807814457e-17,
      "residual_canceled_nonsinglet_exists": true,
      "residual_casimir": "3/4"
    },
    {
      "case": "positive-symbol-depth-5-sample-2",
      "real_depth": 5,
      "momentum": [
        -0.5459395805468256,
        0.057352096085120825,
        -1.2906841743594877,
        1.2592341473877566,
        -1.1005946433257017
      ],
      "algebra_dimension": 3,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 2.7755575615628914e-17,
      "residual_canceled_nonsinglet_exists": true,
      "residual_casimir": "3/4"
    },
    {
      "case": "positive-symbol-depth-5-sample-3",
      "real_depth": 5,
      "momentum": [
        -0.14682556999592994,
        0.5692037972470385,
        1.3733728038168918,
        0.2279616370052262,
        1.834379306281833
      ],
      "algebra_dimension": 3,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 2.7755575615628914e-17,
      "residual_canceled_nonsinglet_exists": true,
      "residual_casimir": "3/4"
    },
    {
      "case": "positive-symbol-depth-6-sample-0",
      "real_depth": 6,
      "momentum": [
        1.086840066193116,
        0.44885262912638,
        0.03051832383231402,
        0.28688512640615477,
        1.3286348455958032,
        -1.1052098893761113
      ],
      "algebra_dimension": 3,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 1.3877787807814457e-17,
      "residual_canceled_nonsinglet_exists": true,
      "residual_casimir": "3/4"
    },
    {
      "case": "positive-symbol-depth-6-sample-1",
      "real_depth": 6,
      "momentum": [
        -2.173525423546686,
        0.5769952760803622,
        0.033001725212844994,
        -0.5632553016899738,
        -1.7727588026772674,
        0.0024459145190200465
      ],
      "algebra_dimension": 3,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 3.230922474006803e-17,
      "residual_canceled_nonsinglet_exists": true,
      "residual_casimir": "3/4"
    },
    {
      "case": "positive-symbol-depth-6-sample-2",
      "real_depth": 6,
      "momentum": [
        0.19036927640013807,
        -0.30249487519079793,
        0.35104611991326806,
        -1.5967697063271389,
        -1.3563910002511192,
        2.1248946432734552
      ],
      "algebra_dimension": 3,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 2.7755575615628914e-17,
      "residual_canceled_nonsinglet_exists": true,
      "residual_casimir": "3/4"
    },
    {
      "case": "positive-symbol-depth-6-sample-3",
      "real_depth": 6,
      "momentum": [
        -0.23432464413565626,
        -1.00574225501709,
        -0.12423192106762444,
        -0.7412994297125164,
        1.1102580248159646,
        -0.7237938606788584
      ],
      "algebra_dimension": 3,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 3.469446951953614e-17,
      "residual_canceled_nonsinglet_exists": true,
      "residual_casimir": "3/4"
    },
    {
      "case": "positive-symbol-depth-10-sample-0",
      "real_depth": 10,
      "momentum": [
        0.16421079661542298,
        -0.5724688661874718,
        2.351569630461972,
        0.1273993698146864,
        -1.503844988982626,
        -0.8354713082234965,
        0.9888607202670637,
        -0.5929749757167068,
        1.327857530985295,
        -1.122790016287682
      ],
      "algebra_dimension": 0,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 0.0,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-10-sample-1",
      "real_depth": 10,
      "momentum": [
        0.5656833903007403,
        -1.8041339415519033,
        0.8625167044816235,
        0.27100520752720164,
        -0.7107751791583671,
        -1.3615375619198098,
        -0.03530296717072518,
        -1.3574359217546035,
        -0.311328079195542,
        0.7344959941230649
      ],
      "algebra_dimension": 0,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 0.0,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-10-sample-2",
      "real_depth": 10,
      "momentum": [
        1.9894099218463972,
        0.27849250298397504,
        1.3024313079171759,
        0.29882621401000775,
        0.377925695096193,
        -0.0300853265657526,
        -0.5526465795370735,
        1.3513862172355673,
        1.373784663000161,
        -0.06145979169727436
      ],
      "algebra_dimension": 0,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 0.0,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "positive-symbol-depth-10-sample-3",
      "real_depth": 10,
      "momentum": [
        -0.4142181797301288,
        0.7213498418312421,
        -0.5831795435186335,
        -1.0676587642138302,
        -2.4022514596667577,
        0.6448454298243742,
        -0.8936399583203479,
        -2.2085276434096546,
        1.0209891064065806,
        0.6398382363923608
      ],
      "algebra_dimension": 0,
      "hodge_coefficient_active": false,
      "maximum_symbol_identity_error": 0.0,
      "residual_canceled_nonsinglet_exists": false,
      "residual_casimir": null
    },
    {
      "case": "residual-packet-and-reality-depth-5",
      "real_depth": 5,
      "full_spatial_clifford_algebra_dimension": 32,
      "coherent_two_mode_source_norms": [
        0.4251865946542618,
        0.35712781962960155,
        0.2314589302790927,
        0.36440014209546007
      ],
      "antiunitary_current_cancellation": true,
      "antiunitary_first_order_symplectic_form": "0",
      "antiunitary_full_wave_energy": "0",
      "pure_residual_color_line_density_norm": "1/4",
      "fixed_colored_complex_linear_full_clifford_dark_subspace": false,
      "all_nonlinear_source_free_packets_excluded": false
    },
    {
      "case": "residual-packet-and-reality-depth-6",
      "real_depth": 6,
      "full_spatial_clifford_algebra_dimension": 64,
      "coherent_two_mode_source_norms": [
        0.3405108665041837,
        0.08010340573435619,
        0.6608122200463155,
        1.2152828987162037
      ],
      "antiunitary_current_cancellation": true,
      "antiunitary_first_order_symplectic_form": "0",
      "antiunitary_full_wave_energy": "0",
      "pure_residual_color_line_density_norm": "1/4",
      "fixed_colored_complex_linear_full_clifford_dark_subspace": false,
      "all_nonlinear_source_free_packets_excluded": false
    }
  ]
}