Recorded data and provenance for the associated calculation.

Download recorded JSON

timestamp20260914T015614_934737Z
scopeFull complex tangent growth and nonlinear difference in the depth-ten control.
passedtrue
View complete data
{
  "timestamp": "20260914T015614_934737Z",
  "scope": "Full complex tangent growth and nonlinear difference in the depth-ten control.",
  "passed": true,
  "checks": [
    {
      "name": "independent full conjugate tangent derivative",
      "error": 0.0,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "exact cubic difference epsilon=0.7",
      "error": 1.0549707127336644e-14,
      "tolerance": 3e-10,
      "passed": true
    },
    {
      "name": "exact cubic difference epsilon=0.03",
      "error": 1.5309479242439712e-14,
      "tolerance": 3e-10,
      "passed": true
    },
    {
      "name": "exact cubic difference epsilon=0.0001",
      "error": 3.94605707295195e-12,
      "tolerance": 3e-10,
      "passed": true
    },
    {
      "name": "independent centered derivative",
      "error": 1.507755574146815e-08,
      "tolerance": 2e-08,
      "passed": true
    },
    {
      "name": "real Hamiltonian Hessian symmetry",
      "error": 3.608224830031759e-16,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "complete independent phase Ward identity family=0",
      "error": 0.0,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "complete independent phase Ward identity family=1",
      "error": 0.0,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "both full variational evolutions completed",
      "error": 0.0,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full tangent growth independent refinement",
      "error": 2.6763070463478166e-09,
      "tolerance": 2e-07,
      "passed": true
    },
    {
      "name": "linearized family norm conservation slice(0, 6, None)",
      "error": 4.2174144186611664e-14,
      "tolerance": 3e-08,
      "passed": true
    },
    {
      "name": "linearized family norm conservation slice(6, None, None)",
      "error": 1.4016483825484536e-11,
      "tolerance": 3e-08,
      "passed": true
    },
    {
      "name": "finite nonlinear differences approach the tangent linearly",
      "error": 0.0033433166934093705,
      "tolerance": 0.015,
      "passed": true
    }
  ],
  "results": [
    {
      "slow_time": 0.0,
      "tangent_norm": 0.9999999999999999,
      "nonlinear_error_epsilon_1e6": 0.0,
      "nonlinear_error_epsilon_5e7": 0.0,
      "actual_difference_epsilon_1e6": 9.999999999999997e-07,
      "refinement_error": 0.0
    },
    {
      "slow_time": 0.25,
      "tangent_norm": 1.7668013647079572,
      "nonlinear_error_epsilon_1e6": 4.84244897076963e-06,
      "nonlinear_error_epsilon_5e7": 2.421226063363348e-06,
      "actual_difference_epsilon_1e6": 1.7668008264775743e-06,
      "refinement_error": 5.660463098477826e-12
    },
    {
      "slow_time": 0.5,
      "tangent_norm": 3.0001431089893553,
      "nonlinear_error_epsilon_1e6": 1.53662443293474e-05,
      "nonlinear_error_epsilon_5e7": 7.683125234874905e-06,
      "actual_difference_epsilon_1e6": 3.000141711916226e-06,
      "refinement_error": 6.72421102178003e-12
    },
    {
      "slow_time": 0.75,
      "tangent_norm": 4.312515925246071,
      "nonlinear_error_epsilon_1e6": 3.166927412458473e-05,
      "nonlinear_error_epsilon_5e7": 1.5834637223369436e-05,
      "actual_difference_epsilon_1e6": 4.31251359142566e-06,
      "refinement_error": 1.6767850298316652e-11
    },
    {
      "slow_time": 1.0,
      "tangent_norm": 5.624463096816387,
      "nonlinear_error_epsilon_1e6": 5.230061274290147e-05,
      "nonlinear_error_epsilon_5e7": 2.6150293321147585e-05,
      "actual_difference_epsilon_1e6": 5.6244595073784694e-06,
      "refinement_error": 2.2726516793646845e-12
    },
    {
      "slow_time": 1.25,
      "tangent_norm": 6.892728782447298,
      "nonlinear_error_epsilon_1e6": 7.50479866190944e-05,
      "nonlinear_error_epsilon_5e7": 3.752395170366351e-05,
      "actual_difference_epsilon_1e6": 6.8927230802169336e-06,
      "refinement_error": 3.272342946217067e-12
    },
    {
      "slow_time": 1.5,
      "tangent_norm": 8.097025914008857,
      "nonlinear_error_epsilon_1e6": 9.786080033985758e-05,
      "nonlinear_error_epsilon_5e7": 4.893031488407722e-05,
      "actual_difference_epsilon_1e6": 8.097016727614847e-06,
      "refinement_error": 8.557920226341932e-12
    },
    {
      "slow_time": 1.75,
      "tangent_norm": 9.237514177853454,
      "nonlinear_error_epsilon_1e6": 0.00011997943113079874,
      "nonlinear_error_epsilon_5e7": 5.9989578864033406e-05,
      "actual_difference_epsilon_1e6": 9.237500312510037e-06,
      "refinement_error": 3.989464042639478e-12
    },
    {
      "slow_time": 2.0,
      "tangent_norm": 10.309536818494543,
      "nonlinear_error_epsilon_1e6": 0.0001424034865437354,
      "nonlinear_error_epsilon_5e7": 7.120155694999857e-05,
      "actual_difference_epsilon_1e6": 1.0309518195625896e-05,
      "refinement_error": 5.614991612527672e-12
    },
    {
      "slow_time": 2.25,
      "tangent_norm": 11.288579604815881,
      "nonlinear_error_epsilon_1e6": 0.00016781751462694266,
      "nonlinear_error_epsilon_5e7": 8.390852862612425e-05,
      "actual_difference_epsilon_1e6": 1.1288557568805436e-05,
      "refinement_error": 4.179038524327998e-12
    },
    {
      "slow_time": 2.5,
      "tangent_norm": 12.150495116964313,
      "nonlinear_error_epsilon_1e6": 0.0002005296819994953,
      "nonlinear_error_epsilon_5e7": 0.0001002645795760013,
      "actual_difference_epsilon_1e6": 1.2150471982180666e-05,
      "refinement_error": 7.031808201452772e-12
    },
    {
      "slow_time": 2.75,
      "tangent_norm": 12.901456900783776,
      "nonlinear_error_epsilon_1e6": 0.000246066748391985,
      "nonlinear_error_epsilon_5e7": 0.0001230330947658918,
      "actual_difference_epsilon_1e6": 1.29014352549192e-05,
      "refinement_error": 3.7971140058331255e-12
    },
    {
      "slow_time": 3.0,
      "tangent_norm": 13.591682489887194,
      "nonlinear_error_epsilon_1e6": 0.00030991484342272354,
      "nonlinear_error_epsilon_5e7": 0.00015495715152567599,
      "actual_difference_epsilon_1e6": 1.3591664518238966e-05,
      "refinement_error": 6.000324423641465e-12
    },
    {
      "slow_time": 3.25,
      "tangent_norm": 14.314943542744208,
      "nonlinear_error_epsilon_1e6": 0.00039571035205342067,
      "nonlinear_error_epsilon_5e7": 0.00019785496423540684,
      "actual_difference_epsilon_1e6": 1.4314930355008626e-05,
      "refinement_error": 4.115455044080882e-12
    },
    {
      "slow_time": 3.5,
      "tangent_norm": 15.199682420144203,
      "nonlinear_error_epsilon_1e6": 0.0005033355072038665,
      "nonlinear_error_epsilon_5e7": 0.00025166767782386644,
      "actual_difference_epsilon_1e6": 1.5199673637232497e-05,
      "refinement_error": 4.550672191427408e-12
    },
    {
      "slow_time": 3.75,
      "tangent_norm": 16.387180082598682,
      "nonlinear_error_epsilon_1e6": 0.0006271899057669992,
      "nonlinear_error_epsilon_5e7": 0.00031359511438049315,
      "actual_difference_epsilon_1e6": 1.638717449832581e-05,
      "refinement_error": 3.5032868226545075e-12
    },
    {
      "slow_time": 4.0,
      "tangent_norm": 17.997085165732848,
      "nonlinear_error_epsilon_1e6": 0.0007559060647772423,
      "nonlinear_error_epsilon_5e7": 0.00037795353307324775,
      "actual_difference_epsilon_1e6": 1.7997082999864096e-05,
      "refinement_error": 1.101889493930467e-11
    },
    {
      "slow_time": 4.25,
      "tangent_norm": 20.088900200312416,
      "nonlinear_error_epsilon_1e6": 0.0008756516917800441,
      "nonlinear_error_epsilon_5e7": 0.00043782675256036075,
      "actual_difference_epsilon_1e6": 2.0088905455099402e-05,
      "refinement_error": 5.7506606808453554e-12
    },
    {
      "slow_time": 4.5,
      "tangent_norm": 22.613289246479955,
      "nonlinear_error_epsilon_1e6": 0.0009769353057281754,
      "nonlinear_error_epsilon_5e7": 0.0004884689665886206,
      "actual_difference_epsilon_1e6": 2.2613309218510963e-05,
      "refinement_error": 5.2982960686106864e-12
    },
    {
      "slow_time": 4.75,
      "tangent_norm": 25.3735208664348,
      "nonlinear_error_epsilon_1e6": 0.001060784856802878,
      "nonlinear_error_epsilon_5e7": 0.000530394068857903,
      "actual_difference_epsilon_1e6": 2.5373562406254115e-05,
      "refinement_error": 6.995202425450838e-12
    },
    {
      "slow_time": 5.0,
      "tangent_norm": 28.07219725237179,
      "nonlinear_error_epsilon_1e6": 0.001140029321812017,
      "nonlinear_error_epsilon_5e7": 0.0005700164538887606,
      "actual_difference_epsilon_1e6": 2.8072263243224282e-05,
      "refinement_error": 6.444046588024362e-12
    },
    {
      "slow_time": 5.25,
      "tangent_norm": 30.436943563122473,
      "nonlinear_error_epsilon_1e6": 0.0012360295936347692,
      "nonlinear_error_epsilon_5e7": 0.0006180164613211462,
      "actual_difference_epsilon_1e6": 3.0437032448757707e-05,
      "refinement_error": 8.759351915560028e-12
    },
    {
      "slow_time": 5.5,
      "tangent_norm": 32.31614620013164,
      "nonlinear_error_epsilon_1e6": 0.0013745364696045588,
      "nonlinear_error_epsilon_5e7": 0.0006872693966612404,
      "actual_difference_epsilon_1e6": 3.231625394673739e-05,
      "refinement_error": 1.0353917577009424e-11
    },
    {
      "slow_time": 5.75,
      "tangent_norm": 33.69694323960512,
      "nonlinear_error_epsilon_1e6": 0.0015826925946077848,
      "nonlinear_error_epsilon_5e7": 0.0007913465504581674,
      "actual_difference_epsilon_1e6": 3.369706569302594e-05,
      "refinement_error": 7.578651117405324e-12
    },
    {
      "slow_time": 6.0,
      "tangent_norm": 34.69435019683259,
      "nonlinear_error_epsilon_1e6": 0.0018854620929752218,
      "nonlinear_error_epsilon_5e7": 0.0009427300408022102,
      "actual_difference_epsilon_1e6": 3.4694484395456035e-05,
      "refinement_error": 1.042127921607502e-11
    },
    {
      "slow_time": 6.25,
      "tangent_norm": 35.56415930365158,
      "nonlinear_error_epsilon_1e6": 0.0022983285172669455,
      "nonlinear_error_epsilon_5e7": 0.0011491617713869254,
      "actual_difference_epsilon_1e6": 3.556430297812426e-05,
      "refinement_error": 6.496763197361661e-12
    },
    {
      "slow_time": 6.5,
      "tangent_norm": 36.72807546735819,
      "nonlinear_error_epsilon_1e6": 0.002815967367259209,
      "nonlinear_error_epsilon_5e7": 0.0014079796638757365,
      "actual_difference_epsilon_1e6": 3.6728224348012666e-05,
      "refinement_error": 9.677631566604533e-12
    },
    {
      "slow_time": 6.75,
      "tangent_norm": 38.73011552699433,
      "nonlinear_error_epsilon_1e6": 0.003404480913394624,
      "nonlinear_error_epsilon_5e7": 0.0017022350831720349,
      "actual_difference_epsilon_1e6": 3.873025969209868e-05,
      "refinement_error": 1.1015307207859957e-11
    },
    {
      "slow_time": 7.0,
      "tangent_norm": 42.04813121362713,
      "nonlinear_error_epsilon_1e6": 0.0040116769913935224,
      "nonlinear_error_epsilon_5e7": 0.00200583226034942,
      "actual_difference_epsilon_1e6": 4.204825466795661e-05,
      "refinement_error": 9.935148040327203e-12
    },
    {
      "slow_time": 7.25,
      "tangent_norm": 46.82143351079514,
      "nonlinear_error_epsilon_1e6": 0.0046002004084234735,
      "nonlinear_error_epsilon_5e7": 0.0023000938587195885,
      "actual_difference_epsilon_1e6": 4.6821519421769245e-05,
      "refinement_error": 1.6676882757563216e-11
    },
    {
      "slow_time": 7.5,
      "tangent_norm": 52.708285682057294,
      "nonlinear_error_epsilon_1e6": 0.005181494892416828,
      "nonlinear_error_epsilon_5e7": 0.002590741490504736,
      "actual_difference_epsilon_1e6": 5.2708322118844494e-05,
      "refinement_error": 1.7068266613589224e-11
    },
    {
      "slow_time": 7.75,
      "tangent_norm": 59.027574258174354,
      "nonlinear_error_epsilon_1e6": 0.005819377348637511,
      "nonlinear_error_epsilon_5e7": 0.002909682320737041,
      "actual_difference_epsilon_1e6": 5.902755609987846e-05,
      "refinement_error": 2.0674465863132674e-11
    },
    {
      "slow_time": 8.0,
      "tangent_norm": 65.08305427076603,
      "nonlinear_error_epsilon_1e6": 0.006604882688657261,
      "nonlinear_error_epsilon_5e7": 0.0033024316016852166,
      "actual_difference_epsilon_1e6": 6.508298510370172e-05,
      "refinement_error": 2.2614063316303374e-11
    },
    {
      "slow_time": 8.25,
      "tangent_norm": 70.43076553699042,
      "nonlinear_error_epsilon_1e6": 0.007640234028972098,
      "nonlinear_error_epsilon_5e7": 0.003820098830168877,
      "actual_difference_epsilon_1e6": 7.043066311298664e-05,
      "refinement_error": 2.227831540262571e-11
    },
    {
      "slow_time": 8.5,
      "tangent_norm": 74.98370926169288,
      "nonlinear_error_epsilon_1e6": 0.009053028962386333,
      "nonlinear_error_epsilon_5e7": 0.004526482100657186,
      "actual_difference_epsilon_1e6": 7.49836122799334e-05,
      "refinement_error": 2.2834616342536735e-11
    },
    {
      "slow_time": 8.75,
      "tangent_norm": 79.03538560237034,
      "nonlinear_error_epsilon_1e6": 0.01101368429218083,
      "nonlinear_error_epsilon_5e7": 0.005506790884244358,
      "actual_difference_epsilon_1e6": 7.903535578006256e-05,
      "refinement_error": 2.3303443308701578e-11
    },
    {
      "slow_time": 9.0,
      "tangent_norm": 83.31741541981108,
      "nonlinear_error_epsilon_1e6": 0.013719119746109653,
      "nonlinear_error_epsilon_5e7": 0.006859487543065088,
      "actual_difference_epsilon_1e6": 8.33175247994876e-05,
      "refinement_error": 2.3430501753783677e-11
    },
    {
      "slow_time": 9.25,
      "tangent_norm": 89.09032640992837,
      "nonlinear_error_epsilon_1e6": 0.01734450270352115,
      "nonlinear_error_epsilon_5e7": 0.008672160070945286,
      "actual_difference_epsilon_1e6": 8.909061402253292e-05,
      "refinement_error": 2.969924383956621e-11
    },
    {
      "slow_time": 9.5,
      "tangent_norm": 98.09382255876324,
      "nonlinear_error_epsilon_1e6": 0.02201774858741673,
      "nonlinear_error_epsilon_5e7": 0.011008775329248365,
      "actual_difference_epsilon_1e6": 9.809420919049242e-05,
      "refinement_error": 2.3550888930454203e-11
    },
    {
      "slow_time": 9.75,
      "tangent_norm": 112.11065385169859,
      "nonlinear_error_epsilon_1e6": 0.027894249783106555,
      "nonlinear_error_epsilon_5e7": 0.013947050297448228,
      "actual_difference_epsilon_1e6": 0.00011211084550614816,
      "refinement_error": 2.7420632633110926e-11
    },
    {
      "slow_time": 10.0,
      "tangent_norm": 132.14794415705774,
      "nonlinear_error_epsilon_1e6": 0.035339999687611076,
      "nonlinear_error_epsilon_5e7": 0.017670024636131314,
      "actual_difference_epsilon_1e6": 0.0001321474159605294,
      "refinement_error": 2.9952689217751224e-11
    },
    {
      "slow_time": 10.25,
      "tangent_norm": 157.73827670186935,
      "nonlinear_error_epsilon_1e6": 0.04505495229174844,
      "nonlinear_error_epsilon_5e7": 0.0225277480282377,
      "actual_difference_epsilon_1e6": 0.00015773640167829526,
      "refinement_error": 3.1539268678465635e-11
    },
    {
      "slow_time": 10.5,
      "tangent_norm": 186.98433515351846,
      "nonlinear_error_epsilon_1e6": 0.057896244750645504,
      "nonlinear_error_epsilon_5e7": 0.02894887523567319,
      "actual_difference_epsilon_1e6": 0.0001869806013072275,
      "refinement_error": 2.6164052770711787e-11
    },
    {
      "slow_time": 10.75,
      "tangent_norm": 217.3926935219271,
      "nonlinear_error_epsilon_1e6": 0.07450918303547897,
      "nonlinear_error_epsilon_5e7": 0.03725610993333086,
      "actual_difference_epsilon_1e6": 0.00021738690821950513,
      "refinement_error": 3.403867376038676e-11
    },
    {
      "slow_time": 11.0,
      "tangent_norm": 246.9324765504583,
      "nonlinear_error_epsilon_1e6": 0.09531241668579152,
      "nonlinear_error_epsilon_5e7": 0.047658745059285273,
      "actual_difference_epsilon_1e6": 0.00024692492674137156,
      "refinement_error": 3.52054971966454e-11
    },
    {
      "slow_time": 11.25,
      "tangent_norm": 274.7930188139279,
      "nonlinear_error_epsilon_1e6": 0.121134951174371,
      "nonlinear_error_epsilon_5e7": 0.060571161039567396,
      "actual_difference_epsilon_1e6": 0.0002747846058869357,
      "refinement_error": 3.548404425667802e-11
    },
    {
      "slow_time": 11.5,
      "tangent_norm": 301.8006938166491,
      "nonlinear_error_epsilon_1e6": 0.154151172514366,
      "nonlinear_error_epsilon_5e7": 0.07708036648486401,
      "actual_difference_epsilon_1e6": 0.0003017930008688234,
      "refinement_error": 3.524453280425418e-11
    },
    {
      "slow_time": 11.75,
      "tangent_norm": 330.78616718779324,
      "nonlinear_error_epsilon_1e6": 0.1985437386561671,
      "nonlinear_error_epsilon_5e7": 0.09927748803596097,
      "actual_difference_epsilon_1e6": 0.0003307812316540969,
      "refinement_error": 3.4347841758916735e-11
    },
    {
      "slow_time": 12.0,
      "tangent_norm": 367.05612183460664,
      "nonlinear_error_epsilon_1e6": 0.2607249439158885,
      "nonlinear_error_epsilon_5e7": 0.13036852195115384,
      "actual_difference_epsilon_1e6": 0.00036705537146079916,
      "refinement_error": 3.415428561174512e-11
    },
    {
      "slow_time": 12.25,
      "tangent_norm": 418.5699554101364,
      "nonlinear_error_epsilon_1e6": 0.3497755137560137,
      "nonlinear_error_epsilon_5e7": 0.17489396363221923,
      "actual_difference_epsilon_1e6": 0.0004185714170158,
      "refinement_error": 3.6551280061980044e-11
    },
    {
      "slow_time": 12.5,
      "tangent_norm": 494.8500898127599,
      "nonlinear_error_epsilon_1e6": 0.4792652800641969,
      "nonlinear_error_epsilon_5e7": 0.2396400654828791,
      "actual_difference_epsilon_1e6": 0.0004948430489358784,
      "refinement_error": 3.7471868538176935e-11
    },
    {
      "slow_time": 12.75,
      "tangent_norm": 603.8682150480214,
      "nonlinear_error_epsilon_1e6": 0.6701128194538587,
      "nonlinear_error_epsilon_5e7": 0.3350714464194891,
      "actual_difference_epsilon_1e6": 0.0006038253599083666,
      "refinement_error": 4.335886377626244e-11
    },
    {
      "slow_time": 13.0,
      "tangent_norm": 747.6821648077674,
      "nonlinear_error_epsilon_1e6": 0.9498099317850249,
      "nonlinear_error_epsilon_5e7": 0.4749485228732497,
      "actual_difference_epsilon_1e6": 0.0007475505054273258,
      "refinement_error": 5.2997853202966566e-11
    },
    {
      "slow_time": 13.25,
      "tangent_norm": 919.53675964255,
      "nonlinear_error_epsilon_1e6": 1.3416440292437701,
      "nonlinear_error_epsilon_5e7": 0.6709412354390808,
      "actual_difference_epsilon_1e6": 0.0009192308438008106,
      "refinement_error": 4.662544453657885e-11
    },
    {
      "slow_time": 13.5,
      "tangent_norm": 1105.475593652739,
      "nonlinear_error_epsilon_1e6": 1.8488565363340097,
      "nonlinear_error_epsilon_5e7": 0.9246955936065304,
      "actual_difference_epsilon_1e6": 0.0011048801484806932,
      "refinement_error": 4.932534213236757e-11
    },
    {
      "slow_time": 13.75,
      "tangent_norm": 1291.0050925916312,
      "nonlinear_error_epsilon_1e6": 2.454128728192396,
      "nonlinear_error_epsilon_5e7": 1.2275456903254143,
      "actual_difference_epsilon_1e6": 0.0012899934753874645,
      "refinement_error": 5.77671355502655e-11
    },
    {
      "slow_time": 14.0,
      "tangent_norm": 1469.2352616369096,
      "nonlinear_error_epsilon_1e6": 3.1430215438809173,
      "nonlinear_error_epsilon_5e7": 1.5722148738009112,
      "actual_difference_epsilon_1e6": 0.001467698257978637,
      "refinement_error": 5.408123056952278e-11
    },
    {
      "slow_time": 14.25,
      "tangent_norm": 1644.677355102291,
      "nonlinear_error_epsilon_1e6": 3.9275038316035498,
      "nonlinear_error_epsilon_5e7": 1.9646115175945917,
      "actual_difference_epsilon_1e6": 0.0016425397119173644,
      "refinement_error": 4.739981506433142e-11
    },
    {
      "slow_time": 14.5,
      "tangent_norm": 1828.7641257861005,
      "nonlinear_error_epsilon_1e6": 4.849606340276439,
      "nonlinear_error_epsilon_5e7": 2.42571669462521,
      "actual_difference_epsilon_1e6": 0.001825961320888979,
      "refinement_error": 4.432955796503155e-11
    },
    {
      "slow_time": 14.75,
      "tangent_norm": 2027.91095016001,
      "nonlinear_error_epsilon_1e6": 5.987758900506443,
      "nonlinear_error_epsilon_5e7": 2.994803398568492,
      "actual_difference_epsilon_1e6": 0.002024319845888559,
      "refinement_error": 4.813687556084183e-11
    },
    {
      "slow_time": 15.0,
      "tangent_norm": 2230.954507139164,
      "nonlinear_error_epsilon_1e6": 7.495602522222158,
      "nonlinear_error_epsilon_5e7": 3.748964517011144,
      "actual_difference_epsilon_1e6": 0.0022263157086816225,
      "refinement_error": 3.8981138280969125e-11
    },
    {
      "slow_time": 15.25,
      "tangent_norm": 2408.4374063978366,
      "nonlinear_error_epsilon_1e6": 9.62946982612141,
      "nonlinear_error_epsilon_5e7": 4.817145619895858,
      "actual_difference_epsilon_1e6": 0.0024023581250364467,
      "refinement_error": 5.989241724158966e-11
    },
    {
      "slow_time": 15.5,
      "tangent_norm": 2524.47878972382,
      "nonlinear_error_epsilon_1e6": 12.553859404510506,
      "nonlinear_error_epsilon_5e7": 6.282979303649213,
      "actual_difference_epsilon_1e6": 0.0025166515882182596,
      "refinement_error": 6.336942435588838e-11
    },
    {
      "slow_time": 15.75,
      "tangent_norm": 2504.3176225905354,
      "nonlinear_error_epsilon_1e6": 15.792543439796747,
      "nonlinear_error_epsilon_5e7": 7.909528048559039,
      "actual_difference_epsilon_1e6": 0.002495057002795029,
      "refinement_error": 9.215341943016769e-11
    },
    {
      "slow_time": 16.0,
      "tangent_norm": 2183.175758894036,
      "nonlinear_error_epsilon_1e6": 17.957124329164397,
      "nonlinear_error_epsilon_5e7": 9.002291074261723,
      "actual_difference_epsilon_1e6": 0.0021744765136035953,
      "refinement_error": 1.1669772466230286e-10
    },
    {
      "slow_time": 16.25,
      "tangent_norm": 1732.1457333894045,
      "nonlinear_error_epsilon_1e6": 16.88268632125807,
      "nonlinear_error_epsilon_5e7": 8.475466215442461,
      "actual_difference_epsilon_1e6": 0.0017298719695560086,
      "refinement_error": 1.5779549778667295e-10
    },
    {
      "slow_time": 16.5,
      "tangent_norm": 1947.3557714388216,
      "nonlinear_error_epsilon_1e6": 12.758474162934638,
      "nonlinear_error_epsilon_5e7": 6.413346166354956,
      "actual_difference_epsilon_1e6": 0.0019507555745651424,
      "refinement_error": 1.6564545495536765e-10
    },
    {
      "slow_time": 16.75,
      "tangent_norm": 2455.962425221644,
      "nonlinear_error_epsilon_1e6": 16.983090272326812,
      "nonlinear_error_epsilon_5e7": 8.503283506712473,
      "actual_difference_epsilon_1e6": 0.0024496686635179176,
      "refinement_error": 1.6327337956335708e-10
    },
    {
      "slow_time": 17.0,
      "tangent_norm": 2605.363256397228,
      "nonlinear_error_epsilon_1e6": 25.201856849207328,
      "nonlinear_error_epsilon_5e7": 12.630229263967685,
      "actual_difference_epsilon_1e6": 0.002587429943938406,
      "refinement_error": 1.7915821351140775e-10
    },
    {
      "slow_time": 17.25,
      "tangent_norm": 2061.219029431517,
      "nonlinear_error_epsilon_1e6": 33.65655161822254,
      "nonlinear_error_epsilon_5e7": 16.902242337937004,
      "actual_difference_epsilon_1e6": 0.002045716663133578,
      "refinement_error": 3.200128664615956e-10
    },
    {
      "slow_time": 17.5,
      "tangent_norm": 1678.142761720026,
      "nonlinear_error_epsilon_1e6": 25.176459163449664,
      "nonlinear_error_epsilon_5e7": 12.672402457926934,
      "actual_difference_epsilon_1e6": 0.0016716277774000573,
      "refinement_error": 3.5663945010397676e-10
    },
    {
      "slow_time": 17.75,
      "tangent_norm": 1963.8045584510764,
      "nonlinear_error_epsilon_1e6": 29.55922748196739,
      "nonlinear_error_epsilon_5e7": 14.755544882544077,
      "actual_difference_epsilon_1e6": 0.0019615462328432306,
      "refinement_error": 4.927955362360799e-10
    },
    {
      "slow_time": 18.0,
      "tangent_norm": 2468.8179296847766,
      "nonlinear_error_epsilon_1e6": 57.41721887651983,
      "nonlinear_error_epsilon_5e7": 28.733181665341608,
      "actual_difference_epsilon_1e6": 0.002439213461033827,
      "refinement_error": 6.298221140966498e-10
    },
    {
      "slow_time": 18.25,
      "tangent_norm": 2423.7169121030734,
      "nonlinear_error_epsilon_1e6": 41.49147184320644,
      "nonlinear_error_epsilon_5e7": 20.812454962814897,
      "actual_difference_epsilon_1e6": 0.002401248134365997,
      "refinement_error": 4.5851532733985934e-10
    },
    {
      "slow_time": 18.5,
      "tangent_norm": 2573.747388128309,
      "nonlinear_error_epsilon_1e6": 92.07767448875019,
      "nonlinear_error_epsilon_5e7": 46.02626373854742,
      "actual_difference_epsilon_1e6": 0.0025144370809932638,
      "refinement_error": 1.0312098895984006e-09
    },
    {
      "slow_time": 18.75,
      "tangent_norm": 2852.512312593543,
      "nonlinear_error_epsilon_1e6": 107.32837536291801,
      "nonlinear_error_epsilon_5e7": 54.05766511433501,
      "actual_difference_epsilon_1e6": 0.002776407088179226,
      "refinement_error": 5.855261244429843e-10
    },
    {
      "slow_time": 19.0,
      "tangent_norm": 3024.787976123352,
      "nonlinear_error_epsilon_1e6": 73.86863082828789,
      "nonlinear_error_epsilon_5e7": 36.82301286678827,
      "actual_difference_epsilon_1e6": 0.00297198759685638,
      "refinement_error": 1.696678197553851e-09
    },
    {
      "slow_time": 19.25,
      "tangent_norm": 5905.872215254565,
      "nonlinear_error_epsilon_1e6": 219.0502871161297,
      "nonlinear_error_epsilon_5e7": 108.66159610705415,
      "actual_difference_epsilon_1e6": 0.005699267401153366,
      "refinement_error": 1.7367074688128329e-09
    },
    {
      "slow_time": 19.5,
      "tangent_norm": 8770.368785464838,
      "nonlinear_error_epsilon_1e6": 411.06308205175645,
      "nonlinear_error_epsilon_5e7": 205.44546417732852,
      "actual_difference_epsilon_1e6": 0.00837259874770377,
      "refinement_error": 1.367103900143897e-09
    },
    {
      "slow_time": 19.75,
      "tangent_norm": 10574.31384984591,
      "nonlinear_error_epsilon_1e6": 620.5284945632279,
      "nonlinear_error_epsilon_5e7": 312.5602392483857,
      "actual_difference_epsilon_1e6": 0.009971497027563479,
      "refinement_error": 1.373666185778444e-09
    },
    {
      "slow_time": 20.0,
      "tangent_norm": 11788.64413015882,
      "nonlinear_error_epsilon_1e6": 857.2827759322923,
      "nonlinear_error_epsilon_5e7": 436.1436737654806,
      "actual_difference_epsilon_1e6": 0.010969894360770302,
      "refinement_error": 2.6763070463478166e-09
    }
  ],
  "sources": {
    "spatial_form_variations.py": "7547907a37ba80d83ca96c8ad3d0e919a88a6f9b2f526153804c5898bb9a46c8",
    "spatial_form_variations_checks.py": "db6dd8224856a94dd1981ec9e8369b8bdfd5ab657d6b1b32b8e0a49d3cfcbc5e",
    "spatial_form_resonance.py": "3eadd72bd1229acaf1283c7b5a54ec8b74ef14a07c80bd64b350bfdd5c993e1d",
    "spatial_form_spectrum.py": "84b1c4345ec7c84f0d2f52c2d1cc41ec5ae1323747cd62893809b26f254daa57",
    "spatial_form_currents.py": "19de395f7b6f3ee4513f265f46f8c3893c04c3a3543896c8440a7d844066dce5",
    "hodge_curvature_chain.py": "207b76d0d4d1f4ba87eff898f653488ecd44ae548deb88d776ec72c66b6e64d5",
    "causal_curvature_chain.py": "d5609e70552f9406a4afec38f2badf3ad6f0ed324b4af9a2b0bb5608fabb2500"
  },
  "raw_data": {
    "path": "spatial-form-variations-20260914T015614_934737Z.npz",
    "sha256": "ed02a6e08b06c5c34030b805a46c9a143c718b0d7db81eed711ca9a78f15b1fb"
  }
}