{
  "experiment_key": "positive-wave-exact-count-completion",
  "created_utc": "2026-10-12T10:45:24.880853+00:00",
  "sources": {
    "experiments/positive-count-wave.py": "80cb47fd98590a2a54a8287f8fa24fcbe0b2a9edb48869402aa98a5166e487dc",
    "experiments/convex-count-envelope.py": "6650f29a11b56cf16794e50c809fb92cf6a25829453698095912b357307ad8d0",
    "experiments/forward-count-action.py": "5f1dd9a03cf8e6b07a56d507791fed8ff859f10abf22bb755c60c3bd1ed6d909",
    "experiments/inverse-current-radial.py": "52d9f1c981635192e06d96b11f0b1e4e5e2d1bf3d5ed420b59411fd45ef7be80",
    "experiments/excited-shell-orientation-current.py": "508484d445dbb86da9f88a31642268b5a1dba8264588e6f48ebb6cc00cf9c264"
  },
  "evaluations": 1850,
  "conditions": {
    "all geometric count tangents occur in their ordered convex envelope": 6,
    "one common smoothing width is fixed by all eligible chart nodes": 6,
    "smoothing leaves every eligible exact count contact value unchanged": 498,
    "smoothing retains an open affine chart at every eligible count state": 498,
    "the regularized count envelope remains convex through every tested transition": 141,
    "independent differentiation verifies the complete smoothed source coefficient": 141,
    "independent differentiation verifies the smoothed current-ratio Hessian": 141,
    "the full infinite wave-spectrum zero test reduces to an exact rational equation": 14,
    "the exact nearest-level comparison excludes every spatial zero mode for this assigned state": 27,
    "the complete self-adjoint count generator has a positive distance from zero": 14,
    "the fully squared field equation retains the exact count frequency relatively": 14,
    "complete positive energy divided by canonical phase action equals the count frequency": 14,
    "every retained wave block has nonnegative squared lab frequency": 112,
    "wave evolution conserves the complete graph-energy block with both initial data": 224
  },
  "maximum_errors": {},
  "sectors": [
    {
      "depth": 2,
      "eligible_charts": 281,
      "smoothing_width": "0.00003970760187135478964154730942511701397745508053711967522862079237823054785248194604771451683588689019",
      "maximum_potential_raising_bound_per_norm": "0.003585093821378549168559495025118241186253617517928073380375393501864096523641699501855511204582680949"
    },
    {
      "depth": 3,
      "eligible_charts": 8,
      "smoothing_width": "0.0003924267933121276164437952255906639261229455238488610838033429377433115595597592376670498932562552898",
      "maximum_potential_raising_bound_per_norm": "0.003915142925425683602964113157773660348457025989177738555926524806796790141116644534681266004380813249"
    },
    {
      "depth": 4,
      "eligible_charts": 108,
      "smoothing_width": "0.00000000002581063064296819424690279470796972440268404712337365137284454566576394261256908977301368676600199175",
      "maximum_potential_raising_bound_per_norm": "0.000001707578249130798982080031332604905422201455063652966627073555796328609603313991076949943205081426199"
    },
    {
      "depth": 5,
      "eligible_charts": 30,
      "smoothing_width": "0.000000000956018676766547348984041687630889079211691889890937181170767800871733405477328131867501683787807783",
      "maximum_potential_raising_bound_per_norm": "0.00001499144380061121219077380146721105450298710462665512577137470004018516452107667311594020313224526163"
    },
    {
      "depth": 6,
      "eligible_charts": 45,
      "smoothing_width": "0.0000000000006880302197329862899450721283956323504916728695858806639617808525104144178465376648296513803804031453",
      "maximum_potential_raising_bound_per_norm": "0.0000005400833739507451649492794164356115030532019807649374434219520324954112116472061697063356944589715328"
    },
    {
      "depth": 10,
      "eligible_charts": 26,
      "smoothing_width": "0.000000000000001201325060964117757081416556663318998012326354893798941037337433849835263025743097820301215906063208",
      "maximum_potential_raising_bound_per_norm": "0.00000005067094335291458350883123592916295490065476480762237361127070332433500777046197486286558922743210529"
    }
  ],
  "cases": [
    {
      "particle": "W",
      "depth": 2,
      "inferred_index": 76,
      "frequency_in_radius_units_exact": "8778/955",
      "zero_condition_rhs_exact": "6521296052/139539825",
      "exact_nearest_spatial_levels": [
        5,
        6
      ],
      "full_generator_gap": "0.003689308619752092164379640552649606612144199110763909813575044090134661506417201497647385281543904495",
      "wave_clock_relative_residual": "1.336370333348398539335512886914522349242569089880898618665886539683722852912013910997875064352746394e-98",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "Z",
      "depth": 2,
      "inferred_index": 81,
      "frequency_in_radius_units_exact": "9963/955",
      "zero_condition_rhs_exact": "10195807122/148660075",
      "exact_nearest_spatial_levels": [
        7,
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      ],
      "full_generator_gap": "0.007492712375695916841243799697406470034838881640088997315187570306993290324878024194526624894394268591",
      "wave_clock_relative_residual": "6.377329891126495064469127101491451590060175652543374050358095628336300675096289783329355190650520363e-99",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "Higgs",
      "depth": 2,
      "inferred_index": 95,
      "frequency_in_radius_units_exact": "2736/191",
      "zero_condition_rhs_exact": "5761921/36481",
      "exact_nearest_spatial_levels": [
        11,
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      ],
      "full_generator_gap": "0.01828491780529445454129251645096740937507590923758427091746825658452532411545664007266238640708417341",
      "wave_clock_relative_residual": "1.631582743271389305557261353255657582294227311306862183535944658221805523543025256747761509533436056e-99",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "down",
      "depth": 3,
      "inferred_index": 1,
      "frequency_in_radius_units_exact": "9/370",
      "zero_condition_rhs_exact": "462483/752950",
      "exact_nearest_spatial_levels": [
        0
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      "full_generator_gap": "0.02432432432432432432432432432432432432432432432432432432432432432432432432432432432432432432432432432",
      "wave_clock_relative_residual": "1.893316069661246350768736328545089052714056467919681603528357456427504151848230862225023909707611831e-95",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "strange",
      "depth": 3,
      "inferred_index": 4,
      "frequency_in_radius_units_exact": "18/37",
      "zero_condition_rhs_exact": "32265/5476",
      "exact_nearest_spatial_levels": [
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      "full_generator_gap": "0.01232553282043655481524433192376195766525804191769744062826652252171685920793719096888888493939919478",
      "wave_clock_relative_residual": "1.822775836699111618405242051519260241154584735810452500328401652287217695698489158664221295624553231e-98",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "up",
      "depth": 4,
      "inferred_index": 3,
      "frequency_in_radius_units_exact": "18/264649",
      "zero_condition_rhs_exact": "10085629427100/1330742770819",
      "exact_nearest_spatial_levels": [
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      "full_generator_gap": "0.00001147746635418078187610727168713729245339266808376156439675583093828172113071829781760198538811936184",
      "wave_clock_relative_residual": "4.173055663481156969180781978332134395678883444124917384546620068116633925345246183261275929414250366e-84",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "charm",
      "depth": 4,
      "inferred_index": 20,
      "frequency_in_radius_units_exact": "138/3437",
      "zero_condition_rhs_exact": "50548343558499/234168484487",
      "exact_nearest_spatial_levels": [
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      "full_generator_gap": "0.001629495096510539774986586950080110657122795731377216131962831827259098935417243273571669470102406663",
      "wave_clock_relative_residual": "6.591857208363502746989522358689035651253225968581530920080977217672107906607785616547089571692466235e-92",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "top",
      "depth": 4,
      "inferred_index": 72,
      "frequency_in_radius_units_exact": "1458540/264649",
      "zero_condition_rhs_exact": "187511772402529/70039093201",
      "exact_nearest_spatial_levels": [
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      "full_generator_gap": "0.05624456682785900270233308935760888468074146980653572687316148841064283963894962183965679528916328544",
      "wave_clock_relative_residual": "5.407017291201622367890355460591752592243388001885729072615922845791928680045366334013991145100697649e-98",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "nu1",
      "depth": 5,
      "inferred_index": 10,
      "frequency_in_radius_units_exact": "18018/412561",
      "zero_condition_rhs_exact": "1344840074061849685/17280052698070804",
      "exact_nearest_spatial_levels": [
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      "full_generator_gap": "0.004474874703979116860722226905829063638295660995373468576399174151132523539284767244623608105535917619",
      "wave_clock_relative_residual": "2.562918771789863771249581431544381684534215382510793339795052469866582532642274615425469280738423613e-93",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "nu2",
      "depth": 5,
      "inferred_index": 15,
      "frequency_in_radius_units_exact": "104652/412561",
      "zero_condition_rhs_exact": "7545094106509022895/46894635742895036",
      "exact_nearest_spatial_levels": [
        10,
        11
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      "full_generator_gap": "0.01058665667897608701715356007528257261216285036593198441142483807579538555310647387633733850197247855",
      "wave_clock_relative_residual": "8.381761760762201054711122244724765139963646886736172675756018834431782951425171029242886484579366417e-96",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "nu3",
      "depth": 5,
      "inferred_index": 22,
      "frequency_in_radius_units_exact": "592020/412561",
      "zero_condition_rhs_exact": "224328482165089/680826314884",
      "exact_nearest_spatial_levels": [
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      "full_generator_gap": "0.08289315802489461113708837178539099781467723108140473485942075905935808668505646496992497877735179548",
      "wave_clock_relative_residual": "4.248676208930492989403334494895243158323595523042125505971664153707044655044033018012179954410785418e-98",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "electron",
      "depth": 6,
      "inferred_index": 13,
      "frequency_in_radius_units_exact": "167076/18462575",
      "zero_condition_rhs_exact": "22088096070800678620911/148792053446199749375",
      "exact_nearest_spatial_levels": [
        9,
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      "full_generator_gap": "0.0005259913698991774802753526773738688112686112785110972762529091404081079134181503493424700605261590098",
      "wave_clock_relative_residual": "2.403929242357553679701607321138376097834746217413339478517022928706371282785598113100571285502603629e-90",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "muon",
      "depth": 6,
      "inferred_index": 35,
      "frequency_in_radius_units_exact": "6909084/3692515",
      "zero_condition_rhs_exact": "12420660177041281/13634667025225",
      "exact_nearest_spatial_levels": [
        27,
        28
      ],
      "full_generator_gap": "0.04513250856098201282610479030118090751618168311671810082828452788953589015991760941458639596638757737",
      "wave_clock_relative_residual": "3.403218121214069179686670356698829898042179528732052874640583892858229063328216188874668711339521497e-98",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    },
    {
      "particle": "tau",
      "depth": 10,
      "inferred_index": 23,
      "frequency_in_radius_units_exact": "12192813360/14943591113",
      "zero_condition_rhs_exact": "130145526863214583869801/223310915352532578769",
      "exact_nearest_spatial_levels": [
        19,
        20
      ],
      "full_generator_gap": "0.03812967508445213647185602115405222322595070226226603651050800196289754391875156014708217178845013901",
      "wave_clock_relative_residual": "2.701489628011394710489071554151323964075525833092071260744650618491483557817038173188764548763339179e-97",
      "positive_phase_action_normalization": "Qplus=2*omega*N; not electric charge",
      "classification": "exact positive count standing wave and nonresonant chart-local persistence"
    }
  ],
  "limits": [
    "the positive square action changes the physical kinetic law",
    "the count interaction and sphere geometry remain effective premises",
    "one common compact convolution is an explicit functional choice, not a master-field derivation",
    "nonlinear persistence uses a nodeless field and an open chart; the full generator gap is proved at the diagnostic scales",
    "positive energy and a finite principal cone do not establish Lorentz boost inertia",
    "contact attraction and orientation response from the first-order action are not transferred",
    "source second variations at vacuum retain their regularity qualification"
  ]
}