Recorded data and provenance for the associated calculation.

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timestamp20260914T070835_580367Z
scopeCommon cavity scales and frequency units of the inverse normal carrier. All numbers are conditional parameter relations. No measured radius, physical texture strength, or new particle assignment is inferred.
passedtrue
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{
  "timestamp": "20260914T070835_580367Z",
  "scope": "Common cavity scales and frequency units of the inverse normal carrier.\n\nAll numbers are conditional parameter relations. No measured radius,\nphysical texture strength, or new particle assignment is inferred.\n",
  "passed": true,
  "checks": [
    {
      "name": "exact common leading frequency unit at common radius gamma6=1000.0",
      "error": 6.661338147750939e-16,
      "tolerance": 2e-13,
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    },
    {
      "name": "independent factorial and spatial count factor n=6,L=14,g=1000.0",
      "error": 0.0,
      "tolerance": 3e-14,
      "passed": true
    },
    {
      "name": "independent factorial and spatial count factor n=6,L=36,g=1000.0",
      "error": 0.0,
      "tolerance": 3e-14,
      "passed": true
    },
    {
      "name": "independent factorial and spatial count factor n=10,L=24,g=1000.0",
      "error": 2.220446049250313e-16,
      "tolerance": 3e-14,
      "passed": true
    },
    {
      "name": "independent high-precision full singular normalization gamma6=1000.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-13,
      "passed": true
    },
    {
      "name": "exact common leading frequency unit at common radius gamma6=10000.0",
      "error": 5.551115123125783e-16,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent factorial and spatial count factor n=6,L=14,g=10000.0",
      "error": 0.0,
      "tolerance": 3e-14,
      "passed": true
    },
    {
      "name": "independent factorial and spatial count factor n=6,L=36,g=10000.0",
      "error": 0.0,
      "tolerance": 3e-14,
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    },
    {
      "name": "independent factorial and spatial count factor n=10,L=24,g=10000.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-14,
      "passed": true
    },
    {
      "name": "independent high-precision full singular normalization gamma6=10000.0",
      "error": 0.0,
      "tolerance": 3e-13,
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    },
    {
      "name": "exact common leading frequency unit at common radius gamma6=100000.0",
      "error": 2.220446049250313e-16,
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    },
    {
      "name": "independent factorial and spatial count factor n=6,L=14,g=100000.0",
      "error": 0.0,
      "tolerance": 3e-14,
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    },
    {
      "name": "independent factorial and spatial count factor n=6,L=36,g=100000.0",
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    },
    {
      "name": "independent factorial and spatial count factor n=10,L=24,g=100000.0",
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    },
    {
      "name": "independent high-precision full singular normalization gamma6=100000.0",
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    {
      "name": "exact common leading frequency unit at common radius gamma6=1000000.0",
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    {
      "name": "independent factorial and spatial count factor n=6,L=14,g=1000000.0",
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    {
      "name": "independent factorial and spatial count factor n=6,L=36,g=1000000.0",
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    {
      "name": "independent factorial and spatial count factor n=10,L=24,g=1000000.0",
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      "name": "independent high-precision full singular normalization gamma6=1000000.0",
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    },
    {
      "name": "exact inverse-entry bound excludes the assigned tau ratio for common radius and dimensional strength",
      "error": 0.0,
      "tolerance": 0.5,
      "passed": true
    },
    {
      "name": "full finite-chain frequency ratio respects the all-strength inverse bound gamma=0.1",
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      "tolerance": 3e-10,
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    {
      "name": "full finite-chain frequency ratio respects the all-strength inverse bound gamma=0.1539926526059492",
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    {
      "name": "full finite-chain frequency ratio respects the all-strength inverse bound gamma=0.23713737056616552",
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      "name": "full finite-chain frequency ratio respects the all-strength inverse bound gamma=0.3651741272548377",
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    {
      "name": "full finite-chain frequency ratio respects the all-strength inverse bound gamma=0.5623413251903491",
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    {
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      "name": "full finite-chain frequency ratio respects the all-strength inverse bound gamma=3.1622776601683795",
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    {
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      "name": "common dimensional strength has the stated leading frequency unit gamma6=1000.0",
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      "name": "common-radius family reaches both declared count-ratio tolerances 0.001",
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    {
      "name": "common-radius family reaches both declared count-ratio tolerances 1e-05",
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      "name": "common-radius family reaches both declared count-ratio tolerances 1e-07",
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      "tau_relative_finite_strength_correction": -1.0000000022740877e-09,
      "requested_count_ratio_tolerance": 1e-09
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  "common_strength_examples": [
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      "radius6_over_electron_frequency_length": 8.722602725053707e-08,
      "radius10_over_radius6_for_exact_assigned_count_ratio": 1.943438539555803e-08
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    {
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      "radius10_over_radius6_for_exact_assigned_count_ratio": 1.946093678733289e-12
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    {
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      "radius10_over_radius6_for_common_leading_unit": 1.9461204951493108e-16,
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      "radius10_over_radius6_for_exact_assigned_count_ratio": 1.946120226985465e-16
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    {
      "gamma": 1000000.0,
      "radius10_over_radius6_for_common_leading_unit": 1.9461204951493104e-20,
      "radius6_over_electron_frequency_length": 8.727747493312007e-23,
      "radius10_over_radius6_for_exact_assigned_count_ratio": 1.9461204924676718e-20
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  ],
  "exact_common_radius_and_strength_bound": {
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