numerical-evidence.json

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5567 bytes, as of the version from 2026-11-02 11:01 (current). Recorded here, not run.

{
  "table": "T650",
  "instruction_manifest": "agents/runs/20261101T114635Z-build-skills/manifest.json",
  "skills": {
    "manifest": "agents/runs/20261101T114635Z-build-skills/manifest.json",
    "sha256": {
      "skill-local.md": "a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278",
      "skill-live.md": "a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278"
    }
  },
  "rigour": "heuristic (agreement-checked)",
  "stored_significant_digits": 100,
  "root_quadrature_working_digits": [
    135,
    185
  ],
  "hypergeometric_working_digits": 125,
  "hypergeometric_output_digits": 120,
  "control": {
    "control": "N(0)=3sqrt(3)L(2,chi_-3)/(4pi)",
    "value": "0.32306594721945051409363651072380639407224184078058701613086847036",
    "known": "0.32306594721945051409363651072380639407224184078058701613086847036",
    "absolute_error": "5.82901e-73"
  },
  "comparisons": [
    {
      "t": "24",
      "independent_agreement_digits": "120.0159703",
      "precision_agreement_digits": "136.78481",
      "negative": true
    },
    {
      "t": "18-6*sqrt(3)",
      "independent_agreement_digits": "119.4050336",
      "precision_agreement_digits": "136.41509",
      "negative": true
    },
    {
      "t": "-27/2+27/2*sqrt(5)",
      "independent_agreement_digits": "119.9210833",
      "precision_agreement_digits": "124.24802",
      "negative": true
    },
    {
      "t": "-4320+1944*sqrt(5)",
      "independent_agreement_digits": "120.3066282",
      "precision_agreement_digits": "134.83153",
      "negative": true
    },
    {
      "t": "-864+216*sqrt(17)",
      "independent_agreement_digits": "119.8528052",
      "precision_agreement_digits": "135.05779",
      "negative": true
    },
    {
      "t": "-163296+35640*sqrt(21)",
      "independent_agreement_digits": "119.8598323",
      "precision_agreement_digits": "132.18593",
      "negative": true
    },
    {
      "t": "4+4*sqrt(33)",
      "independent_agreement_digits": "120.3614768",
      "precision_agreement_digits": "136.17999",
      "negative": true
    },
    {
      "t": "-16740+2916*sqrt(33)",
      "independent_agreement_digits": "119.618397",
      "precision_agreement_digits": "134.74018",
      "negative": true
    },
    {
      "t": "-55296+8640*sqrt(41)",
      "independent_agreement_digits": "119.7794718",
      "precision_agreement_digits": "134.32197",
      "negative": true
    },
    {
      "t": "-13500000+1431000*sqrt(89)",
      "independent_agreement_digits": "119.6733935",
      "precision_agreement_digits": "131.03401",
      "negative": true
    }
  ],
  "minimum_precision_agreement_digits": 124.24802,
  "minimum_independent_agreement_digits": 119.4050336,
  "gamma_coefficient_simplification_absolute_error": "1.9010916e-211",
  "limitations": [
    "Numerical convergence estimates and precision agreement are not certified error bounds.",
    "The abandoned Arb integration returned nonfinite values and is not evidence for the stored digits."
  ],
  "source_archive": [
    {
      "url": "https://arxiv.org/html/2301.05390v3",
      "file": "samart-v3.html",
      "sha256": "cfd64f6ef10f960fbfeaa88c0e50b6deccfd0daca82ea106b20e372f3cdba425"
    },
    {
      "url": "https://arxiv.org/html/2409.14714v3",
      "file": "samart-tao-v3.html",
      "sha256": "006e2e287b38a67c42f3336e1570d161cb01813df6e837b21862a7599c73da96"
    },
    {
      "url": "https://arxiv.org/html/2310.12510v2",
      "file": "tao-guo-v2.html",
      "sha256": "e0706983ebd2fb92f0854dc178f9a5f664b26b5c25ceb195c9ea3518ede7bed5"
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  ],
  "versions": {
    "python": "3.12.3 (main, Mar 23 2026, 19:04:32) [GCC 13.3.0]",
    "sage": "10.9",
    "numberdb": "0.1.10",
    "mpmath": "1.4.1"
  },
  "cm": {
    "symbolic_model_check": true,
    "all_33_candidates_satisfy_their_Hilbert_polynomial": true,
    "polynomials_match_live_T129": true,
    "selected": [
      "24",
      "18-6*sqrt(3)",
      "-27/2+27/2*sqrt(5)",
      "-4320+1944*sqrt(5)",
      "-864+216*sqrt(17)",
      "-163296+35640*sqrt(21)",
      "4+4*sqrt(33)",
      "-16740+2916*sqrt(33)",
      "-55296+8640*sqrt(41)",
      "-13500000+1431000*sqrt(89)"
    ]
  },
  "dry_run": {
    "passed": true,
    "entries": 10,
    "longest_intermediate_characters": 133,
    "entries_block_kb": 2.2,
    "log": "dry-and-exact.log"
  },
  "elliptic_L_value_control": {
    "conductor": 27,
    "working_digits": [
      145,
      195
    ],
    "precision_agreement_digits": "153.900855",
    "quadrature_agreement_digits": "175.4185079",
    "source": "Tao--Guo v2 Theorem 1.5 and the weight-two functional equation"
  },
  "source_sha256": {
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    "periods.py": "c34b3672c20780860a68b7e61ec751386c68b9874fd0c2955af32ad231e512ce",
    "cm_checks.py": "602bbc7d5b96af28ed5436e1060de4dd719fd3b29ce8b5f591a75113cd9e976e",
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    "argument-selection.md": "3524b8de47af7109eceed7c3cac5299ed0fd9430ef672a41991e07b5b7fffb18"
  }
}