{
  "table": "T443",
  "baseline_sha256": "6f74dc8c0cedc74973b3620d024efb80c1ce12962d0b69d0fd2af3fdf5f8cdb7",
  "candidate_sha256": "0d2dc7beeb02a5441857bf55aa37d60b1809221118010cc8719d07b2ed41f829",
  "proof": {
    "generator_sha256": "c934365c747765746ebf794bdff31c0c27756902c89a18a2aef06f044a871a79",
    "entries_sha256": "ae057f7f2cf1f91ed81e9921362b67fae29462909f60772d863b344b76bede9b",
    "all_entries_checked": true,
    "source_analysis": "The attached baseline generator used SciPy/NumPy double precision, a finite BVP on [-20,8], double-precision Airy-kernel Nystr\u00f6m checks, and MAX_DIGITS = 10. The low precision was therefore caused by machine doubles plus intentional truncation after comparison, not by a source-limited published bound. No parameter singularity occurs in the retained range, but the left endpoint is the most ill-conditioned Fredholm control.",
    "convergence_settings": {
      "standard_taylor": {
        "working_digits": 230,
        "series_terms": 180,
        "max_step": "1/8",
        "right_boundary": 40,
        "max_hamiltonian_abs": "0e-229"
      },
      "strong_taylor": {
        "working_digits": 280,
        "series_terms": 240,
        "max_step": "1/12",
        "right_boundary": 48,
        "max_hamiltonian_abs": "0e-279"
      },
      "agreement_tolerance_relative": "1e-112",
      "hamiltonian_tolerance_absolute": "1e-112",
      "stored_digits": 100,
      "entries_checked": 49
    },
    "worst_discrepancies": {
      "taylor_relative": "6.6318618168586463930e-146",
      "taylor_absolute": "1.1479918328505783441e-145",
      "taylor_argument": "-6",
      "standard_hamiltonian_abs": "0e-229",
      "strong_hamiltonian_abs": "0e-279",
      "fredholm_relative": "1.4054574233560079477e-100",
      "fredholm_argument": "-6"
    },
    "supported_significant_digits": {
      "minimum_for_stored_entries": 100,
      "basis": "All 49 stored entries were computed in two Taylor integrations with different working precision, order, step size and right boundary; the worst relative difference was 6.6318618168586463930e-146. The independent Fredholm controls compare only selected values and are limited by comparison to the rounded 100-digit stored strings."
    },
    "independent_checks": [
      {
        "method": "Airy-kernel Fredholm resolvent midpoint Nystrom solve",
        "artifact": "fredholm-check.json",
        "arguments": [
          "-6",
          "0",
          "2"
        ],
        "nodes": 260,
        "length": 52,
        "working_digits": 210,
        "worst_relative_difference": "1.4054574233560079477e-100",
        "worst_argument": "-6",
        "evidence": {
          "-6": {
            "taylor_value": "1.731024958831778696439750036134546689878380010507474620889719462214571389378920575487212313277153177e+0",
            "fredholm_value": "1.73102495883177869643975003613454668987838001050747462088971946221457138937892057548721231327715317675671181215953485798",
            "relative_difference": "1.4054574233560079477e-100"
          },
          "0": {
            "taylor_value": "3.670615515480784277477921131756109615121920536131394537086149438391963071001863772228898876675201135e-1",
            "fredholm_value": "0.367061551548078427747792113175610961512192053613139453708614943839196307100186377222889887667520113463020818869514817119",
            "relative_difference": "1.0074381523895884976e-100"
          },
          "2": {
            "taylor_value": "3.492814926459571958921428955778459735345322608330103507014801854907177190796936867949892157068458802e-2",
            "fredholm_value": "0.0349281492645957195892142895577845973534532260833010350701480185490717719079693686794989215706845880216632454382852859503",
            "relative_difference": "4.7619054353137579594e-101"
          }
        },
        "interpretation": "Checks the Tracy-Widom/Hastings-McLeod normalization and representative endpoint/interior values through a method independent of the ODE Taylor stepper."
      }
    ],
    "limitations": "The repair is heuristic (agreement-checked), not proven. Arb is used for multiprecision arithmetic, but Taylor step results are advanced by midpoints; the Airy right-boundary replacement, Taylor remainder, Fredholm finite-interval truncation and Fredholm matrix conditioning are not rigorously enclosed. The interval Fredholm matrix solve at the left endpoint could not certify invertibility, so the independent Fredholm check is explicitly a midpoint numerical control.",
    "commands": [
      "bash /home/ubuntu/numberdb-precision-20260925/repo/agents/precision-repair/sage.sh probe_versions.py",
      "bash /home/ubuntu/numberdb-precision-20260925/repo/agents/precision-repair/sage.sh generate.py --sample -6 -4 0 2",
      "bash /home/ubuntu/numberdb-precision-20260925/repo/agents/precision-repair/sage.sh generate.py --compute-json entries.json --summary-json taylor-summary.json",
      "bash /home/ubuntu/numberdb-precision-20260925/repo/agents/precision-repair/sage.sh generate.py --fredholm-json fredholm-check.json --fredholm-arguments -6 0 2",
      "python3 assemble_candidate.py",
      "python3 make_verification.py"
    ],
    "artifacts_sha256": {
      "entries.json": "ab8c40a7b33c6a2e19456ee90577a70ae11ec4e074d72384e9d1d6dda6cfdaab",
      "taylor-summary.json": "ffd3b1cd76bee93edebe22c8a64c3cc031bf1b5e546793b0539d46d69578922f",
      "fredholm-check.json": "a8b7b94871e81db03bf6f50c54e5711763a0c385084889ef906df3a540ac5643"
    }
  },
  "provenance": {
    "repair": {
      "stage": "repair",
      "engine": "codex",
      "session": "01a0da5c-368e-7a81-bf5f-9afc58baf470",
      "model": "gpt-5.5",
      "log": "/home/ubuntu/numberdb-precision-20260925/queue/jobs/T443/20260925T205751Z-repair-codex-e4c1a2c2.jsonl",
      "started": 1790369871.061924,
      "exit_code": 0,
      "finished": 1790371546.829837,
      "native_session": "/home/ubuntu/numberdb-precision-20260925/queue/jobs/T443/native-repair-01a0da5c-368e-7a81-bf5f-9afc58baf470.jsonl",
      "native_session_sha256": "b06eeab234a798775671e0e7747d39fd654a847390f5f1eab515208c33e73c5f"
    },
    "critique": {
      "stage": "critique",
      "engine": "codex",
      "session": "01a0da75-c8b3-7fc3-937d-e115abf282b5",
      "model": "gpt-5.5",
      "log": "/home/ubuntu/numberdb-precision-20260925/queue/jobs/T443/20260925T212546Z-critique-codex-8087f6f9.jsonl",
      "started": 1790371546.9519773,
      "exit_code": 0,
      "finished": 1790372258.688504,
      "native_session": "/home/ubuntu/numberdb-precision-20260925/queue/jobs/T443/native-critique-01a0da75-c8b3-7fc3-937d-e115abf282b5.jsonl",
      "native_session_sha256": "84a7a1c72255a337506c13cb17f109db6ba347d1eb05f204fdd148ece41c017c"
    }
  },
  "batch": "precision-20260925",
  "authority": "Website database and revisions; cloud files are supporting evidence."
}