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6569 bytes, as of the version from 2026-09-25 22:17 (current). Recorded here, not run.
{
"table": "T436",
"baseline_sha256": "54fc13a8ab6bf86bb6706fe1de42b456d483d0371426daa1eefce02b60d54ee0",
"candidate_sha256": "0fcc6ec4d112a8982674a6a16ff4a3573f15d6f928522fa44938c10dd87d067a",
"proof": {
"generator_sha256": "0108bfc7d4f6f1ac36ba3f68811ae2fc26a5d69090cc99556bd45bfd7406802a",
"entries_sha256": "19db7721e51f07f326530e7062b299c16245c8b4c05539a31beb653ed46c5b1e",
"all_entries_checked": true,
"independent_checks": [
{
"name": "q=0 exact limit",
"scope": "n=0..10",
"max_absolute_residual": "3.17772832238e-129"
},
{
"name": "DLMF symmetry a_2m(-q)=a_2m(q)",
"scope": "all stored q and even n",
"max_absolute_residual": "0.00000000000"
},
{
"name": "interlacing with companion b_n(q)",
"scope": "all stored q, a_0 through a_10 and b_1 through b_11",
"minimum_gap": "5.39587724423e-26"
},
{
"name": "DLMF small-q expansions through the stated terms",
"scope": "auxiliary q=1/10, n=0..6",
"max_absolute_residual": "1.17567731844e-13",
"note": "This is a convention/source check; the truncated DLMF series is not a 100-digit reference."
},
{
"name": "SciPy mathieu_a double-precision comparison",
"scope": "all stored entries",
"max_relative_difference": "4.16051763608e-16",
"worst_case": {
"q": "8",
"n": 1
}
},
{
"name": "independent ODE shooting residuals",
"scope": "selected ordinary and endpoint cases on [0, pi/2]",
"cases": [
{
"q": "1/8",
"n": 0,
"residual": "1.642298040249508231406909e-115"
},
{
"q": "1",
"n": 4,
"residual": "1.169492350956895676999889e-114"
},
{
"q": "8",
"n": 0,
"residual": "9.248050278850284937831486e-113"
},
{
"q": "8",
"n": 1,
"residual": "-4.650022591507828828304849e-114"
},
{
"q": "8",
"n": 10,
"residual": "8.072471975303189798749545e-113"
}
],
"note": "Even n uses y'(pi/2), odd n uses y(pi/2), with y(0)=1 and y'(0)=0."
}
],
"limitations": "The finite Hill matrices are solved at high precision and checked against stronger finite sections and independent identities/shooting residuals. No rigorous bound for the infinite Fourier tail is proved, so the computation supports heuristic agreement-checked precision, not proven enclosures.",
"commands": [
"bash /home/ubuntu/numberdb-precision-20260925/repo/agents/precision-repair/sage.sh experiment_mathieu.py | tee experiment_mathieu.out",
"bash /home/ubuntu/numberdb-precision-20260925/repo/agents/precision-repair/sage.sh generate.py --write-computation computation.json | tee full-computation.out",
"bash /home/ubuntu/numberdb-precision-20260925/repo/agents/precision-repair/sage.sh versions.py | tee versions.out"
],
"convergence_settings": {
"generation_truncations": [
90,
120
],
"generation_working_decimal_digits": [
220,
260
],
"check_truncation": 150,
"check_working_decimal_digits": 320,
"bit_guard": 96,
"bisection_guard_decimal_digits": 28
},
"all_entry_convergence": {
"all_entries_checked": true,
"entries": 165,
"worst_generation_spread": "6.68434263938e-129",
"worst_generation_case": {
"q": "1/2",
"n": 6
},
"worst_check_relative_difference": "4.42984972439e-100",
"worst_check_case": {
"q": "4",
"n": 3
},
"minimum_supported_digits_from_stronger_finite_section": 99
},
"worst_discrepancies": {
"generation_spread": {
"value": "6.68434263938e-129",
"case": {
"q": "1/2",
"n": 6
}
},
"stronger_finite_section_center_relative_difference": {
"value": "4.42984972439e-100",
"case": {
"q": "4",
"n": 3
}
}
},
"significant_digits_supported": {
"stored_significant_digits_minimum": 100,
"stored_significant_digits_maximum": 100,
"printed_interval_supported_digits": 100,
"center_to_center_floor_digits_from_stronger_finite_section": 99,
"note": "The center-to-center floor is 99 because rounded 100-digit decimal strings may differ from a stronger check by about half a final printed unit; the stronger finite-section values lie within the printed 100-digit intervals."
},
"comparison_counts_against_baseline": {
"refines": 165
},
"environment_versions": {
"sage": "SageMath version 10.9, Release Date: 2026-05-04",
"mpmath": "1.4.1",
"scipy": "1.17.1",
"python-flint": "0.6.0"
},
"primary_sources_used": [
"https://dlmf.nist.gov/28",
"https://dlmf.nist.gov/28.6.i",
"https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.mathieu_a.html"
]
},
"provenance": {
"repair": {
"stage": "repair",
"engine": "codex",
"session": "01a0da80-ca69-7520-ba3c-0af418de3235",
"model": "gpt-5.5",
"log": "/home/ubuntu/numberdb-precision-20260925/queue/jobs/T436/20260925T213748Z-repair-codex-7eeccbc3.jsonl",
"started": 1790372268.2741544,
"exit_code": 0,
"finished": 1790373379.4008484,
"native_session": "/home/ubuntu/numberdb-precision-20260925/queue/jobs/T436/native-repair-01a0da80-ca69-7520-ba3c-0af418de3235.jsonl",
"native_session_sha256": "f7004499d2fcf4ddb7f488029609ee43b63d42436d11fa5477fceb5ecf4b46ed"
},
"critique": {
"stage": "critique",
"engine": "codex",
"session": "01a0da91-bfdf-7e41-a7d1-bb0951ea45ee",
"model": "gpt-5.5",
"log": "/home/ubuntu/numberdb-precision-20260925/queue/jobs/T436/20260925T215619Z-critique-codex-9e8bf49c.jsonl",
"started": 1790373379.7018213,
"exit_code": 0,
"finished": 1790374665.1915371,
"native_session": "/home/ubuntu/numberdb-precision-20260925/queue/jobs/T436/native-critique-01a0da91-bfdf-7e41-a7d1-bb0951ea45ee.jsonl",
"native_session_sha256": "294bad520f2d0664da48f143d6028f69af6c9c9a6b4f45905bdc7bbcb7abf04b"
}
},
"batch": "precision-20260925",
"authority": "Website database and revisions; cloud files are supporting evidence."
}