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29488 bytes, as of the version from 2026-09-26 18:54 (current). Recorded here, not run.
{
"table": "T441",
"baseline_sha256": "c5598a58a753ef07ad376efe5ed3707743e2bb062a23fcfecbd278d5a094ca29",
"candidate_sha256": "ea44451ccead08ad02f2bb67f3532c5881f43f4785341ef1a3790c244630c9fc",
"proof": {
"generator_sha256": "31b06e0db21c4791ff1b77b176c81f2dc31d097e3f42f7fc7c8fe93042e9270f",
"entries_sha256": "528081c50812780faaa926a22ffe56034aceade2dba4549645f7336938a9e479",
"all_entries_checked": true,
"independent_checks": {
"method": "Direct Bornemann Fredholm determinant identities with Gauss-Legendre Nystrom discretisation; no import of generate.py.",
"environment": {
"python": "3.12.3 (main, Mar 23 2026, 19:04:32) [GCC 13.3.0]",
"platform": "Linux-7.0.0-1012-aws-x86_64-with-glibc2.39",
"python-flint": "0.6.0"
},
"samples": [
{
"entry": "1,-6",
"reason": "left endpoint, small F1"
},
{
"entry": "1,0",
"reason": "ordinary central F1"
},
{
"entry": "1,3",
"reason": "right endpoint, near-one F1"
},
{
"entry": "2,-6",
"reason": "left endpoint, smallest F2"
},
{
"entry": "2,-11/2",
"reason": "disputed old interval F2"
},
{
"entry": "2,-13/3",
"reason": "disputed old interval F2"
},
{
"entry": "2,0",
"reason": "ordinary central F2"
},
{
"entry": "2,3",
"reason": "right endpoint, near-one F2"
},
{
"entry": "4,-6",
"reason": "left endpoint with sqrt2 scaling"
},
{
"entry": "4,-11/2",
"reason": "disputed old interval with sqrt2 scaling"
},
{
"entry": "4,0",
"reason": "ordinary central F4 with sqrt2 scaling"
},
{
"entry": "4,3",
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}
],
"results": [
{
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{
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{
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{
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{
"configuration": {
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},
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"relative_difference_to_entries_json": "5.38625984382e-101",
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"absolute_radius": "5.70988144128e-229",
"finite": true
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{
"configuration": {
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"nodes": 260,
"length": 56,
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},
"entry": "2,-13/3",
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"scaling": "plain",
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"relative_difference_to_entries_json": "4.70189548139e-101",
"relative_difference_to_baseline": "1.65673692284e-12",
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"finite": true
},
{
"configuration": {
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},
"entry": "2,0",
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"scaling": "plain",
"fredholm_value": "0.9693728283552626683498782494508137827306020107664514853125418085926383608838626593913161183187484529607004748509432",
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"finite": true
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{
"configuration": {
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"nodes": 260,
"length": 56,
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},
"entry": "2,3",
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"scaling": "plain",
"fredholm_value": "0.9999970059566076483077760218866718349160270750592038228183225684283664978334650151185273643641933164531775597961283",
"relative_difference_to_entries_json": "4.68225803927e-101",
"relative_difference_to_baseline": "3.92352866945e-13",
"absolute_radius": "1.15298851227e-227",
"finite": true
},
{
"configuration": {
"name": "B",
"nodes": 260,
"length": 56,
"dps": 230
},
"entry": "4,-6",
"reason": "left endpoint with sqrt2 scaling",
"scaling": "sqrt2",
"fredholm_value": "1.451774540059169155423889819981252882164734957744257794650687559374561798293029560211527582974899097929347061498159e-9",
"relative_difference_to_entries_json": "4.86666052836e-101",
"relative_difference_to_baseline": "2.75932440266e-8",
"absolute_radius": "5.11165871732e-229",
"finite": true
},
{
"configuration": {
"name": "B",
"nodes": 260,
"length": 56,
"dps": 230
},
"entry": "4,-11/2",
"reason": "disputed old interval with sqrt2 scaling",
"scaling": "sqrt2",
"fredholm_value": "2.481261946380455144752892360090282881334052465448006349525686285220907624164087149488269067699780603619641557040555e-7",
"relative_difference_to_entries_json": "1.53292337197e-100",
"relative_difference_to_baseline": "8.84811277452e-11",
"absolute_radius": "5.45319501020e-228",
"finite": true
},
{
"configuration": {
"name": "B",
"nodes": 260,
"length": 56,
"dps": 230
},
"entry": "4,0",
"reason": "ordinary central F4 with sqrt2 scaling",
"scaling": "sqrt2",
"fredholm_value": "0.9985741973581685402167048089588001920045534684113751159403404896516268942355433412683067653814745766639137479186539",
"relative_difference_to_entries_json": "3.61377774199e-101",
"relative_difference_to_baseline": "1.68780864908e-13",
"absolute_radius": "1.81222826133e-227",
"finite": true
},
{
"configuration": {
"name": "B",
"nodes": 260,
"length": 56,
"dps": 230
},
"entry": "4,3",
"reason": "right endpoint, near-one F4 with sqrt2 scaling",
"scaling": "sqrt2",
"fredholm_value": "0.9999999998328804780003568407875292745376769407884345820823704710984784225072746219733942991292294488389921250517125",
"relative_difference_to_entries_json": "3.89921250582e-101",
"relative_difference_to_baseline": "1.19521999663e-13",
"absolute_radius": "5.57722702737e-228",
"finite": true
}
],
"quadrature_convergence": [
{
"entry": "1,-6",
"relative_difference_between_quadratures": "0e-15"
},
{
"entry": "1,0",
"relative_difference_between_quadratures": "0e-15"
},
{
"entry": "1,3",
"relative_difference_between_quadratures": "0e-15"
},
{
"entry": "2,-11/2",
"relative_difference_between_quadratures": "0e-15"
},
{
"entry": "2,-13/3",
"relative_difference_between_quadratures": "0e-15"
},
{
"entry": "2,-6",
"relative_difference_between_quadratures": "0e-15"
},
{
"entry": "2,0",
"relative_difference_between_quadratures": "0e-15"
},
{
"entry": "2,3",
"relative_difference_between_quadratures": "0e-15"
},
{
"entry": "4,-11/2",
"relative_difference_between_quadratures": "0e-15"
},
{
"entry": "4,-6",
"relative_difference_between_quadratures": "0e-15"
},
{
"entry": "4,0",
"relative_difference_between_quadratures": "0e-15"
},
{
"entry": "4,3",
"relative_difference_between_quadratures": "0e-15"
}
],
"max_relative_difference_to_entries_json": "4.09545589338e-100",
"max_relative_difference_between_quadratures": "0e-15"
},
"limitations": "Arb is used internally, but Taylor step midpoints are retained. Taylor truncation and nonlinear boundary errors are tested by convergence and independent determinants, not rigorously enclosed.",
"convergence": {
"configurations": [
[
230,
180,
8,
40
],
[
270,
230,
10,
46
]
],
"agreement_tolerance": "1e-110",
"identity_tolerance": "1e-112",
"worst_relative_difference": "1.36026781873e-144",
"worst_relative_difference_entry": "4,-6",
"first_run": {
"worst_hamiltonian_error": "0e-228"
},
"second_run": {
"worst_hamiltonian_error": "0e-268"
}
},
"fresh_recomputation": {
"configurations": [
[
230,
180,
8,
40
],
[
270,
230,
10,
46
]
],
"agreement_tolerance": "1e-110",
"identity_tolerance": "1e-112",
"worst_relative_difference": "1.36026781873e-144",
"worst_relative_difference_entry": "4,-6",
"first_run": {
"worst_hamiltonian_error": "0e-228"
},
"second_run": {
"worst_hamiltonian_error": "0e-268"
}
},
"cdf_controls": "Every value lies in (0,1); each beta family is strictly increasing in s.",
"authorization": {
"date": "2026-09-26",
"decision": "User explicitly approved these three corrections and the 100-digit update.",
"corrections": {
"2,-11/2": {
"before": "6.7138387900e-7",
"after": "6.713838789865410167674493916412417817737075455005658174976848233127922634513016497128519800710851266e-7"
},
"2,-13/3": {
"before": "0.000825047383733",
"after": "8.250473837316331135362759508688492256831557302400394180558870408082542082115456260086533170251676255e-4"
},
"4,-11/2": {
"before": "2.4812619466e-7",
"after": "2.481261946380455144752892360090282881334052465448006349525686285220907624164087149488269067699780604e-7"
}
},
"comparison_counts": {
"refines": 162,
"contradicts": 3
}
},
"original_critique": {
"decision": "approve",
"independent_check_performed": true,
"summary": "Approved the repair's blocked disposition, not a publication candidate. There is no candidate.json or verification.json to approve. The saved 100-digit entries preserve all 165 entry identities and the documented beta/s coverage, and the repair correctly stopped because a values-only candidate would refine 162 entries but contradict the old claimed intervals for 2,-11/2, 2,-13/3, and 4,-11/2. An independent Fredholm determinant check, written separately from generate.py and run through the required Sage wrapper, checked ordinary, endpoint and disputed values for beta=1,2,4, including the beta=4 sqrt(2) convention; its worst relative difference to entries.json was 4.09545589338e-100. The numerical support is heuristic rather than proven, and the repair states that limitation. Human review is genuinely needed before correcting the three old intervals or choosing a partial candidate that leaves them unchanged.",
"findings": [
{
"severity": "info",
"summary": "No candidate artifact is present; approval applies to repair-result.json status=blocked.",
"detail": "candidate.json and verification.json are absent. Since the repair did not submit a candidate, candidate_sha256, generator_sha256 and verification_sha256 are intentionally not included."
},
{
"severity": "info",
"summary": "Definitions, formulas, conventions, parameter coverage and entry identities were preserved in the saved values.",
"detail": "The structural audit found 165 baseline entries and 165 saved entries, with identical identity order and set. Coverage remains beta=1,2,4 at the 55 reduced rationals with denominator at most 4 in [-6,3]. The beta=4 sqrt(2) convention is present in baseline.json and references/T451.json and is used by the proposed generator and by the critique Fredholm check."
},
{
"severity": "info",
"summary": "Full-table convergence evidence supports the attempted 100-digit values heuristically, not rigorously.",
"detail": "diagnostics.json records two Painleve/Taylor configurations, (230 digits, 180 terms, step 1/8, boundary 40) and (270 digits, 230 terms, step 1/10, boundary 46), with worst relative difference 1.36026781873e-144 at 4,-6. All entries in entries.json have digits='100' and 100-significant-digit scientific decimal strings. The generator describes its rigour as heuristic (agreement-checked), which is appropriate because midpoint Taylor steps do not retain rigorous enclosures."
},
{
"severity": "info",
"summary": "Independent Fredholm controls corroborate representative values and the three disputed corrections.",
"detail": "critique_artifacts/fredholm_independent.py directly evaluates the Bornemann determinant identities with Gauss-Legendre Nystrom matrices and does not import generate.py. It checked 12 entries under two quadrature settings. The worst relative difference to entries.json was 4.09545589338e-100 at 2,-6; the disputed entries agreed with entries.json to 5.38625984382e-101, 4.70189548139e-101 and 1.53292337197e-100 relative."
},
{
"severity": "info",
"summary": "The reported block is genuine.",
"detail": "The structural audit reproduced the coordinator comparison counts {'refines': 162, 'contradicts': 3}. The three contradictions are outside the old decimal intervals by about 1.35, 1.37 and 2.20 old last-place units respectively, so silently publishing them as refinements would violate the repair rules."
}
],
"evidence": [
{
"path": "critique_artifacts/structural_audit.py",
"command": "python3 critique_artifacts/structural_audit.py | tee critique_artifacts/structural-audit-output.txt",
"outputs": [
"critique_artifacts/structural-audit.json",
"critique_artifacts/structural-audit-output.txt"
]
},
{
"path": "critique_artifacts/fredholm_independent.py",
"command": "bash /home/ubuntu/numberdb-precision-20260925/repo/agents/precision-repair/sage.sh critique_artifacts/fredholm_independent.py | tee critique_artifacts/fredholm-independent-output.txt",
"outputs": [
"critique_artifacts/fredholm-independent.json",
"critique_artifacts/fredholm-independent-output.txt"
]
},
{
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]
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{
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