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6101 bytes, as of the version from 2026-11-02 01:23 (current). Recorded here, not run.
# T663 presentation repair, 20261102T001449Z
The coordinated skill manifest is `agents/runs/20261102T001449Z-repair-skills/manifest.json`, attached as `repair-skill-manifest.json`. Both archived versions were read and verified: local `.claude/skills/numberdb-table/SKILL.md` and live `https://numberdb.org/skill` each have SHA-256 `a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278`. The current source file has the same digest. The archived instructions agree; no remembered or older policy was substituted.
Authenticated reads of `/api/table?id=T663`, `/T663`, `/files/T663`, and `/api/table/T663/audit` confirmed all three ranked critique findings. An unauthenticated document read returned no table, confirming this was an unpublished draft. All 14 argument identities, their order, stored values, parameter declarations, completeness note, rigour statement, and program were retained.
The Jensen identity was split into three inline mathematical expressions connected by “where” and “and”. Rejoining those expressions reconstructs the previous mathematics exactly. At 1440 by 1100, the initial Formulas section had client width 648 and scroll width 750 pixels. The final local browser preview has client width and scroll width both 648 pixels, with no descendants extending beyond the section. A first comma-only preview left hidden MathJax accessibility content protruding; ordinary connecting words give the piecewise definition a clear second line. No CSS or rendering source was changed.
The comments for k=3,10,18 now read “An integer CM example CITE{BF}, Section 2.3.” The cited source, [Bertin et al., section 2.3, PDF page 5](https://arxiv.org/pdf/1208.6240), explicitly lists 0,2,3,6,10,18 and their imaginary quadratic eta parameters. The CM identification and citation remain; only the incidental, undefined tau clauses were removed. The exact same three comment replacements were made in generate.py so a future regeneration will preserve the repair. An AST comparison established that this is its only change. The checker and argument-selection attachment are untouched.
The unsupported Data properties.digits key was removed. The generator still requests 100 digits, the existing rigour details explicitly state that 100 significant digits are retained, and all stored decimal strings are unchanged. The initial browser showed “digits: 100 (Unknown key)”; the final preview has no unknown-key error. No new values were generated or submitted.
## Numerical and consistency checks actually run
Run the attached focused checker with SageMath, numberdb and mpmath, alongside generate.py, checks.py, table-before.json and table-proposed.json:
```
sage -python repair_checks.py
```
The campaign executed it using `agents/sage.sh`, supplying those five dependencies as mounted files. Its complete output is attached as repair-checks.json. Software: Sage 10.9, Python 3.12.3, mpmath 1.4.1.
The repair re-used the existing attached checker's modular series routine, recomputing all 14 rows at 140 and 180 working decimal digits. This is a repair verification, not a new independent critique and not a claim to have newly authored that modular checker. The zero-value dilogarithm control ran first, agreed within 5.285e-151, and a deliberate 1e-90 perturbation was rejected. Every recomputation was finite and within its stored decimal interval, with maximum discrepancy 0.479657386769102 ulp. Minimum agreement between working precisions was 139.585133975655 digits relative to max(1,|value|). Auxiliary eta parameters were recomputed at each precision; they were not copied from printed decimals. The table arguments are exact integers, so no input rounding uncertainty was introduced. These checks remain heuristic: the series-tail estimate does not enclose numerical root solving or floating-point error, and no stronger rigour claim was made.
At 200 working digits, seven checks of the equivalent elliptic-density expressions differed by at most 4.083e-202. Nine checks of the piecewise Jensen expression against the roots of z^2-az+1, including both signs and the endpoints +/-2, differed by at most 8.166e-202. The mathematics of the formatting edit is also checked by exact text reconstruction. Enumeration exactly matches the 14 stored identities, the generator's comments match the repaired document, and AST comparison confirms that the displayed program's density and compute functions match the generator.
## Independent review boundary
The original `agents/critiques/T663-arguments.json` is preserved unchanged. Formula text, entry annotations and generate.py bytes are fingerprinted, so this repair requires a fresh independent critique of the same T663 draft, even though the selected arguments and numerical algorithm are unchanged. The repair does not write or accept an independent review sidecar. The controller must recover this same draft; no second draft, offer, publication or human review action was taken.
## Saved result
The API accepted the document with `reviewed: false`, and the readback exactly matches table-proposed.json. The saved page was checked afresh in Chromium 156.0.8078.4 / Playwright 1.64.1 at 1440 by 1100: the Formulas section is 648 pixels wide with scroll width 648, no overflowing descendants, no page errors, no MathJax errors, and no unknown metadata key. The saved audit response has `findings: []` and `clean: true`. The current generator, unchanged checks.py and unchanged argument-selection.md were fetched and compared byte for byte with their intended versions. The checked mathematical table still holds the same 14 decimal strings.
The initial independent selection fingerprint was `1465daaa67cc2144bdc4ba005049aec17226581f7642b5f5b51e58dc6382a09c`; the repaired fingerprint is `51b4855081c9e0876fbb8c7c34d6af3ded80599bc1f267d10a3b39f07df91209`. This difference is evidence that another independent critique is required, not permission to rewrite the old verdict. The original sidecar SHA-256 is `fb7b8a2c5993ac88cdac2756ea996dc6459a35b8d0258d604631144fba2ae923` and remains unchanged.