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4463 bytes, as of the version from 2026-11-01 06:59 (current). Recorded here, not run.
# T643 presentation repair, 20261101T065245Z
The live draft was reread through `GET /api/table?id=T643` and `GET /T643`
before any change. Its document matched the independently critiqued version.
An unauthenticated read returned no table, confirming it was not published.
Only `Formulas.formula-generating` was edited, through the authenticated API as
zeta3. The API recorded revision
`3aa2fe0b4ad140e1f37eba765013d23ecc9941ee896ab52d556bfa236179fa6a`
and `reviewed: false`.
The generating identity now uses a two-line display, breaking at the equality.
Its comma remains with the equation. Removing only display delimiters, alignment
commands and the added line break reproduces the prior mathematical tokens and
prose exactly. The other three formulas did not need changes. The saved proposal
and live API readback agree exactly. All 400 stored integers, their identifiers
and order, parameter declarations, definition, completeness note and programs
are unchanged.
## Checks actually performed in this repair
`repair_check.py` expands the displayed generating identity independently of the
attached generator and its checkers. It uses exact integer arithmetic, expanding
q times the identity through degree 201. Six-colour partition additions produce
the inverse product; convolution with the Eisenstein coefficients and the theta
series produces the traces. All 100 ordinary traces through discriminant 200
agree exactly with the stored integers. The principal coefficient is -1, the
constant coefficient is 2, and all 100 forbidden discriminant indices vanish.
Known-answer controls at discriminants 3, 4 and 12 pass; an intentionally wrong
value fails. Higher Hecke orders were preserved, not recomputed in this repair.
No approximate values were added and no argument uncertainty or new accuracy
claim is involved.
The checker was run with the prescribed wrapper:
```sh
agents/sage.sh "$TMPDIR/repair_check.py" "$TMPDIR/document-before.json" "$TMPDIR/document-proposed.json"
```
Download `repair_check.py`, `document-before.json` and `document-proposed.json`
together to reproduce with `sage -python repair_check.py`.
SageMath 10.9, Python 3.12.3. The output is `repair-check.json`.
Checker SHA-256:
`b54d76c8e2c8965050c0753442b937210a377f694848412c8ecafdfb1f0532aa`.
Chromium 156.0.8078.4 / Playwright 1.64.1 rendered the actual saved page.
At viewport widths 1440, 1920 and 900 pixels, the Formulas section has matching
client and scroll widths of 648, 696 and 804 pixels respectively. Before repair,
the first two scroll widths were 759 pixels. All four formula blocks now fit.
There were no page exceptions or MathJax errors. `browser-after.json` holds the
measurements; screenshots and the browser script remain with the run artifacts.
The post-edit API audit reports no new finding. Its sole existing warning says
`modular form` reaches only this table. The live tag API for `modular+form`
returns T84 with 69 numbers, and T84's document contains that tag. The warning
therefore does not justify removing this valid link between related tables.
The tag was retained. Raw audit and tag responses are retained in this run.
## Governing instructions and independent review
Manifest: `agents/runs/20261101T065245Z-repair-skills/manifest.json`, also attached
as `repair-skill-manifest.json`. Both archived versions were read and verified
against the manifest; they match the canonical source snapshot.
- Archived canonical local skill SHA-256: `a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278`.
- Archived live https://numberdb.org/skill SHA-256: `a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278`.
- Manifest SHA-256: `2ed18a5ba549629b2149341ece7834c3c10445d5345622bccc42c66178a837ba`.
The existing `generate.py`, `check.py`, `checks.py` and `argument-selection.md`
remain byte-identical; the generator still has SHA-256
`deb4b0f019f65cae316215bbd5ed7270afaf4c7671ff46e446dc43d107dc66a7`.
No existing source attachment was rewritten.
A fresh independent critique is required on this same draft. The campaign
fingerprint includes Formulas, so it changed from
`f711a119e9299ae2f4858eac28c92a588726b7ee629882d272c145243e4a0110` to
`608bd0ecd7ce646724047532c59931232ab3d00fa8b63185b164e014910f2619`.
The original critique and argument-review sidecar were neither changed nor
accepted by this repair. The controller must recover T643, not create a
replacement. No offer, publication or review action was taken.