back to table · edit · history · where entries came from · files · download
5399 bytes, as of the version from 2026-10-24 21:41 (current). Recorded here, not run.
# T468 repair evidence, 2026-10-24
The live document was fetched afresh through the authenticated `/api/table?id=T468` endpoint before the findings were assessed. The unauthenticated API returned no table, while the authorized API returned the document. The draft's main `/T468` page returned HTTP 404 without a website login. No publication, offer, or review action was performed.
Both the canonical local skill and a freshly fetched https://numberdb.org/skill were read. Where their range guidance differs, the stricter local guidance applies. This repair changes no range, numbers, precision settings, generator, or parameter order.
The complete proposed change was printed and the revised paragraphs read before submission. The write succeeded through `POST /api/table/T468`, as the supplied zeta3 account, with `reviewed: false`, at document revision `0c143f191dda06325880e473957381fd16b77a793c303a6a33535934d4fa7008`. The exact ordered document was fetched again immediately before submission to detect intervening changes. Subsequent read-back exactly matches the proposal.
## Numerical verification
`repair_checks.py` was run through `agents/sage.sh`, against freshly retrieved T468 and T264 documents and T468's live attached `generate.py`. All computations completed successfully before editing.
- All 13 exact entries agree with independent factorial formulas, or the exact three-point value for the disk.
- All five decimal entries contain the independent 768-bit Arb evaluations inside their stated last-place intervals. Every discrepancy is less than 0.465 units in the last place, with independent ball radii below 10^-220.
- The original generator's results agree throughout. Its precision remains 100 significant digits with 80 guard bits, and its five numerical ball radii meet the existing claim of less than 2 times 10^-123.
- All six parallelogram identities agree with an independent count of nonnegative Dyck walks. T264's stored polynomial rows of semilength 3 through 7 give the required counts at q=1; the semilength-2 case uses T264's explicitly stated C_2(q)=q+1.
- All 18 stored entries, their comments and order are identical after the write. The numerical checks therefore also apply to the read-back values.
The independent formulas were read directly from [Marckert's preprint](https://arxiv.org/pdf/1402.3512), equations (7), (9), and (10). Equation (7) gives complementary disk probabilities. Page 5 explicitly identifies the four-point case as Sylvester's problem, supporting the added citation. These comparisons check transcription and numerical enclosures; they do not re-prove the disk formulas. This repair did not repeat the builder's simulations or convolution quadratures.
To reproduce offline, download `generate.py`, `repair_checks.py`, `T264-document.json`, and `T468-document-after.json` from this draft into one directory, install `numberdb` in Sage, and run:
```sh
sage -python repair_checks.py
```
Within this campaign the executed command was:
```sh
agents/sage.sh "$TMPDIR/repair_checks.py" "$TMPDIR/generate.py" "$TMPDIR/T264-document.json" "$TMPDIR/T468-document-before.json"
```
The complete output is `T468-checks-before.json`. The original generator remains attached, unchanged, with SHA-256 `578c76a7bf0adf82696788e658a78ccb63e5371959ba902e10ade360b4ded511`.
## Rendering and audit
The live `/preview` renderer received unchanged sections of the retrieved before/after documents. The metadata preview confirms the diagnostic disappears; the method preview contains one working link to T264; the Comments preview contains one citation link to the existing Marckert reference. HTML and extracted text are retained as `T468-before-*` and `T468-after-*`; the reproduction script is `repair_t468.py`. These are section-level HTML checks, not a claim to have inspected the complete draft page or rerun MathJax in a browser. The initial rendering assertion assumed a root-relative href; the actual valid relative href was inspected, the checker was corrected to resolve it against the preview URL, and the rerun passed without another table edit.
The authenticated post-edit audit returns exactly its one pre-existing finding and no new findings. The suggestion to split by `region` is declined: the table defines one probability p_K(n); K names the convex body to which that probability applies. The definition, parameter constraint, affine-invariance formula, and common value heading are consistent with the skill's permitted case of one quantity taken on different objects. Altering the mathematics or splitting the table to silence this heuristic would make the table less coherent. `clean` remains false; that audit result is not represented as clean.
## Handoff and retained artifacts
`T468-repaired.md` has exactly one line for each of the two ranked critique findings. Under the artifact-run override it lives in this run's work directory, rather than creating a shared `agents/critiques/T468-repaired.md`. The original critique is preserved here as `T468-critique.md`. Existing website generator, numerical evidence, and build handoff attachments are retained; the repair checks and this repair record are added beside them. No source, prompt, skill, or shared lesson file was edited, and no commit or deployment was made. This is a repair of an existing draft, not a new build; no build-result table marker is created.