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4702 bytes, as of the version from 2026-10-27 06:00 (current). Recorded here, not run.
# T539 repair evidence, 20261027T055528Z
The controlling skill manifest is `agents/runs/20261027T055528Z-repair-skills/manifest.json` (manifest SHA-256 `468f5191d13df1eaecac71d659cc26682a40378c5982ce84143ed004d1933cc7`). The archived local and live skills and the source snapshot's `.claude/skills/numberdb-table/SKILL.md` were read and have identical SHA-256 `e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`. Per-version paths and hashes are in `skill-evidence.json` in the repair work directory.
## Change and provenance
A fresh authenticated GET of T539 confirmed the three uncaptioned related-table links. Each destination was read from the API; its actual Title supplies the caption. Only `Similar tables[*].table` changed. Targets, relation sentences, all twelve entries, parameter identities/order, definitions, Programs, completeness and precision metadata were preserved. The diff was printed and read before the API write as zeta3. The write returned `reviewed: false`, revision `b560928ef547deaddba0c561464003624d9464e08abf85254f91d27503a95e73`. Readback exactly matched the proposed document. The fresh post-edit audit returned `findings: []`, `clean: true`.
## Reproducibility check
The attached original generator was downloaded without modification. Its SHA-256 remains `f4bc550222c956aa8448fb7bca140b41321ab70c7feb1881536bc7b8eab19e30`. The original `checks.py` and `argument-selection.md` are also retained without changes.
Executed through the approved wrapper:
```
cat "$NUMBERDB_KEY_FILE" | NUMBERDB_KEY_FROM_STDIN=1 agents/sage.sh "$TMPDIR/numerical_recheck.py" "$TMPDIR/generate.py"
```
The attached repair check is named `repair-20261027T055528Z-checks.py`; download it beside `generate.py` and run it with SageMath and the key on stdin as documented in its docstring. This is a reproducibility check, not a replacement independent critique. It executed the generator's default enumeration and checked exactly N=1,...,12 in live entry order. `verify(sample=None)` reported 12/12 matched, zero differing, missing or extra.
For each entry, evaluations requested at 100 and 200 decimal digits used exact rational nu=1/(N+2), with its conversion uncertainty and all subsequent Gamma, power and pi operations propagated by Arb. Each ball was finite, sufficiently narrow and wholly contained in the stored interval parsed from the exact decimal and its last-place unit. The minimum relative accuracies were 424 and 756 bits respectively. Every deliberate perturbation of 10^(-90) was rejected. No values were added, removed, recomputed into storage or rounded anew. Software: SageMath 10.9, Python 3.12.3, numberdb 0.1.10. Per-entry measurements are attached as `repair-20261027T055528Z-results.json`.
## Rendering and remaining work
A fresh browser visit to https://numberdb.org/T539 returned HTTP 404, with “Nothing at this address” and the sign-in explanation for private drafts. Anonymous API reads likewise cannot see T539; authenticated API reads succeed. No browser-session credentials were available. The normal complete draft page and its first-screen layout were therefore not checked.
Live `/preview?table=...` responses for the affected sections were rendered in Chromium 156.0.8078.4 with Playwright 1.64.1. The original captions visibly contained underscores; the proposed captions display the destination titles correctly and preserve identical hrefs. No JavaScript page errors or MathJax error nodes appeared. The previews retain the actual parameter declaration, number heading and first row. They are section checks, not a substitute for a complete-page check. HTML, text, screenshots, scripts and `browser-report.json` are saved in `agents/runs/20261027T055528Z-repair-work`.
The second finding remains a site issue: the live precision properties preview still prints `digits: 100 (Unknown key)`. Source inspection of the data-property label mapping in `numberdb_app/views.py` confirms that `digits` is missing. The valid precision metadata was preserved. This run did not edit or deploy site source.
## Independent review boundary
The selection fingerprint is unchanged: `f59760d59b0c207974542b328c9c932fcdb5b2170ec2b71fd17d4fc403ddad42`. No mathematical definition, selected argument or reviewed generator source changed. `agents/critiques/T539-arguments.json` remains byte-for-byte unchanged, SHA-256 `df2bfb4794f6586ab894aab954d4bbf10085d37a01fcaf07b263dd5e81bcf90f`; its decision remains `revise`. A fresh independent critique is still required to resolve the outstanding full-page rendering check. The controller must retain this same draft T539. This repair makes no acceptance, offer, publication or human-review action.