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6135 bytes, as of the version from 2026-10-26 21:30 (current). Recorded here, not run.
# T528 repair handoff
Both numbered findings in agents/critiques/T528.md were still present and were repaired through the authenticated NumberDB API as zeta3. The resulting document revision is `5e9af21e35416959fa6e2236b85f83580039da4f6ad16252cb9a8b7f1aaad3f9`. The table remains a private, unreviewed draft; nothing was offered, published or reviewed. No second draft or replacement handoff was created.
The first named Gamma factors mention now links to T9, whose live definition specifies Gamma at rational arguments. The planar graph similar-table link now displays its title with spaces. Both destinations returned HTTP 200, and T9's document was read. The complete changed paragraph and a two-line diff were printed and read before the write. A fresh authenticated read immediately before PUT matched the original document. Readback matched the proposed document exactly, including ordered parameter keys and all twelve Numbers entries. The public API did not expose T528 before writing, so this was not a published-table edit. The audit returned clean=true and no findings.
## Required next stage
A fresh independent critique is required on **the same T528 draft**. The only fingerprinted change was the Gamma link in Comments; no argument, mathematical definition, formula, program, completeness note, value or reviewed generator source changed. The campaign fingerprint includes all Comments, so its digest changed from `d8b9ad5e5082bcfbac2ff98d2de6bc9c0e9b095dbae61e40f619e8f7110fe501` to `dcbdbc36143a8898fcf7a0070fab3b6b572e3737ba2ed4f9d2fb87dbfb0d4bde`. The read-only gate correctly reports stale selection_sha256. The existing independent sidecar was not edited or replaced; its SHA-256 is `549cb06d55fa1b08f9f6b5011f0599b22ec94eb4a1c9673fa2db896ef7a6e12d`. This repair supplies no new independent argument-selection verdict. The controller retains the existing draft and controls any later offer.
## Governing instructions
Read the canonical source skill, both archived versions, and a fresh live /skill. All four are byte-identical, SHA-256 `b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18`. The governing manifest is `agents/runs/20261026T212537Z-repair-skills/manifest.json`, SHA-256 `d03b756eaa1cd22ce39c8cee78fb3a44b052146786d6371925ac7bc9dec564f3`. `instructions-read.json` records every source and hash, including the fresh live read. This manifest is also cited inside the numerical result. The campaign gate, argument_review.py and table-build/PROMPT.md were read.
## Numerical evidence
`repair_checks.py` independently implements the d-coefficient recurrence in Janson, https://arxiv.org/pdf/0704.2289, equations (24)-(25), checked afresh against the source. It simplifies integer and half-integer Gamma factors exactly and evaluates remaining square roots with 768-bit Arb. It does not import the attached generator. All twelve entries were checked: six fractions matched exactly and all six 100-significant-digit decimal intervals strictly contain the computation balls. The even cases retained at least 765 accurate bits. The direct Gamma formula agrees for every k=1,...,11. Controls d_1,d_2,d_3 and the first four rho factors agree with the paper's Table 1. All inputs are exact integers/rationals; no uncertain root or rounded argument is introduced. The computation balls carry the error from rational conversion and pi through the square root and multiplication. Numbers hash: `f4cbfb5274b16027b03ade453fcc50832c4ed60a50cfe74899b41290eae8ddc9`.
Invocation:
```sh
cat "$NUMBERDB_KEY_FILE" | NUMBERDB_KEY_FROM_STDIN=1 agents/sage.sh "$TMPDIR/repair_checks.py" > "$TMPDIR/repair-checks.json"
```
Sage 10.9, Python 3.12.3, numberdb 0.1.10. The first attempt used the unavailable RealBall.rel_accuracy_bits method, failed before any write, and was corrected to the documented accuracy() method. Its script and traceback are preserved as repair_checks_failed.py and repair-checks-failed.txt. The complete corrected computation succeeded; repair-checks.json contains its results. A contributor lesson is recorded at agents/lessons/proposals/20261026T212537Z-repair.md.
The attached original generator remains unchanged at SHA-256 `a53d171ee1826ab236dd3b3e8070159f931a9ef6b20d1ebad80d2522e68a823e`; argument-selection.md remains unchanged at `9619d5f64ab899cdb36d7f616d09604cbc99a4e41f9491ec576fe27acf5ad20c`. Both were fetched from the website and compared before and after repair. Existing source and numerical attachments remain in place. The generator still enumerates k=0,...,11; the corresponding definition, program and completeness note are unchanged.
## Rendering and access limits
GET /T528 returned HTTP 404 with the available access. The authenticated API provided the full private document. Both affected sections were inspected through live server previews of the definition, parameters, comments, formulas, references, similar tables and one numeric control row. They are section previews, not the complete private-page layout. Both preview requests returned HTTP 200. Chromium typeset 37 math containers in each with no MathJax errors, broken citations, broken links or JavaScript errors. The proposed screenshot was visually inspected: Gamma factors is linked and the planar graph caption uses spaces. The screenshot, HTML, extracted text and browser versions remain in the run directory. Readback equalled the previewed document.
## Artifacts
The exact two-line disposition is agents/critiques/T528-repaired.md. This run directory contains before/proposed/after API documents, proposed.diff, write-response.json, audit responses, instruction hashes and live skill, independent numerical source/results, preview HTML/text/screenshots, browser-checks.json, fingerprint-before.json, fingerprint-after.json and argument-gate-after.txt. The unchanged original generator and its argument justification were downloaded here for evidence. Repair checks, numerical results, instruction hashes and these notes are attached to T528 with names recorded in attachment-write-results.json. No pipeline source, prompts, skills, Git state or supervisor receipts were changed.