T636 repair evidence, run 20261031T103707Z, 2026-10-31.

Instruction record: agents/runs/20261031T103707Z-repair-skills/manifest.json. Both archived skill-local.md and skill-live.md were read and SHA-256 verified as a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278; the snapshot canonical skill has the same bytes. The manifest SHA-256 is 2ed18a5ba549629b2149341ece7834c3c10445d5345622bccc42c66178a837ba. The attached repair-skill-manifest.json is an exact copy. The campaign gate, argument-review implementation and table-build prompt were read.

Finding: the defining Faber polynomial was unlinked at first mention in the live API document and rendered page. The exact companion slug resolved to the intended polynomial table. Both definitions use the monic normalization P_{n,g}(T_g)=q^(-n)+O(q). Sage 10.9 independently checked the link target against the existing root generator: all 99 class-degree polynomials equal the companion's exact entries. Three known-answer controls passed; an intentionally wrong polynomial was rejected. There are 594 root entries. This repair did not recompute their numerical intervals or make any new root-accuracy claim; no new values, arguments, uncertainty propagation or precision changes were introduced.

Reproduction: place the existing, unchanged generate.py and the attached repair-check.py, repair-table-before.json, repair-companion.json and repair-skill-manifest.json together, then run `sage -python repair-check.py`. In the campaign this was run to completion with `agents/sage.sh` and all dependencies supplied as mounted files. repair-check-result.json records the result. Existing generate.py SHA-256 remains 40a09b1cccca83c4cb49d8377dcf0a6f1622016dd761c990b12eebddc23c11c2; no reviewed source was replaced.

The proposed Definition change was printed and read before sending. Authenticated API PUT, as zeta3, created unreviewed revision acee3e2ab75dab795066e02be9ee8d5c0466204e6922a97af1425d93c62b4476. It added only HREF markup around the defining polynomial phrase and retained the paper citation. The browser rendered the link and its mathematical label correctly.

The resulting authenticated audit reported: "Definition links to another table; a cross-reference belongs in Similar tables or a comment". The snapshot audit implementation at numberdb_app/management/commands/audit_table.py:550 checks every occurrence of HREF in Definition, without distinguishing an inline first-mention link from a digressive cross-reference. This conflicts with the archived skill's first-mention linking rule. The report is right about the missing link; the audit conflict requires a person's policy decision. No syntax workaround or source change was attempted.

To comply with the requirement to leave no introduced audit finding, authenticated API PUT restored the original Definition at unreviewed revision bb30ece4ce82bc45eaf444d459dc9ec77e5c5f4967c216c0bdf6d9254bc1e9ec. The final document equals the original parsed ordered document in every section and entry. The final audit is clean with zero findings. The API did not refuse a parameter change. All old revisions remain; the same draft T636 is retained. It was not offered, published or reviewed.

The successful browser checks used Chromium 156.0.8078.4 and Playwright 1.64.1, serving the exact current HTML with live site assets. The attempted link and restored final page had zero math-error nodes and zero JavaScript errors. An initial browser assertion failed before recording its diagnostic details; a fresh run passed. A later assertion used a leading-slash href selector although NumberDB emits relative hrefs; resolving the anchor's URL confirmed the correct target. The failure log and corrected checks are preserved in the run directory. Neither browser-check issue was a mathematical discrepancy.

The Definition edit temporarily changed the selection fingerprint to a129a21bbd75c46c967bad3c098449d05b19b31b1019c72d55d093651a89fddf. Restoration returned it to 30d5838726a88e783882c3ffdf8619567dd4175ab9b4f76b858360da40cc9594. agents/critiques/T636-arguments.json remains untouched, SHA-256 79712c74b17ba5938e4be2cf97b41e7bb8dbce3a1a1883639be01202a785ac9d. This repair does not accept or refresh that verdict. Human alignment is needed for the sole finding; any subsequently retained Definition link requires a fresh independent critique. The controller must retain this same draft.