T521 remains the same private draft. Finding 1 is repaired: the two Similar tables captions now contain literal TeX `\nu`, replacing the newline-plus-`u` text that rendered as Latin u. Both original target pages returned HTTP 200, and their API definitions confirmed the first- and second-kind modified Bessel functions. Live MathJax section previews were checked before the edit, for the proposal, and after the final write. The final preview renders Greek ν in both captions without MathJax or JavaScript errors.

Finding 2 is left for a person. The canonical and live skill require first-mention links once per section. Adding the requested two HREF links in Definition did work and render correctly, but the required live audit introduced two findings: "Definition is 327 characters (median here is 195); check whether part of it belongs in Comments or Formulas" and "Definition links to another table; a cross-reference belongs in Similar tables or a comment". The snapshot auditor unconditionally flags HREF in Definition at numberdb_app/management/commands/audit_table.py:550. This conflicts with the linking instruction. The original Definition was restored, preserving the caption repair. Both link destinations remain available in Comments and Similar tables. Resolving the audit/skill conflict requires a person; no source, prompt or skill was edited. See audit-after.json, restore-definition.diff and audit-final.json. The final audit has findings: [] and clean: true.

All 40 stored decimal strings, ordered parameter declarations, entry identities, completeness text, programs, and reviewed generator sources are unchanged. The live generator's selection() was executed in isolation and exactly matches all 40 stored parameter dictionaries. The attached generate.py, checks.py and argument-selection.md were fetched and hashed again; their original bytes were retained rather than rewritten. The final selection fingerprint is 69010a3ecd871699190e9aed2c4e4b6e05affffe93d389b6d96cf6a89a00cb83, identical to the original. The independent T521-arguments.json was never edited or accepted by this repair actor; its unchanged SHA-256 is 977659badabed56e29949b5ed037762222eac376944602eae82b2444255de2e7.

The experimental Definition edit had fingerprint c89bba9aed7ece15fe99631cdb8f7d3de36a9fba6880d819f7c9885aadeeac26 and would require a fresh independent critique. That edit was reverted. If a person restores those links, a fresh independent critique is required for that changed fingerprint. The controller should retain T521, not create a replacement. This handoff is not argument-selection acceptance or a stage-completion receipt.

I ran supplemental Sage checks with agents/sage.sh repair-numerical-checks.py document-before.json. Sage 10.9 and 700-bit Arb balls independently evaluate eleven pre-existing closed forms: all four moments for (a,b)=(1,2) and (1,3), plus (0,3;1), (0,4;1), and (0,4;3). Every finite enclosure is strictly within the interval denoted by its stored decimal; the largest error is less than 0.399747 last-place units at (1,3;7). Exact rational inputs, including 1/3 and 2/3 in the Hurwitz-zeta expression, enter balls before evaluation, propagating argument uncertainty. The nonzero zeta(2)=pi^2/6 control and ten-last-place perturbation controls pass. This checks eleven rows, not a new integration of all forty. No numerical value or rigour claim was changed. Two initial checker type/coercion errors were fixed in the disposable check script; failed outputs are preserved in attempt-1/ and attempt-2/.

The actual https://numberdb.org/T521 page was fetched but returned HTTP 404 for the unsigned browser; the authenticated API returned the complete draft. Full-page layout remains unverified. Rendering evidence is explicitly from read-only live section previews, not a signed-in draft page. The final screenshots and DOM records are render-final-definition.* and render-final-similar.*. No offer, publication, human review, commit, push, deployment or second draft was attempted.

Instruction provenance: agents/runs/20261026T171740Z-repair-skills/manifest.json, SHA-256 d03b756eaa1cd22ce39c8cee78fb3a44b052146786d6371925ac7bc9dec564f3. Both archived versions, the canonical .claude/skills/numberdb-table/SKILL.md and a fresh https://numberdb.org/skill fetch were read and byte-compared. Each has SHA-256 b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e06ded40b18. There was no convention difference. instruction-evidence.json records individual paths and hashes; repair-numerical-results.json and preservation-evidence.json cite the manifest. The build prompt, campaign gate and argument-review helper were also read.

Reproducing the supplemental numerical check from website attachments: download repair-checks-20261026T171740Z.py and repair-stored-document-20261026T171740Z.json, then run `sage -python repair-checks-20261026T171740Z.py repair-stored-document-20261026T171740Z.json`. The stored-document attachment is a snapshot; the website API remains authoritative. The unchanged original generator and checks remain attached with their original names.