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5275 bytes, as of the version from 2026-11-09 09:32 (current). Recorded here, not run.
# T686 repair handoff, 20261109T092414Z
T686 remains the same private, unreviewed draft. Three presentation findings were
corrected through the authenticated API as zeta3. No offer, publication or review
action was performed. The unchanged original generator remains attached as
`generate.py`; it was not rewritten or reattached.
## Instructions and independent review
The controlling archive is
`agents/runs/20261109T092414Z-repair-skills/manifest.json`.
Both archived versions and the snapshot's canonical skill were read and match.
The local SHA-256 and live SHA-256 are each
`886390324dd1971e381a43cf3b46b822ab0bc67d62f31d8481e29ec79556746b`.
`repair-skill-evidence.json` records the manifest digest as well.
A fresh independent critique is required on this same draft. Programs and a
link caption in Comments changed, and both sections are covered by the campaign
fingerprint. The argument identities, definitions, default enumeration,
completeness note and reviewed generator did not change. The repair did not
create, edit or accept an independent argument-review sidecar.
Before selection fingerprint:
`ed83e6bd60f69f905e2e0eb30b826204ab33760185a4e640e514ca489b924509`.
After selection fingerprint:
`7a3229f622edb44d55dc172fba4721d6b7fa125de44becd778ce57040d05be2a`.
Unchanged `generate.py` SHA-256:
`c1e9d54efcac9c230fa8d48b5434091fea7550a1f11d5bc162ccbf58cc9016b9`.
The original `agents/critiques/T686-arguments.json` remains untouched, SHA-256
`f839e1edfa10c05807bcb75b5a418045aedc7423003b7401eefe8395a22f267f`.
## Changes and checks
1. Programs now contains a self-contained mpmath evaluation of the three-step
generating function in BBSW Theorem 4.1, equation (23), differentiated at zero.
The source was read at https://arminstraub.com/downloads/pub/logsin2.pdf and
archived as BBSW.pdf. The example explicitly selects n=3 and states 150 decimal
working digits and heuristic precision. It reproduces all seven stored n=3
values. The worst discrepancy is 0.3192855186099034 units of the written last
place, at k=7. Runs at 150 and 180 decimal digits agree to a scaled discrepancy
at most 6.064e-152 through k=9. The k=9 computation verifies that the example
can compute another order; it was not added to the table. Controls were
W3(0)=1, the known first moment from a dilogarithm, and an independently
integrated log-sine second-moment formula (BBSW Theorem 5.4, equation (37)).
This is heuristic agreement, not interval certification. All inputs in this
example are exact indices or exact rational constants converted at working
precision; there is no uncertain root or rounded external input.
2. All seven Similar tables links and the radial-moment link in Comments have
readable captions checked against the live target documents. The relation
renders W_n(s) and s=0 as mathematics. Browser anchor destinations are
unchanged, including the existing entry links.
3. The redundant Data properties.digits field was removed. The explicit
100-significant-digit statement, rigour details, all 14 stored value strings,
parameter order and attached generator digits=100 remain unchanged.
Chromium rendered 47 MathJax containers, with no math errors or JavaScript page
errors. The raw link names and Unknown key diagnostic are absent. The final
screenshot was inspected. Browser versions: Playwright 1.64.1, Chromium
156.0.8078.4. Numerical versions: SageMath 10.9, Python 3.12.3, mpmath 1.4.1,
numberdb 0.1.10. The n=4 values were not recomputed in this presentation repair;
they are unchanged and retain the build and critique evidence already attached.
## Audit warning deliberately retained
The post-repair audit has exactly the same one finding as the initial audit:
`Tags: "moments" reaches only this table; a tag that leads nowhere else leads nowhere`.
The public tag API actually lists T36, not T686. Authenticated live documents
show the tag on T685 and T686 as well. The skill permits a shared tag with three
tables including drafts in the same batch. The audit reads a published-only
count and does not distinguish a draft from the one counted published table.
The critic's suggestion to remove this tag is therefore declined. No new audit
finding was introduced. `moments-tag.json`, `T36.json`, `linked-0.json`, and
`audit-before.json`/`audit-after.json` preserve the live evidence in this run's
work directory; the pre-existing `audit-note.md` attachment already explains
this count discrepancy.
## Reproduction
Download `program.py`, `repair_checks.py`, and `document-before.json` together,
then run:
```sh
sage -pip install numberdb mpmath
sage -python repair_checks.py
```
The checker only reads these local files and performs numerical checks; it does
not send data to NumberDB. Its completed output is attached as
`repair-numerical-evidence.json`. The repair used:
```sh
agents/sage.sh "$TMPDIR/repair_checks.py" "$TMPDIR/program.py" \
"$TMPDIR/document-before.json" > "$TMPDIR/repair-checks-final.log" 2>&1
```
Working files, browser evidence, API responses, original attachments and source
bytes are preserved under
`agents/runs/20261109T092414Z-repair-work/`. The finding-by-finding outcome is
`agents/critiques/T686-repaired.md`. No new draft or build handoff was created.