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4091 bytes, as of the version from 2026-10-28 13:58 (current). Recorded here, not run.
# T582 Programs repair evidence
Run: 20261028T134956Z, 2026-10-28. Account: zeta3. Only the private T582 draft was edited through the authenticated NumberDB API. The change adds a standalone Sage basis calculation accepting a finite simple matroid. The existing Programs example and all 37 exact polynomials, parameter identities, definitions, completeness notes, and original attachments are retained.
Policy archive: `agents/runs/20261028T134956Z-repair-skills/manifest.json`.
Manifest SHA-256: `468f5191d13df1eaecac71d659cc26682a40378c5982ce84143ed004d1933cc7`.
Both archived versions were read and matched the snapshot's canonical skill:
- Local `skill-local.md`: `e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
- Live `/skill`, archived as `skill-live.md`: `e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
## Sources checked
Sage's [Chow-ring documentation](https://doc.sagemath.org/html/en/reference/matroids/sage/matroids/chow_ring.html) documents `basis()` as a monomial basis, `homogeneous_degree()`, and the Fano augmented example. Its augmented flag and Feichtner–Yuzvinsky presentation match the simple-matroid domain of T582. [Ferroni–Matherne–Stevens–Vecchi, Theorem 3.14](https://arxiv.org/html/2212.03190v3#Thmtheorem3.14) supplies the independent Möbius recurrence; Theorem 3.21 supplies the low-rank Boolean controls.
## Checks performed in this repair
The exact Programs code is attached as `standalone-program.py`. It does not import `generate.py`. The checker `check-program.py` executes those exact bytes and reads the saved live API document `table-before.json`.
The command run in this environment was:
```sh
agents/sage.sh "$TMPDIR/check-program.py" "$TMPDIR/standalone-program.py" "$TMPDIR/table-before.json" > "$TMPDIR/check-program.log" 2>&1
```
For reproduction elsewhere, download the three files together and run:
```sh
sage -pip install numberdb
sage -python check-program.py
```
Sage 10.9, Python 3.12.3. Six exact coefficient comparisons passed:
- Boolean ranks 1, 2 and 3: `1+t`, `1+3*t+t^2`, `1+7*t+7*t^2+t^3`.
- Fano and NonFano: equality with the complete polynomials fetched from T582, respectively `1+15*t+15*t^2+t^3` and `1+17*t+17*t^2+t^3`.
- The unlisted `Wheel(4)`: `1+42*t+114*t^2+42*t^3+t^4`. The comparison independently constructs the flat lattice using all subset ranks, then applies the Möbius recurrence. This checks a matroid outside the generator's named dispatch.
The first control run confused the circuit matroids `U(r,r+1)` with Boolean `U(r,r)` for ranks two and three. It stopped before any website edit. Specializing Theorem 3.21 to `n=r` and counting proper flats corrected the expected values; the initial script and failure log remain in the run artifacts. No table or Programs value was changed to accommodate that failure. The successful log is attached. These checks concern the added program; this repair did not repeat the critic's independent checks of all 37 stored values. All arithmetic is exact, so argument rounding and a significant-digit target do not apply.
## Rendering, API, and review boundary
The current `/T582` and `/preview/T582` requests returned 404 for the private table. The authenticated table API and audit were accessible. A live `/preview?table=...` request rendered both Programs examples, the definition, and the actual Fano row. Chromium 156.0.8078.4 with Playwright 1.64.1 rendered zero MathJax errors; the screenshot and extracted text were inspected. This checks the changed section, not the combined authenticated private-page layout.
The API write returned revision `1cc841b9a2223eea9411e00cea9b28b4da88a4c932ea7bd0cbc3cac99fda12ee` and `reviewed: false`. The document readback exactly matched the proposed document. The post-edit audit returned `clean: true`, with no findings.
Programs is part of the campaign fingerprint. A fresh independent critique is required for this same T582 draft. The previous critic's report and argument-review sidecar remain untouched. No offer, publication, or human review action was taken.