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5543 bytes, as of the version from 2026-11-01 16:17 (current). Recorded here, not run.
# Build handoff: T654
Built the private draft [Low-degree growth constants of finite p-group algebras](https://numberdb.org/T654), the selected proposal from family #287. It contains 25 values at 100 significant digits with proven enclosures. No publication, offer, human-review action, Git commit or source edit was performed. No independent argument-review acceptance was created; that belongs to the next critique actor.
## Skill and family evidence
Read family #287 first using `python3 agents/queue.py show 287`. The family coverage map and the live T653, T5, T257 and T258 documents were read. T653 is the Hilbert-series companion; T5 provides the application context. Its table address and T653's address were resolved from live responses. T653 was read and a no-change writability probe resolved its private address; it was not edited. The reverse companion link is left for the final family review, as required.
The controlling manifest is `agents/runs/20261101T154704Z-build-skills/manifest.json`, also attached as `skill-manifest.json`. Both archived valid versions were read and their SHA-256 hashes matched:
`a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278`.
`screen.json`, `screen.log` and `lookup.log` preserve duplicate screening. Both requested screen helpers ran. Three sample values returned no lookup matches. Searches for Jennings, augmentation, Heisenberg, unitriangular and Chernoff found no duplicate scalar table. The four requested tags already existed. The sample lookup computation completed; its subsequent unauthenticated attempt to resolve the private companion page returned 404, so the address was resolved through an authenticated no-change API probe instead.
## Convention and selection
Store C_G=min H_G(t)t^(-d_G/3) for 0<t<=1, with prime-field augmentation grading. The single symbolic parameter G identifies the group. Retained all 25 proposed groups after reassessment: 13 unitriangular groups at p=2,3,5,7, 3<=n<=6 and degree<=80, plus 12 Heisenberg groups at the same primes and 2<=r<=4. Rank-one Heisenberg groups use the U_3 identities. The one-third threshold is fixed by zero triple products, not a sampled probability. `argument-selection.md` justifies every embedded index, both branches, finite cutoffs and breadth. `derivation.md` proves uniqueness of the minimum and the direct-power growth interpretation.
The finite bounds were accepted as noncanonical discrete reference coverage, not an application claim for every group. There was no unresolved convention. The definition was shortened after audit, moving the explicit augmentation grading into Comments; all mathematical choices remain unchanged.
## Numerical evidence
`generate.py` uses exact integer sign evaluations at dyadic rationals to bracket the unique root of 3tH'(t)-dH(t). Arb evaluates the objective over the entire root bracket. The 413-bit run retained at least 404 bits of relative accuracy. All 100-digit decimal intervals contain the full certified enclosures.
`checks.py` passed known-answer controls for H=1+t and H=(1+t)^3, and a separate factor-based optimizer control on C_2. For every selected group it checked exact agreement with the T653 polynomial snapshot, coefficient symmetry, degree, order, the derivative identity, a separate 180-digit factor-moment optimizer, a 140-digit certified computation and the entropy identity. Direct bounded-composition counts match H(t)^k for k=1,2,3,4 and satisfy L_G(k)<C_G^k. Direct-power minima for k=2,3 agree with C_G^k. The program snippet was executed.
After the numerical fill, `verify(sample=None)` reported 25/25 matched, 0 differing, 0 missing and 0 extra. The independent computation, bounds and stored-decimal containment checks passed again on all 25 values read from T654. `numerical-evidence.json` is attached and records `stored_checked: true`, exact root brackets, all values, finite counts, dependency versions and the skill manifest. Versions: Sage 10.9, mpmath 1.4.1, numberdb 0.1.10.
The first draft contained no entries. The numbers were filled once in the final document from freshly computed generator values. The generator subsequently found 25 unchanged values and attached its declared files. Later edits changed presentation and evidence only; there were no numerical corrections.
## Audit and review handoff
The final site audit has one residual finding: the `matrix multiplication` tag allegedly reaches only this table. This is a draft-counting false positive: the public tag already contains T5, while unpublished T654 is excluded from the public count. The tag is retained to follow the family convention; no new tag was invented. `environment-note.md` records the source and live evidence. The other audit findings were resolved (install command, definition length and definition cross-reference). The final audit result is `audit.json`; it is explicitly not clean because of that warning.
The eight attached generator/evidence files match local SHA-256 hashes. `selection-fingerprint.json` records the final live selection and all eight attachments. It is a fingerprint only, not critique approval. The separate critic must evaluate the argument selection and numerical claims, generate its own current fingerprint, and write its own required sidecar with its own reviewer run. No earlier acceptance is being asserted.
The controller handoff is `agents/runs/20261101T154704Z-build.table.json`. The table remains private and unoffered; only the controller may offer it after critique and repair succeed.