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5634 bytes, as of the version from 2026-10-31 10:42 (current). Recorded here, not run.
# T636 build handoff
Built draft **T636**, “Zeros of Hecke-type Faber polynomials of monstrous McKay–Thompson series”, at https://numberdb.org/T636. It remains unoffered and unpublished. The controller must arrange the independent critique and argument-selection sidecar before any offer. No review/publication endpoint was called and the family queue has not been marked built by this stage.
Selected coverage is the complete set of distinct roots for degrees 2 through 10 in the family order `1A,2A,2B,3A,3B,5A,5B,7A,7B,13A,13B`: 594 entries from 99 polynomials, including 88 nonreal roots and two exact integers. Every polynomial is squarefree. The approximate components are recorded to 100 significant digits with proven enclosures; 429 working bits produced at least 427 bits of relative accuracy. Longest final spelling: 213 characters; actual flat YAML entries block: 113.57 KB.
Read family #254 first, then the archived coordinated skill copies. Manifest: `/home/ubuntu/numberdb-campaign-20261026-hundred/repo-tables-wanted-label/agents/runs/20261031T100952Z-build-skills/manifest.json`. Local and live SHA-256 are both `a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278`. The attached skill-manifest.json preserves this record. The canonical snapshot file has the same digest.
The title claim succeeded as T636 with published=false and ready_for_review=false. Existing tables T634 and T635 were read from the authenticated API; both are still drafts. Actual companion slugs came from their file pages, not title-derived guesses. Links explain that T635 supplies these polynomials and T634 supplies arguments for their CM evaluation. Published tables were not changed.
The cheap screen used already_here and already_asked from screen.py, text searches, the tag API and api/lookup via the client. No duplicate family was found. Values such as i*sqrt(2) occur in other mathematical contexts, which is not a duplicate construction. Initial manual tag and lookup requests used incorrect URL/query shapes; screen-finish.json and lookup-final.json contain the corrected successful checks. The absent tag `moonshine` is proposed for T79, T255, T634, T635 and T636; no new tag or retagging was performed.
The family fixed all mathematical conventions. This build retained its monic normalization and zero constant term, including 13A; selected no extra quantity, class or table; used exact real-part/imaginary-part root ordering; retained conjugates and signs; and stored multiplicity in entry comments. The practical degree bound is noncanonical and justified across all selected structural classes in argument-selection.md. Every parameter is a discrete index. Degree one is the common zero 0 and is stated in prose.
Validation completed:
- Repository dry_run.py and check.py: all 594 entries have exact values or their own finite error bounds, with no suspicious exact-value decimals or prose complaints.
- Independent root certificates on both generated and stored text: 504 rational real sign brackets, two exact integer evaluations, two imaginary-axis sign brackets, and 86 Taylor/Rouché disk certificates. Disjointness and degree counts account for every root.
- Exact comparison with all 99 selected polynomials from T635; Laurent principal parts through the constant term; four external polynomial examples from Bannai–Kojima–Miezaki; nine j coefficients from T79; and nine 13A coefficients from OEIS A034319.
- Full-range conjugation, ordering, multiplicity, root-sum and root-product checks; known-answer and deliberately wrong-enclosure controls.
- Generator preview accepted all 594 without sending. Values were filled together with the completed document. The subsequent generator submission changed no values (594 unchanged) and attached source and checks.
- `verify(sample=None)`: 594 checked, 594 matched, no differing, missing or extra entries.
- Site audit: clean=true, findings=[]. Its two initial prose findings were resolved by moving normalization details and a cross-reference out of the 416-character Definition into Comments. The final Definition is 205 characters; the stored Numbers block was explicitly confirmed unchanged.
Reproduction attachments: generate.py, checks.py, argument-selection.md, T635.json, T79.json, numerical-evidence.md, validation-result.json and skill-manifest.json. Additional result artifacts document the stored-value verification and final audit. No generator helper or external input data is needed to compute the values; the two table snapshots are checker inputs.
The build fingerprint is in build-selection-fingerprint.json. The independent critic should inspect the current live table and obtain a fresh fingerprint, for example:
python3 agents/argument_review.py fingerprint T636 --generator generate.py --generator checks.py --generator T635.json --generator T79.json --generator argument-selection.md
At handoff, selection_sha256 is `30d5838726a88e783882c3ffdf8619567dd4175ab9b4f76b858360da40cc9594`. This builder has not written a critique sidecar or an acceptance decision. The critic must independently review the three parameter justifications and numerical claims, with its own NUMBERDB_RUN_ID as reviewer_run.
Lessons are saved as this run's `lessons.md`, not changes to the canonical skill. They concern named QQbar initialization and efficient exact conjugate ordering. Failed checker experiments and their causes remain in the artifacts. The temporary midpoint-centered complex disks were insufficient geometrically; rational Newton-centered disks passed without changing the roots. No research artifacts were deleted.