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5788 bytes, as of the version from 2026-10-31 10:48 (current). Recorded here, not run.
# Build handoff: T634
Built **Values of monstrous McKay–Thompson series at rectangular CM points**,
https://numberdb.org/T634 , from family numberdb-data#254. The website draft
contains 300 values, one quantity T_g(i sqrt(r)), for
2A,2B,3A,3B,5A,5B,7A,7B,13A,13B and r=1,...,30.
It is private and was not offered, reviewed or published by this actor.
The controller must run the separate critique, argument review and any repair.
No independent critique sidecar was created by the builder.
## Policy and selection
Read the family issue first. Then read the coordinated archived local and live
skills, checked both hashes against
`agents/runs/20261031T091932Z-build-skills/manifest.json`, and checked the
snapshot's canonical source. All three have SHA-256
`a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278`.
The two archived copies agree. The manifest is also cited in attached
skill-evidence.json and numerical-evidence.md.
The proposed selection was reassessed and retained. Class g is a discrete
Monster conjugacy-class index, and r has arithmetic structure through the
principal form [1,0,r] and its order of discriminant -4r. The prime subfamily
is structurally complete for genus-zero X_0(p), with both Fricke types. The
cutoff |D|<=120 is explicitly practical and noncanonical. Square factors are
retained. General ideal classes and level structures are not silently mixed
in. The default enumeration, parameter identities, completeness note and
attached argument-selection.md agree. No continuous reference mesh or
excluded quantile quantity is present.
## Verification
- The prescribed dry_run.py/check.py checks pass for every entry. The
serialized block is 43,178 bytes and the longest value is 101 characters.
- Generator.verify(sample=None) reports **300/300 matched, 0 differing,
0 missing, 0 extra**.
- Independent 560-bit product enclosures check all 300 values; all 298
approximate enclosures fit inside the represented 100-significant-digit
decimal intervals. The primary 429-bit computation retains at least
418 relative bits, and the independent calculation at least 545 bits.
- T_2A(i)=544 and T_2B(i)=536 are exact, certified by the level-two modular
equation and positivity. The other 298 entries provably exclude integers
and therefore rationals, since the values are algebraic integers.
- A separate theta computation checks all 30 Hilbert class equations and all
150 canonical modular equations, using exact coefficients archived from
T129 and T309. The A/B identity passes on all 150 pairs. These checks were
repeated using the actual stored decimal intervals.
- Known-value, disjoint-value, wide-enclosure, NaN and decimal-parser controls
pass. The user-facing program snippet agrees on all 300 parameter pairs.
- The site audit is clean: **findings=[]; clean=true**. Its sole initial
finding was a missing internal Hilbert-class-polynomial link in the method
description; that prose was fixed. No numerical repair was needed.
The initial empty claim is archived in claim.json. All values and the settled
prose were sent together from the certified serialized generator results;
the write-document API refuses an empty metadata update on an existing draft.
The generator then recomputed the upload, found all 300 unchanged and attached
its source and checks. A later metadata-only edit resolved the audit finding.
## Evidence and attachments
Attached: generate.py, checks.py, algebraic-check-data.json,
argument-selection.md, numerical-evidence.md, skill-evidence.json,
source-checks.md. The build also attaches the computed/stored numerical result
logs and clean audit as evidence. Source snapshots, full corpus documents,
searches, size results and the standard-program check remain in this run's
work directory. Source-checks.md states the source locators and the failed
DLMF .tex download attempts; the HTML equations were accessible and checked.
The current selection fingerprint is
`1daccbf4287b884842b92d864af61044a43a209c3d4eb6a1122028890ac49b96`.
selection-fingerprint.json records the hashes fetched from the website for
all seven generator files. The critic must obtain a fresh fingerprint, not
reuse the builder's as an independent acceptance. Relevant source dependencies
are generate.py, checks.py, and algebraic-check-data.json; the selection note
and attached method/policy notes were also fingerprinted.
The exact controller handoff is
`agents/runs/20261031T091932Z-build.table.json`, with only `{"tid":"T634"}`.
The queue is left to the controller, which records a successful build after
its critique/repair/offer stages. No batch-exhausted marker was made, no
published table was edited, and no commit, push or deployment was performed.
## Further review notes
No mathematical convention was guessed: the sources fix the pA/pB labels,
zero constant term (including 13A), q=exp(2 pi i tau), eta normalization and
positive rectangular square root. The builder chose the ball implementation,
explicit error bounds and exactness certificate. This table does not absorb
the Faber polynomial or zero proposals and does not invent links for them.
The existing tags are used. Proposed future tags: **moonshine** would connect
this table, the two Faber proposals, T79 and T255; **complex multiplication**
would connect this table, T83, T129, T297 and T506. Neither tag currently exists,
and no published companion was retagged.
A local lesson proposal, lessons-proposal.md, records a Sage parent-coercion
issue when comparing an Arb radius with a ball bound. It is an artifact,
not a skill or pipeline edit. Method-discovery failures occurred privately
before filling and are described in source-checks.md. All started computations
have finished and their successful outputs were inspected.