# T621 numerical build evidence

The draft holds 56 entries: n=3,...,30, with det followed by logdet at every n.
All entries are 100 significant digits. The longest serialized value is
101 characters; the supplied dry-run helper measured
12.3 KB and a longest 170-character working-ball representation before serialization.

The archived skill manifest is
`../20261030T080603Z-build-skills/manifest.json`. Both archived copies and the
canonical local source have SHA-256
`28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
`skill-evidence.json` records the exact local and live copies read.

Production: Arb at 513 bits, minimum 499 relative accuracy bits over all 56
entries. Every serialized interval contains a fresh 750-bit ball. All balls
are finite; narrowness and deliberate-perturbation controls passed.
Independent integral computations at 150 and 200 decimal digits, with 40
additional guard digits, agree with maximum absolute discrepancy
2.0451148E-170 across both conventions. The integral is a
corroborating check, not the source of certified error bounds. The finite Arb
formula supplies certification. The small-x and large-x truncation bounds are
derived in derivation.md; the finite quadrature error is agreement-checked.

The square and triangle checks use convergent spectral products with rigorous
tails and independently derived contributions of the Neumann axis modes.
They pass before fill and on the stored intervals. The two closed forms also
pass. Nonzero quadrature controls are evaluated before each integral; a
zero-returning checker would fail them.

`verify(sample=None)` after filling: 56/56 matched, 0 differing, 0 missing,
0 extra. The full independent suite was repeated on values read from T621:
all 56 interval/independent-integral comparisons, all 28 exp/log relations,
and all 28 determinant ratios and 28 log-differences to live T620 pass.
Family ingredient checks: 28 areas against T17, 28 conformal radii against
T554, 84 scale substitutions, the eta value in T506, and the two positive
low-mode normalizations in T485 all pass.

Versions: Sage 10.9, numberdb 0.1.10,
mpmath 1.4.1. The site remains authoritative; source
attachments are reproducible without this source snapshot. All numerical
outputs and the prefill and stored-check logs are retained in the run directory.

The source-to-source checks are not a review of the entire proof in the 2026
preprint. Its geometric hypotheses and Neumann zero-mode convention were
checked. The independent critic must assess this dependency as well as the
selection and numbers. No independent-critique sidecar is created by the build.

The final site audit retains one structural advisory for the two conventions.
See audit-disposition.md; no finding was suppressed. No offer, publication,
human-review action, or edit of another table was performed.