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5504 bytes, as of the version from 2026-11-01 09:03 (current). Recorded here, not run.
# Build handoff: T644, Báez-Duarte coefficients
Built and filled [T644](https://numberdb.org/T644) as a private draft. No offer,
publication, review, queue completion, or published-table edit was performed.
The controller must run its separate critique and repair stages before offering.
The build has not authored an independent argument-review acceptance sidecar.
Family #283 was read first; its archived body is `family-283.md`. Both accent
spellings were passed to `already_here` and `already_asked`; broader family
searches and lookups of c_0, c_1, c_2 were performed. The only c_0 matches were
different quantities. The family coverage map and live T13, T14, T31, T378,
T639, T640, T641, T642 were read. No coefficient or Riesz table was found.
T13, T14, T31 and the T378 notation collision have explanatory live-slug links.
No placeholder links for future family tables were invented.
## Scope and decisions
Exactly 257 signed real coefficients are stored, indexed by each integer
k = 0,...,256, with domain k >= 0. The definition is the signed binomial
transform of 1/zeta(2j+2), as in Báez-Duarte (1.1) and Cisło-Wolf (4).
The proposal's convention was unambiguous. Its proposed cutoff was retained
after reassessment as a practical, noncanonical initial segment of genuine
finite-difference orders, rather than a continuous-input mesh. The full
justification is attached as `argument-selection.md`; the generator default,
completeness note and Programs enumeration agree. This is one quantity only.
The table has 100 significant digits and proven real-ball enclosures.
The existing tags `number theory`, `L-function`, and `sequence` were verified.
The absent tag **Riemann hypothesis criteria** remains a proposal: this table,
T31, T641 and T642 would use it, as would the planned Riesz-function table.
It was not created or added as an unsupported singleton tag.
## Numerical evidence
`numerical-evidence.json` records a successful full readback, including
`verify(sample=None)`: 257 matched, no differing, missing or extra entries.
The generator uses 669-bit Arb arithmetic and successive differences. Its
minimum relative accuracy is 398 bits. The independent computation uses
exact Bernoulli recurrence through B_514, an explicitly bounded Machin series
for pi, and rational-polynomial Horner evaluation at 883 bits; its minimum
relative accuracy is 611 bits. Every independent enclosure lies inside its
stored 100-digit interval, so this is stronger than midpoint agreement.
Known Bernoulli values, the first three coefficient closed forms, an exact
Machin tangent identity, sign-reversal rejection, and a ten-last-place
perturbation control all passed. No comparison used a nonfinite or broadly
uninformative enclosure.
All 257 binomial inversions and all 257 exponential-generating-function
coefficients were checked both before filling and on the stored intervals.
Stored inversion has at least 84 relative accuracy bits because it amplifies
rounding uncertainty; it is not claimed to independently establish 100 decimal
digits. The Bernoulli check establishes containment at the stored precision.
The displayed Programs snippet was separately executed for all 257 orders.
The longest serialized value is 106 characters and the block is about 36 KB.
Versions: SageMath 10.9, numberdb 0.1.10, Python 3.12.3.
Initial audit findings concerned two cross-reference placements. These were
corrected without changing any number or selected argument. `final-audit.json`
is clean with no findings. This is the API audit, which does not include the
optional database-backed outward-link checker. The source papers were read
and archived. DLMF 25.6.1–2 were read through the web tool; a separate direct
HTML archival fetch returned HTTPError, recorded in `source-evidence.json`.
## Policy and freshness
Read the coordinated archive manifest `agents/runs/20261101T072807Z-build-skills/manifest.json`. Both archived versions
were read and byte-compared; each SHA-256 is
`a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278`.
`skill-evidence.json` and the attached `skill-manifest.json` preserve this.
The campaign gate and `agents/argument_review.py` were read. The fingerprint
is evidence of current bytes, not an independent selection verdict:
`9ef6691bf369208bd682a194f8c74ab664d7a9e8c9393bf464411393c74a4f98`
The critic should obtain its own live fingerprint and inspect `generate.py`,
`checks.py`, `check.py`, `argument-selection.md`, and `program.py`; their local
hashes match the live attachment hashes in `selection-fingerprint.json`.
Only `generate.py` controls the default enumeration; it imports no local helper.
The other files expose the checks, justification, and displayed example.
The independent critic must use its own NUMBERDB_RUN_ID and write its own
required sidecar beside the controller-specified critique report.
A genuine unauthenticated GET confirms the draft is invisible. The earlier
`Client(api_key='')` probe was mistakenly labelled anonymous because an empty
key activates key discovery. `public-access.json` and `lesson-proposal.md`
record the correction; no credentials were printed. The draft was created
with `ready_for_review=false`, and no offer endpoint was called.
The exact controller handoff is
`agents/runs/20261101T072807Z-build.table.json`, containing only T644.
All working scripts and numerical outputs remain in this run's work directory;
no source, skills, pipeline code, supervisor state, or Git history was changed.