back to table · edit · history · where entries came from · files · download
5785 bytes, as of the version from 2026-11-02 13:07 (current). Recorded here, not run.
# Build handoff: T678, Values of the Wilton function
Draft: https://numberdb.org/T678
Canonical slug returned by creation: Values_of_the_Wilton_function.
Family: numberdb-data issue #300, read first using `python3 agents/queue.py show 300`.
This run filled this one draft. It did not publish, offer, review, edit a
published table, or create independent critique evidence. The controller must
run the separate critique and repair stages before offering it.
## Skill alignment
Manifest: `agents/runs/20261102T123618Z-build-skills/manifest.json`.
The archived local and live files both have SHA-256
`a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278`.
The source snapshot's canonical file also matches. `skill-evidence.json`
records both digests and the manifest digest. All work is in the run work
directory; no source, skill, pipeline, Git, or supervisor-state changes were made.
## Result and scope
141 signed Wilton values at 100 significant digits, with `proven` rigour.
The argument family contains every purely periodic quadratic x in (0,1) with
conjugate less than -1 and primitive polynomial discriminant D<=100.
There are 40 discriminants, 45 complete cycles, and 40 negative outputs.
The sole real parameter uses exact identities quad_A_B_mK and radical labels.
The noncanonical cutoff is an arithmetic coverage choice, not a count target.
General preperiodic quadratics remain outside the computed subset.
`argument-selection.md` explains the family, breadth, extent, and bound proof.
The proposal's sign, logarithm, map, domain, and identity conventions were
retained; no unresolved convention was guessed.
## Corpus and sources
`already_here` found no Wilton table. `already_asked('Wilton')` found #300.
Three fixed-point probes were sent to `/api/lookup?text=...`; the a=2 value
matches existing zeta-residue/hypergeometric/L-value contexts, not an existing
Wilton family. All three proposed tags already exist. See `screening.json`.
The family coverage map and live T677, T131, T174, T430, and T639–T646 documents
were read. Specific links use addresses read from live search/page metadata,
and the golden-ratio and regulator entry keys were checked.
T677 is an existing unpublished companion draft; cross-links from T678 are
intended for the family, and its publication dependency belongs in the final
family review. No published companion was changed.
Balazard–Martin arXiv:1305.4395, §§2.1–2.2, §§3.1–3.2, Theorem 1 and
Propositions 6–9 were checked. Waldschmidt's 2016 lecture notes, §3.6,
Lemmas 46–47, support the quadratic periodicity criterion. The sources were
read through the web research tool; direct PDF archival timed out. Details
and exact URLs are in `source-notes.md`.
## Numerical evidence
- Exact integer enumeration and independent discriminant-factor enumeration
agree on all 141 arguments. All cycles stay inside the selection.
- A matrix fixed-point polynomial independently recovers each primitive
polynomial; the period histogram agrees with the proposal and T677.
- The 429-bit cycle calculation has at least 419 relative accuracy bits.
- An independent 4096-bit calculation uses 800 terms, integer convergents,
and a separate complete-quotient recurrence. Its rigorous absolute tail
is 4*log(M+1)*2^(-400), with M<=9 verified exactly.
- Both enclosures are finite, relatively narrow, and wholly inside each
written 100-digit last-place interval. Maximum cycle radius/ulp:
1.1925276875760965e-27; maximum independent-series radius/ulp:
3.221131415306204e-19.
- Nonzero alternating-geometric and four fixed-point controls ran first.
Functional equations passed for every written value, as did all nine
fixed-point formulas, the D=5 regulator control, and the Brjuno bound.
- The displayed Sage program passed all 141 least periods and their doubled
periods, including the denominator parity change.
- Stored readback repeated the numerical checks and `verify(sample=None)`:
<VerifyReport T678: 141/141 matched, 0 differing, 0 missing, 0 extra>.
- Longest written decimal: 104 characters. The standard dry-run measure,
including ball/entry representations, is about 32.6 KB.
The reproducible evidence is `generate.py`, `checks.py`, the unchanged common
`check.py`, `numerical-evidence.json`, and `stored-evidence.json`. The generator
has no local source or input-data dependencies; the checker imports it and
`check.py`. `fill.log` records the displayed-program check and successful write.
The library's `publish()` method was used only to fill the already-private
T678; it is not the website publication or offer action.
## Audit and critique handoff
`audit.json` contains one finding: all 141 rows use `param-latex` on the real
parameter. This is intentional exact-argument notation, not a function-value
label or a numeric row number. The canonical skill explicitly permits a stable
symbolic identity for a real argument to display its exact radical. The x
column displays (-B+sqrt(D))/(2A); the value column is headed W(x).
There are no other audit findings. This finding is documented, not suppressed.
The independent critic must reassess the entire arithmetic argument family,
read the current live attachments, independently check values and prose, and
write the required fingerprinted argument-review sidecar with its own run ID.
No such acceptance is supplied by this build. The fingerprint artifact is a
binding of the current selection and sources only, not a review decision.
All computations launched by this run finished. Failed pre-write checker
attempts are retained as logs. They were API/coercion mistakes and draft
access setup in checking scripts; no disagreeing numerical method was chosen
over another. The actual fill occurred once after checks passed.