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5438 bytes, as of the version from 2026-10-25 08:29 (current). Recorded here, not run.
# T479 build handoff
Built draft: https://numberdb.org/T479
Title: Tammes problem: the minimum angle of the best known spherical codes.
Proposal: numberdb-data family #202.
The draft contains 194 entries: n=4..100, each in angle (degrees) and chord
length (unit-sphere) normalisations, in ascending n order. It remains
unpublished and was NOT offered for review. The controller owns that action
after the separate critique and repair sessions. No published table was edited,
no publication/review endpoint was called, and no source or skill was changed.
## Numerical provenance and decisions
Snapshot date: 2026-10-25. Cohn's current Table of spherical codes supplies
n=7..100; Sloane/Hardin/Smith supplies n=4..6, where exact regular-polyhedron
formulas are used. Cohn's archived dataset is cited as requested by the source,
and the current source is linked separately. sources.json preserves the
coordinates, source URLs and SHA-256 hashes, cosines, polynomials and references.
There are 27 source-polynomial cases plus three elementary cases. They give
60 entries at 100 significant digits except the two exact angles of 90 degrees.
The other 134 entries carry ten significant digits, justified by the source's
printed cosine accuracy and coordinate agreement. No optimization result is
presented as a globally optimal value without separate proof attribution.
The measured algebraic precision floor is 431 bits. Longest stored number:
102 characters. All 194 numbers were uploaded together after local checking.
Range n=4..100 follows the earliest source case and provides a contiguous
reference for small spherical codes. Parameters describe the mathematical
domain n>=2, not this computed range. The two normalisations follow the family
convention and determine each other by the displayed sine/arcsine formulas.
The row n=97 uses Cohn's newer configuration, credited to Lai et al. (2023),
which improves the older Sloane angle from 21.4006197 to about 21.40065028 degrees.
This discrepancy was traced to the source configuration, not rounded away.
Published optimality references cover n=4..14 and n=24. Cohn additionally
marks n=15 optimal with a 2026 preprint citation. That newer claim is separately
attributed; this run did not rerun its certificates or check its proof.
## Completed checks
- `screen.already_here` and `already_asked`: no duplicate proposal/table found.
- API numerical lookups at four characteristic angles/chords: no matching family.
- Existing tags checked: discrete geometry and sequence. The proposed tag
extremal configurations is absent; it would fit T394, T449, T446, T477,
T478 and T479.
- Repository dry_run.py and check.py: exactness, named imports, prose and size
checks passed. Generator imports numberdb.sage before named Sage rings.
- Independent normalized-coordinate computation for all 97 configurations:
all pairwise inner products and all pairwise Euclidean distances checked.
- Three known-answer controls, plus tetrahedron, octahedron, square antiprism,
n=9 and icosahedron formulas passed.
- Both conversions on all 194 written values passed, before and after upload.
- All source-polynomial roots have rational isolation and a uniqueness check.
- `verify(sample=None)`: 194/194 matched, zero differing/missing/extra.
- Six original attachments downloaded and matched byte for byte by SHA-256.
- Representative browser preview: no math rendering errors; checked labels,
number header and wrapping of long numerical values.
- Anonymous API read cannot see T479. No offering or publication action occurred.
## Audit and deferred links
Final API audit has one finding, so `clean` is false. It asks whether the
categorical angle/chord parameter represents multiple tables. This is the
family's explicitly permitted one-number-in-two-conventions exception. The
definition says "two invertible normalisations", and both conversions are
written and checked over the whole range. The audit is structural and retains
this question even when an exception is explained. No other findings remain.
The separate critic should confirm the exception rather than split the table.
T394, T449 and T446 are linked using slugs read from live search. T477 and T478
are still unpublished and invisible in anonymous search, so links to those
siblings are deferred until they are published. Their documents were read.
No guessed slugs were used.
## Evidence and reproduction
The website carries generate.py, checks.py, the unmodified shared check.py,
sources.json, checks-result.json and source-notes.md. The final readback output,
audit, versions, dry-run log and this handoff are attached as build evidence.
Download these files together, then run `sage -python checks.py` and
`sage -python generate.py` (the latter needs authorized draft access).
To repeat the stored-number checks offline, download the document via the API
as stored-document.json beside checks.py. The checker then checks all stored
spellings as well as repeating the numerical computation.
Local artifacts are in agents/runs/20261025T075541Z-build-work/. They include
raw source pages and coordinate files, all failed private checker attempts,
final JSON documents, screenshots, source checks, audit outputs and attachment
hashes. The lesson artifact is
agents/lessons/proposals/20261025T075541Z-build.md. Deployment observations are
in environment-notes.md inside the work directory. No Git actions were taken.