back to table · edit · history · where entries came from · files · download
3458 bytes, as of the version from 2026-10-27 13:15 (current). Recorded here, not run.
# T549: pre-fill numerical evidence
Skill manifest: `agents/runs/20261027T125634Z-build-skills/manifest.json`, attached
as `skill-manifest.json`. The local and live skill files both have SHA-256
`e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
The run read the family in numberdb-data#221 before implementation and retained
its proposed 242-index selection. No independent critique acceptance is asserted.
The generator computes Matsumoto's character sum (arXiv:1301.5401, equation 2.1)
using integer rim-hook characters, integer hook-length dimensions, and Sage QQ
arithmetic. Exact fractions, rather than approximate 100-digit decimals, are
appropriate to this definition. The table stores the unscaled signs.
## Checks completed before filling
- `agents/table-build/dry_run.py`, through `agents/sage.sh`: all 242 values
exact, no disguised decimals, no prose complaints, named imports, longest
fraction 20 characters, estimated flat block 12.5 KB. The shared measure
utility using tuple keys in the fuller checks estimates 12.89 KB; the key
serialization accounts for this harmless difference.
- Independent permutation enumeration and Python Fraction Gaussian elimination:
242/242 rational solutions agree, with all 242 conjugacy-class inverse
equations exactly satisfied. The largest group enumerated is S_6, 720
permutations; the largest reduced central system is 11 by 11.
- Every one of the 57 selected (N,k) slices gives the known Haar moment
E|U_11|^(2k) = k!/[N(N+1)...(N+k-1)] when the integration formula is summed.
This uses the uniform complex-sphere marginal, independently of characters.
- All 34 admissible degree-one and degree-two rows agree with Matsumoto's
Example 2.1, including Wg_2((2))=-1/6.
- All 242 values independently agree with Sage's symmetric-function character
expansion in `program.py`. The program also gives the extension example
Wg_13((3,1))=67/149909760. Its implementation uses Sage's scalar products,
rather than the generator's rim-hook or hook-length code.
- Controls run first: a known nonzero linear system, cycle type and permutation
inverse identities, the N=2,k=2 inverse, and moments 1/2 and 1/3. Deliberately
adding one to a coefficient is rejected by the inverse test.
- Expected argument identities and their order are derived independently from
permutation cycle types; they match generator enumeration exactly.
`checks-output.json` records the full structured summary. To reproduce:
sage -python checks.py
Download generate.py, checks.py, check.py and program.py together. A local
SageMath installation with numberdb is sufficient. After filling, the builder
also runs generator.verify(sample=None) and checks.main(stored=True) on values
read from the authenticated API; those outcomes are preserved in the run's
handoff and readback artifacts rather than predicted here.
## Resolved checking-environment failures
The first checking attempt used QQ on a rational string, which reached an
uninitialized real_mpfr module. Parsing through Python Fraction and passing
integer numerator and denominator to QQ avoids that dependency; no numerical
disagreement occurred. An initial Sage symmetric-function check lacked symbolic
initialization and failed in Symmetrica. Explicitly importing
`sage.symbolic.ring.SR` before the symmetric-function operations resolved it;
the complete 242-value comparison then passed. The failed logs are preserved.