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2960 bytes, as of the version from 2026-10-26 16:11 (current). Recorded here, not run.
# Build evidence for T520
Run: 20261026T155642Z-build. Source instruction manifest:
`agents/runs/20261026T155642Z-build-skills/manifest.json`, also attached as
`skill-manifest.json`. The local and live archived instructions, canonical
local file and live /skill fetched in this run all have SHA-256
`b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18`.
The exact quantity is a_(0,n,k) in chi_n(sqrt(q))=sum a_(0,n,k) q^k at q=0,
with q=c^2 and x in [-1,1]. DLMF lambda is chi-q. The table stores rational
numbers, with rigour exact. Decimal precision and numerical error estimates
are unnecessary; no coefficient is inferred from rounded digits.
## Computation and controls
The generator uses a finite-support Legendre perturbation recurrence.
`checks.py` independently solves the ODE in powers of x, fixing a monomial
coefficient instead of a Legendre coefficient. The expected coefficients share
no perturbation or multiplication code with the generator.
Controls ran before comparisons: P_0=1, P_1=x, P_2=(3x^2-1)/2;
(a_(0,0,0),a_(0,0,1),a_(0,0,2))=(0,1/3,-2/135);
(a_(0,1,0),a_(0,1,1))=(2,3/5). The external-formula routine also returned
(0,1/3,-2/135,4/8505,26/1913625) for the first five ground-mode terms.
The offline dry run and checks completed successfully:
- 156 exact rational entries, all m=0, n=0,...,11, k=0,...,12.
- 156/156 agree exactly with the independent monomial calculation.
- 60/60 match DLMF 30.3.9--12, covering k=0,...,4 in every selected mode.
- 156/156 polynomial differential-equation residuals are identically zero,
one for each mode and Taylor order, using Rodrigues' formula to reconstruct
the Legendre eigenvector corrections in powers of x.
- `exactness`, `agrees_with`, and `names_its_rings` report no complaints.
- The standard `agents/table-build/dry_run.py` passes. Longest value: 222
characters at (m,n,k)=(0,10,12). Estimated block: 16.0 KiB.
The range measurements for k_max=8,12,16,20 gave longest entries of
128,222,316,406 characters. The selection keeps twelve corrections per mode;
argument-selection.md explains the mathematical indices and editorial bounds.
The checks are exact finite rational calculations. They establish the
coefficients, not an error bound for evaluating a truncated series at a
nonzero bandwidth. No nonzero bandwidth is a table argument.
## Reproduction and read-back
Download generate.py and checks.py together. With SageMath and numberdb:
sage -python checks.py
sage -python generate.py
sage -python checks.py --stored
The last two commands require a reading key while the table is a private
draft. `generate.py` without --fill invokes verify(sample=None) and writes
nothing. `checks.py --stored` runs the independent checks on every database
coefficient. The build's subsequent fill, read-back, audit and attachment
fingerprints are recorded in the run artifacts and handoff; those outcomes
are not presumed by this pre-fill evidence file.