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2851 bytes, as of the version from 2026-10-28 03:46 (current). Recorded here, not run.
# Exact computation evidence for T570
Build run: 20261028T033309Z-build. The governing archived manifest is
`agents/runs/20261028T033309Z-build-skills/manifest.json`.
Both available skill versions and the source snapshot match SHA-256
`e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`;
see `skill-evidence.json`. No older skill policy was substituted.
The generator computes DLMF 10.17.8 in Q[v], with v denoting nu. Every
coefficient is exact. The campaign's 100-significant-digit target is
inapplicable to rational polynomials; these values lose no digits, and no
claim about the error of a truncated Bessel expansion is made.
Before sending numbers, the campaign's unmodified `dry_run.py` and `check.py`
reported 21 entries, exact coefficients throughout, no disguised approximations,
and a longest expanded polynomial of 1,209 characters at k=20. Its generic
entry wrapper occupies 9.673828125 KiB. The run log is retained as
`dry-run.log` in the build work directory.
The independent `checks.py` uses the elementary half-integer K recurrence to
construct P_n(x), n=0..20. After removing sqrt(pi/(2z))*exp(-z), differentiation
of P_n(1/z) gives D_n(x)=(1+x/2)P_n(x)+x^2 P_n'(x). The coefficient of x^k
is b_k(n+1/2). Lagrange interpolation at the 21 distinct rational nodes
(n+1/2)^2 reconstructs each even polynomial of degree at most 40. This route
shares no coefficient-product code with the generator.
All 21 reconstructed polynomials match exactly, as do all 441 half-integer
specializations. Full derivative-polynomial identities hold for n=0..19;
for n=20 the omitted x^21 coefficient lies outside this table's range.
All 21 recurrence polynomials P_n match the stored T116 values. Both
b_k(nu)=a_k(nu)+(k-1/2)a_(k-1)(nu) (k=1..20) and
b_k(nu)=(a_k(nu-1)+a_k(nu+1))/2 (k=0..20) match T569's stored values.
Degree, evenness, leading coefficient and the stated half-integer roots all
pass throughout the range.
Controls run before the comparisons: P_0 through P_3 have known nonzero
coefficients; D_0=1+x/2 and D_1=1+3x/2+3x^2/2; interpolation reproduces
1,t,t^2. A perturbation of 10^(-20) to b_20 is rejected. This is exact
arithmetic, so there is no tolerance that could mask a discrepancy.
Environment recorded by the computation: Python 3.12.3, numberdb 0.1.10,
Sage 10.9. All Sage computation used `agents/sage.sh` with separate build
containers. No production-shell computation was used.
The full pre-fill log and polynomial strings are preserved in
`checks-before-fill.log`. After the draft is filled, the build must run
`verify(sample=None)`, fetch T570 again and run this same independent verifier
on its stored values and Programs snippet. Those outcomes belong in the
final build handoff and post-fill log. This file records the completed
pre-fill evidence and does not attest to an independent critique.