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3222 bytes, as of the version from 2026-10-27 11:08 (current). Recorded here, not run.
# Build evidence for T545
The draft holds 142 adjacency Estrada indices, all connected simple undirected
unweighted graphs of orders 2 through 6. SageMath 10.9 and numberdb 0.1.10 were
used. The runner's authoritative archived skill manifest is
`agents/runs/20261027T103803Z-build-skills/manifest.json`; its exact copy is
attached as `skill-manifest.json`. Both archived local and live skill SHA-256
values are `e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
The source-snapshot canonical file has that same digest. The run is
`20261027T103803Z`; skill-evidence.json records the manifest and versions read.
The primary computation isolates the real algebraic roots of exact integer
adjacency characteristic polynomials and evaluates exp and its sum in Arb.
At 413 working bits, the minimum measured result accuracy was 408 bits. No
adaptive precision increase was needed. Every serialized number has 100
significant digits; the longest number is 101 characters. The provided dry-run
checker passed on all 142 rows, with no float, nonfinite value, suspicious
exact-in-disguise value or prose finding. Its measurement was a 26.2 KB block
and 141 characters for the longest full-precision internal value string;
those strings include extra certified working digits, not just stored digits.
The independent algorithm in checks.py uses a separately written graph6 decoder
and integer walk-counting dynamic programming. It sums the trace divided by
factorials as exact rationals. For maximum degree d and order n, the omitted
positive tail after degree N is bounded by
n*d^(N+1)/(N+1)! / (1-d/(N+2)), N+2 > d.
This follows from at most n*d^k closed walks of length k and a geometric bound
on consecutive terms in the exponential tail. Each bound is less than 10^-120;
the largest N was 124. Controls K2, K3 and the three-vertex edgeless graph were
checked first against known answers, and a shift by 1 was rejected in each.
The resulting independent enclosures and the spectral enclosures both fit
inside every serialized interval. Checks test finiteness and diameter,
so neither a NaN nor an excessively wide enclosure can pass by overlapping.
All 142 graph6 strings agree with canonicalized McKay catalogue graphs and
with the order-2-through-6 subsets of four live NumberDB tables: T237, T238,
T397 and T400. All adjacency characteristic polynomials agree exactly with
T237. All five complete-graph cases and nine complete-bipartite cases agree
with their closed forms. Eighteen rows have names certified by construction of
the corresponding graph and its canonical identity. No polynomial coincidences
or repeated numerical values were used to drop graph contexts.
Reproduce the pre-fill check with `sage -python checks.py`; the attached
checks-before.json contains all per-row values, independent enclosures, degrees
of truncation and measured accuracy. Reproduce the post-fill check with
`sage -python checks.py --stored`, authenticated while the table is private.
`generate.py` without a fill flag runs `verify(sample=None)`. The controller's
separate critique must independently assess both arithmetic and selection;
these build checks do not constitute the independent critique sidecar.