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4627 bytes, as of the version from 2026-10-27 11:53 (current). Recorded here, not run.
# T547 build numerical evidence
The authoritative result is the private draft https://numberdb.org/T547.
It contains all 142 connected simple graph isomorphism classes of orders 2–6.
No publication, offer, or human review action was taken.
The governing instructions are recorded in
`agents/runs/20261027T114054Z-build-skills/manifest.json`.
Both archived skill versions have SHA-256
`e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
`skill-evidence.json` records each digest, the manifest path and its digest.
## Methods and outcomes
* The standard `dry_run.py` checked every generated entry, exactness, finite
enclosures, suspicious decimal zeros, comments and size. It exited zero.
The generator imports `numberdb.sage` first and names its Sage imports.
* Exact AA isolation selects the least positive Laplacian eigenvalue.
Degree-one minimal polynomials identify 59 exact integers. The other
83 entries use 413-bit MPFI enclosures. All carry 100 significant digits
when serialized, and the entire enclosure fits in the written interval.
* Maximum measured enclosure width: 1.89091402092e-124. Longest written value:
102 characters. Entries JSON including comments: 12,923 bytes. The dry-run
tool measures working-precision representations at 127 characters and
16.5 KB; this is distinct from the serialized 100-digit measurement.
* A second graph6 decoder and direct permutation determinants reproduce all
142 corresponding T238 polynomials. Exact rational Sturm counts certify
the root order and containment for every stored value, including exact rows
and repeated eigenvalues.
* Independent mpmath symmetric diagonalization at 150 decimal digits agrees
on all 142 rows. This is numerical corroboration, not the error proof.
* Five complete graphs, five paths, four cycles and nine unordered complete-
bipartite part-size pairs satisfy the displayed formulas. The special
K_(1,1)=K2 value is 2; the bipartite minimum formula is restricted to at
least three vertices. Fiedler's definition and Sections 3.11 and 4.4 were
checked, including images of pages 298, 303 and 304.
* Independent McKay catalogue sets and counts agree, as do the 2–6 subsets
of T237, T238, T397 and T400 and the full 142-row sets of T545 and T546.
The Sage canonical identity was checked for every selected graph.
* The displayed Programs snippet was executed and checked against
a(P4)=2-sqrt(2). It is a one-value example, not a truncated enumeration.
* After filling, `verify(sample=None)` reported 142/142 matched, zero differing,
missing or extra. `checks.py --stored` repeated all independent checks on
data retrieved from the website. `audit.json` has `clean: true` and no findings.
## Controls and corrected measurement
The graph6 specification's DQc example, K2's spectrum {0,2}, an edgeless
matrix, a polynomial with a repeated positive root, and rejected incorrect
root intervals were checked before the census. A control confirms that the
exact MPFI endpoints around 1/3 have positive width and straddle 1/3.
The first width calculation incorrectly used QQ(binary_endpoint), which can
produce the same rational approximation at both ends. The preliminary
`numerical-dry.log` therefore has a zero-width measurement and is retained
only as diagnostic evidence. The actual generated intervals and values were
unchanged. `checks.py` now uses `exact_rational()` on both endpoints, asserts
strictly positive widths for irrational values, and passes the added 1/3
control. The authoritative results are `numerical-dry.json` extracted from
`numerical-dry-corrected.log` and `numerical-stored.json`. The lesson is recorded
in `20261027T114054Z-build-lesson.md` as an artifact, without editing the skill.
## Reproduction and independent critique boundary
SageMath 10.9; numberdb 0.1.10; mpmath 1.4.1. The builder ran Sage exclusively
through `agents/sage.sh`. Download `generate.py`, `checks.py` and
`argument-selection.md`; the independent checks use attached McKay files when
present, otherwise download them from their original URLs. Public neighbouring
tables are read through NumberDB unless adjacent JSON snapshots are available.
The live draft needs an authorized NumberDB API key for verification.
`selection-fingerprint.json` records the live selection hash and hashes of
`generate.py`, `checks.py` and `argument-selection.md`. It is a fingerprint,
not a critique or acceptance. A separate critique actor must independently
assess the sole parameter as a justified discrete index and provide its own
required arguments sidecar. The builder created no such sidecar.