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3779 bytes, as of the version from 2026-10-27 11:53 (current). Recorded here, not run.
# Build handoff: T547
Built https://numberdb.org/T547, **Algebraic connectivity of connected graphs**,
as a private draft. It has 142 entries and is neither published nor offered.
The controller must run the separate critique and repair stages before any
review offer. The exact controller handoff is
`agents/runs/20261027T114054Z-build.table.json`.
The family was read using `python3 agents/queue.py show 220` before any build.
The current-corpus screen found T238's Laplacian polynomials and related graph
invariants, but no duplicate algebraic-connectivity value table. Sample lookups
for 2, 2-sqrt(2) and 2-sqrt(3) found other mathematical contexts. `already_here`,
`already_asked`, tag results, table documents and lookup results are preserved
in `screening.json` and `screening.log`. The draft title claim succeeded.
The skill manifest is
`agents/runs/20261027T114054Z-build-skills/manifest.json`.
Both archived versions were read and their bytes verified against SHA-256
`e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
See the attached `skill-evidence.json` and `numerical-evidence.md`.
The generator follows the family census exactly: every graph class of orders
2–6, with counts 1, 2, 6, 21 and 112. There is one free parameter, `g`, with
role `discrete_index`; no continuous grids or hidden couplings. The full domain
remains unbounded in vertex count, and the completeness note explains the
noncanonical practical cutoff and structural coverage. Shared identities use
SageMath 10.9 canonical_label(algorithm='sage') followed by graph6. The order is
vertex count and then ASCII graph6 order. `argument-selection.md` explains all
of these choices and supports a separate independent selection review.
There are 59 exact integer values and 83 irrational values at 100 significant
digits. Independent exact Sturm certificates and mpmath eigenvalues agree on
all rows, including website readback. The generator verifies 142/142 entries.
The site audit is clean. Complete, path, cycle and complete-bipartite controls
cover every such graph in the chosen range. The program example was executed.
The largest enclosure width is below 1.891e-124 and the longest written value
is 102 characters. Detailed rows, versions, controls and hashes are in
`numerical-stored.json` and `numerical-evidence.md`.
One small convention needed explicit treatment: K_(1,1)=K2 has connectivity 2;
the complete-bipartite min(a,b) identity applies when a+b>=3. The original
Laplacian definition settles the exception directly. No convention was guessed.
A width-measurement defect in the build checks was corrected before filling:
QQ(endpoint) did not preserve exact binary endpoints. The final checks use
exact_rational(), assert positive widths, and test an interval around 1/3.
The failed measurement log is retained and clearly superseded. The numerical
values did not change. The lesson is an artifact, not an edit to the skill.
Existing tags `combinatorics` and `eigenvalue` were used. No `graph theory` tag
was found. Such a tag would group T237, T238, T397, T400, T545, T546 and T547,
among others; this build proposes it without creating it. T546 was accessible
through the authenticated API but absent from text search, so its Similar
tables link uses the supported permanent HREF{T546} target rather than an
invented slug. Other slugs were read from live search results.
The draft carries `generate.py`, `checks.py`, `argument-selection.md`, numerical
and skill evidence, the McKay input catalogues, and build check logs.
`selection-fingerprint.json` contains the current live hashes. No independent
critique sidecar was manufactured. No existing published table was changed,
no queue item was marked as published, and no source snapshot file was edited.