back to table · edit · history · where entries came from · files · download
3864 bytes, as of the version from 2026-10-27 03:45 (current). Recorded here, not run.
# Argument selection for T536
Policy read: the coordinated archive at
`agents/runs/20261027T033406Z-build-skills/manifest.json`. Its local and live
skill files both have SHA-256
`e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
This is the builder's justification, not an independent critique or acceptance.
The sole free parameter is `g`, a symbolic identity for a finite, connected,
simple, undirected, unweighted graph on at least two vertices. Its category is
`discrete_index`: the argument is a genuine discrete object, not a continuous
argument encoded by an index. There is no separate size, edge weight,
temperature, coupling or eigenvalue-index parameter. The quantity is always the
largest eigenvalue of the shortest-path distance matrix, with distances in
numbers of edges. Graph order is derived from the graph.
The default enumeration includes **all** connected isomorphism classes on
2, 3, 4, 5 and 6 vertices, respectively 1, 2, 6, 21 and 112 graphs, for 142
entries. These are frozen, in order by vertex count and then ASCII graph6
string, in `selected-graphs.json`. Sage's explicit
`canonical_label(algorithm='sage')` defines the labels. They match the
corresponding identities in the live T237 and T238 documents downloaded in
this run. Named entries copy T237's common graph names.
This small-order reference census is meant to identify outputs of shortest-path
network calculations and spectral experiments. A complete census avoids
selecting only graphs with exceptional names or simple radicals. It covers
paths and branching trees, cycles, bipartite and non-bipartite graphs, and
regular and irregular distance patterns. At six vertices it includes both
C6 and K3,3; the latter has two positive distance eigenvalues. This breadth
matters for a distance-matrix family and prevents treating tree behavior as
universal. No molecular application is asserted for every graph.
Six is a practical, noncanonical reference boundary. Seven would add 853
isomorphism classes, a substantial increase dominated by extension of the
small-order census. The present range covers the structural families just
listed; future extension should be assessed on identification benefit rather
than the capacity of a file or an older graph table's bound. The one-vertex
graph contributes the elementary radius zero, which is stated in a comment.
The graph selection is independent of numeral base, graph labelling, and the
spelling of numerical eigenvalues. Canonical graph6 is only an address.
This is one exhaustive discrete group, not a mixture of continuous reference
samples and intrinsic points. The proposed cutoff is a reference choice,
while the underlying argument family is the connected-graph domain. There is
no rectangular parameter product and no arbitrary decimal mesh.
Checked sources: Zhou and Ilić, arXiv:1101.4393, Introduction and Section 2,
for the distance matrix, largest-eigenvalue convention and distinction from
adjacency spectra; Hogben and Reinhart, arXiv:2103.00647, Sections 1, 3 and 5,
for the distance-spectral family and its structural cases; McKay's Graphs
catalogue, Simple graphs section, for the exhaustive counts and independent
graph6 files on 2 through 6 vertices. Sources support the mathematical family
and conventions; the finite reference cutoff is ours. `source-notes.md`
records precise links and the checks that use them.
The generator, the stored keys and the completeness note must describe these
same 142 graphs. `checks.py` verifies the enumeration against both nauty geng
and canonicalized McKay catalogue files. The separate critique must evaluate
this rationale independently and bind its sidecar to the current selection
and at least `generate.py` and `selected-graphs.json`, plus every other
selection-relevant attachment it reviews. No acceptance sidecar is created by
this build.