# Hom-test classification verification report

The general proof transfers pair homology and inclusion diagrams naturally
through first-variable folds, reduces to a stiff core, and gives two
exhaustive obstructions. The unlooped-twin case has a split R summand in
the middle defect; the reflexive nonpoint case has a split R summand in
the cokernel. For the positive looped point, relative cellular chains
give excision. The intermediate CW union proves excision implies the
degree-zero Mayer-Vietoris condition without assuming that Hom preserves
an arbitrary graph cover. Empty pieces and the single unlooped vertex
are included. The proof works over every nonzero commutative unital ring.

Exact finite checks enumerate 1,098 labeled optional-loop graphs: 596
dismantlable cases and 502 negative witnesses (293 twins, 209 reflexive
nonedges). They verify 2,374 folds and 46,758 induced clique covers.
An independently coded cellular-boundary implementation replays all 31
negative sources of size at most three, with exact rational ranks and
zero boundary squares. The shared witness data is disclosed. Neither
finite enumeration nor rational ranks replace the general proof.

The research checks passed twice each in normal and optimized isolated
Python processes. Package readiness additionally requires four runs from
an extracted ZIP: normal and optimized executions of both checkers, with
byte-identical reference output and no workspace-path dependencies.

The five-page PDF compiled with the built-in compiler and cached Tectonic.
All five rendered pages were visually inspected. The title, author
footnote, formulas, two obstruction proofs, disclosure and bibliography
are legible, without overlap, clipping or missing symbols. The log has no
errors, undefined references, missing characters or box warnings.

This is originating-researcher self-audit, not independent review or
formal verification. The fixed-test result is complete; the full AIM
program and absolute novelty remain uncertified.