# Verification report

The five-page manuscript proves its stated sharp tensor-nilpotence theorem
and finite-module graph realization. The originating researcher's detailed
self-audit found no mathematical gap within that scope. The broad source
AIM-OTHER-0067 is not resolved. This is not independent review or
proof-assistant verification.

The general upper proof checks duality, braiding only inside the base,
arbitrary homogeneous sums, nonabelian prefix cancellation, weak action
coherences, zero components and the trivial subgroup. The module proof
checks inverse pullback, coordinate projectivity, integer direct-sum
multiplicities and the exact stable matrix-unit formula. No support-variety
conjecture is needed. Earlier cyclic examples and categorical constructions
are credited. The bounded literature review does not certify absolute priority.

The standard-library checker passed 136,296 explicit conditions in both
ordinary and optimized Python. The reports are byte-identical. It covers
all 66,066 labelled directed graphs with loops on one to four vertices,
twisted word expansions for the stated finite groups and deterministic
samples, and the saved small permutation-module domains over F2 and F3.
The 24-dimensional V4 example has index four; the C2 two-cycle shows
failure of additivity. These finite regressions supplement the written proof.

The desktop LaTeX compiler succeeded. The distributable PDF was exported
from the same source with Tectonic and its log has no errors, undefined
citations or overfull/underfull boxes. All five final rendered pages were
visually inspected: title and author footnote, equations, theorem statements,
page transitions, disclosure and all six references are legible. An initial
six-page layout with one orphaned reference was retained privately and
superseded by the five-page version.

The author is Alper Ferudun. Mercury Software GmbH and contact information
appear in the author footnote; AI assistance is disclosed in ordinary prose.
The public source archive excludes third-party PDFs and private controls.
Package hashes, source provenance, and portable rerun outputs accompany
the manuscript. Readiness alone does not imply DOI assignment or publication.