# Verification report

Accepted scope: the neighbourliness-plus-hereditary-component-symmetry
characterization of characteristic-two tightness for every finite
nonempty simplicial complex of dimension at most two; the consequence
from tightness over any field; and the four-vertex counterexample to
the statement with neighbourliness omitted.

The all-size proof is in the manuscript. It uses a credited adaptation
of Bagchi–Datta–Spreer Lemma 3.4, induced-cycle generation of graph
homology, mod-two fundamental chains and Mayer–Vietoris.

The C++ program enumerated all 1,048,576 triangle subsets on a complete
six-vertex one-skeleton, as well as all smaller cases. All 37,692
hereditarily symmetric six-vertex complexes passed the homology check.
The independent Python implementation tested the equivalence for all
1,044 labelled complexes through five vertices and checked explicit
surface fillings and counterexample families. Its 23,616 checks agree
in normal and optimized interpreter modes. C++ optimized output agrees
with an undefined-behavior-sanitized replay.

Known surface criteria and the projective-plane field contrast are
credited prior facts, not new discoveries. No independent human or
outside-model review, formal proof-assistant verification, or certified
literature priority is claimed. The bounded source comparison did not
locate the exact characterization already stated.

All four manuscript pages were visually inspected after compilation.
The author's name alone appears at the top, with Mercury Software GmbH
and contact information in a footnote. AI assistance is disclosed in an
ordinary paragraph. The release contains no third-party source PDFs.