# Verification report

The full counterexample family is proved by the integral cut-surface presentation and a determinant multiplicity argument. The counterexample resolves the source conjecture negatively, not the broader classification of all realizable pairs.

The self audit checks the primitive connected surface, the integral Mayer-Vietoris sequences, the rank of the cut manifold's first homology, retention of torsion cross terms, the specialization coker P(1)=T, and the determinant's Laurent unit ambiguity. It rejects the false general rule that reduction modulo a prime commutes with taking the gcd of presentation minors.

Normal and optimized executions agree on 6,817 exhaustive two-by-two pencils, 480 larger sampled pencils, 240 integral Smith-ideal pencils, 80 counterexample-family instances and 64 cyclic torus-bundle controls. The sharp noncyclic torus-bundle control is also checked. These checks are not a formal verification of the topology.

The built-in LaTeX compiler reports success. The exported five-page PDF has been rendered and each page inspected for readable formulas, complete proofs, author footnote placement and references. The AI disclosure is ordinary prose, not a separate heading. The package builder additionally recompiles the extracted source archive and replays the checker in an isolated temporary directory.

The author is Alper Ferudun, Mercury Software GmbH. This is an unrefereed, originating-researcher self audit; it is not independent review or proof-assistant certification. A bounded primary-literature check found no matching counterexample, but does not establish absolute originality.