# Verification report

The manuscript gives a complete self-audited proof for the explicitly fixed binary interior-cover axiom package. It does not settle every strengthened variant of the source question. The known simplicial constructions and general closure-space nonuniqueness are attributed; originality of the exact consequence is not certified.

The mathematical audit checks functoriality, intrinsic subspace witnesses, both cover identities, the relative chain isomorphism, the pair-preserving contiguous-map prism, the natural long exact sequence, point normalization and coproduct additivity. The four-cycle complexes are explicitly a circle and the boundary of a tetrahedron, which establishes their integral homology, not merely field ranks. The finite-graph interval argument uses the finiteness of the source graph and is not asserted on the whole closure-space category.

The finite regression checker covers 4,166 closure relations with at most four vertices, 139,426 binary interior covers, 278,852 excision identities, 45,462 continuous maps and 577,500 contiguity checks. Four negative controls reject incorrect cover and subcomplex substitutions. The normal and optimized results agree. Package readiness additionally requires fresh runs of the copied checker to match the sealed research outputs byte for byte.

The five-page PDF compiled in the built-in LaTeX compiler and was exported with Tectonic. Every rendered page was visually inspected: title and author footnote, quotient chains, cover argument, homotopy proof, graph example, interval limitation and references are legible. The final package manifest binds the inspected PDF and source by SHA-256.

This is not independent peer review or formal proof verification. The public source archive contains original material and references, not third-party source PDFs. No DOI, live website release or Hugging Face notice is implied by local package readiness.