# Verification report

Verification date: 2026-08-29.

Verdict: complete counterexample for integral
`H_*^(J_+,boxdot)`; unrefereed.

Proof obligations checked:

- the four singleton closures follow from the inductive-product definition;
- `i(U)={11}` and `i(V)=V`, so the two sets form an interior cover;
- the induced subspace closures, rather than an informal graph model, are
  used throughout;
- the relative degree-one boundary matrix is `[-1 -1]`;
- all four normalized relative two-cubes in `(V,U∩V)` were exhaustively
  listed and have zero boundary;
- the primitive difference `(1,-1)` therefore has infinite order;
- the identity square in `(X,U)` has boundary `(1,-1)`; and
- the induced excision map has a nonzero kernel.

The main checker enumerates cubes by singleton-successor closures and generic
face maps. A separately written checker tests the defining continuity
condition on every subset of every domain cube and constructs the boundary
matrices directly. Both pass. The proof in the manuscript is symbolic and
lists the complete degree-two basis; computation is only a falsification aid.

The direct-prior search found no same result but cannot exclude unindexed or
differently phrased work. No independent expert or peer review is claimed or
required before an honestly labelled preprint. Human author metadata, responsibility review, CC BY 4.0 licensing, and explicit public-release approval were supplied on 2026-09-02. The manuscript remains unrefereed.

## Public release and license

The author approved public release on 2026-09-02. This paper, its source files, and this verification report are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0): https://creativecommons.org/licenses/by/4.0/