# Verification and scope

## Accepted theorem

For A = {(3,0,0), (0,3,0), (0,0,3), (2,1,0), (2,0,1), (0,1,2)}, the optimized strict affine two-cell bound is 5 and the actual secant cone is C^6. The associated irreducible cone has dimension 3. Disjoint coordinate blocks yield, for every r >= 1, optimized bound 5r and actual secant dimension 6r.

## Proof evidence

1. The universal upper bound uses only convexity on each triangle edge and the pigeonhole principle. Ties and empty cells are explicitly covered.
2. The affine forms 0 and a_1 - 1 attain the value 5.
3. At p = (1,1,1), q = (1,2,3), the six-by-six Jacobian has exact determinant 216. The complex inverse function theorem proves Zariski dominance of the sum map.
4. Constant positive degree identifies affine rank with linear rank, so ranks split across coordinate blocks. A single pair of global forms attains 5r in all blocks.
5. The missing integral monomial xyz proves nonnormality. Normality is not a hypothesis of the source's unrestricted question.

## Exact regression checks

Both ordinary and optimized Python runs agree byte for byte. All 729 ternary sign patterns were tested by rational Fourier-Motzkin elimination; 87 are feasible and none has score greater than 5. Two determinant algorithms give 216. Additional checks cover 4913 integer linear forms, eight block sizes and 729 quadratic-Veronese control pairs. No floating point arithmetic is used.

The finite checks are diagnostic regression evidence, not a proof assistant or a substitute for the general proof. The written proof has no outstanding identified mathematical obligation after self-audit. Independent review has not occurred.

## Sources and novelty

Six primary-source PDFs were retained locally, with fifteen relevant complete pages inspected. The publisher and MFO versions of the original report have different pagination; their mathematical statements agree. Theorem 7 and Question 1 are at publisher pages 3293-3294, MFO pages 3353-3354.

The prior-art review includes Draisma, Baur-Draisma, Develin, and Laface-Massarenti-Rischter. General tropical methods and Jacobian dominance are not claimed as new. The exact sparse cubic counterexample and block amplification were not located in the bounded search. Absolute novelty and priority are not certified.

## Publication honesty

This is an unrefereed complete counterexample to the unrestricted monomial-map equality question. It does not disprove the lower-bound theorem, normal-toric exactness, or a Segre-Veronese claim. External publication is separate from local readiness; no DOI or public release is claimed here.