# Verification report

Complete self-audited counterexample family: smooth IDP lattice polytopes in dimension34, h-star degree17 and h15>h16<h17 for every integer t>=1. They refine Ferroni's displayed smooth40-dimensional example. This is not a first disproof or a minimality theorem. New whole-source and source-subquestion closures: zero. The general Gorenstein-domain question remains outside the result.

Written proof: integral Cayley-box geometry, unimodular edge bases for smoothness, greedy integer allocation for IDP, exact interior counts at dilations18,19,20, Ehrhart reciprocity, positivity of36 integer coefficients after u=t-1, and increasing volumes for pairwise inequivalence. The Ehrhart rings are normal standard graded CM domains of dimension35 and not Gorenstein.

Exact verification: symbolic binomial expansion/convolution equals independent rational Newton interpolation from18 direct interior counts for each degree-at-most17 polynomial. All36 gap coefficients are strictly positive; every printed floor-table entry matches. Full forward h-vectors at t1 andt2 independently match the interior tails. No floating-point arithmetic, random tests, or external Python dependencies are used. The all-t proof uses positivity, not sampling.
Checker SHA-256: 557be1b7b86d06f6267eb1e3caeee135c5fc1abd1fa205b191061417f8ab8f32.
Certificate SHA-256: 9f938fc664d56842dace71cd3208fea67ed130b70e7a58d5baa2ed7314aca0a2.

Known mathematical gaps in stated theorems: none. Independent review and formal proof-assistant verification: not performed. Absolute priority and minimum dimension: not certified. The five-page PDF compiled in the built-in editor and portable Tectonic; all pages were visually inspected. Author name is prominent, affiliation and contacts are a footnote, and AI assistance is disclosed in prose.