Smooth 34-Dimensional IDP Polytopes with Nonunimodal h*-Polynomials

Ferroni constructed smooth 40-dimensional lattice polytopes with the integer decomposition property whose h-star polynomials are not unimodal. This paper refines the parameters in his Cayley-box construction to obtain infinitely many pairwise lattice-inequivalent examples in dimension 34. For every integer t >= 1, the matrix [100000t*ones_17 | 1310000t*I_17] + J_(17x18) defines a smooth IDP polytope with h-star degree 17 and h15 > h16 < h17. Exact positivity of all coefficients of two gap polynomials in t-1 proves the inequalities uniformly. A standalone verifier independently reconstructs the polynomials by rational interpolation of direct interior counts and checks forward h-vectors. The associated Ehrhart rings are standard graded normal Cohen--Macaulay domains of dimension 35 and are not Gorenstein. This is a dimension refinement of Ferroni's prior counterexamples, not a first disproof of unimodality or a minimal-dimension claim. The general standard graded Gorenstein-domain unimodality question in OWR-15587-015 remains outside the result. AI-assisted, self-audited and unrefereed; no independent review, formal verification or absolute priority certification is claimed.