Off-line Ehrhart roots for complete multipartite symmetric edge polytopes

We disprove the 2016 conjecture of Higashitani, Kummer and Michałek that the Ehrhart polynomial of every complete multipartite symmetric edge polytope has all its roots on the line Re z = −1/2. The graph with six parts of size two gives an eleven-dimensional example with exactly four off-line roots and a simple negative-real-rooted h*-polynomial. Deleting q² disjoint edges from K_(q³+1) also gives an infinite family with simple negative-real-rooted h* and gamma polynomials, for which the number of simple off-line Ehrhart roots grows faster than every fixed multiple of log q. The proofs combine an exact matching-deletion formula, finite rational certificates, compact-uniform asymptotics and a Legendre-polynomial perturbation estimate. A directed-interval certificate gives q = 10 as an explicit member with at least four off-line roots.This record contains the preprint and its source, certificates and reproducibility files. Lean verification is limited to selected finite arithmetic statements; it does not cover the complete geometric or analytic proof. The archive documents the scope and retained compilation evidence.