Gamma-positivity conjecture for locally anti-blocking reflexive polytopes

Let ${\mathcal P}\subset {\mathbb R}^d$ be a locally anti-blocking reflexive polytope, and let $h^*({\mathcal P},x)$ denote its $h^*$-polynomial. Locally anti-blocking reflexive polytope conjecture. The $h^*$-polynomial of any locally anti-blocking reflexive polytope is $\gamma$-positive. The preceding corollary proves the claim for polytopes whose orthant sections have the specified enriched chain-polytope or symmetric-edge-polytope structure; the general assertion remains open in the supplied source.