Castillo–Liu conjecture on Ehrhart positivity of generalized permutohedra

Let $\mathscr{P}$ be an integral generalized permutohedron. An integral polytope is Ehrhart positive if its Ehrhart polynomial has positive coefficients.

Castillo–Liu conjecture. Every integral generalized permutohedron $\mathscr{P}$ is Ehrhart positive.

Generalized permutohedra form a class containing matroid polytopes, so this is stronger than the De Loera–Haws–Köppe conjecture. It was posed by Castillo and Liu in 2018 and is open in the supplied source.