The positroid Ehrhart-positivity conjecture

A matroid is Ehrhart positive if its associated base polytope has an Ehrhart polynomial whose coefficients are positive. A positroid is a matroid in the class of positroids introduced by Postnikov.

Positroid Ehrhart-positivity conjecture. Every positroid is Ehrhart positive.

The paper's result proves Ehrhart positivity for a certain class of panhandle matroids, which are positroids, and therefore supports this conjecture. The conjecture is attributed to the cited source and remains open in the supplied text.