Ju's palindromicity conjecture for graph polytope Ehrhart numerators

Let $G$ be a finite simple connected graph, and let $P(G)$ be its graph polytope. Write its Ehrhart series as

$$\mathrm{Ehr}(P(G),x)=\sum_{n\geq 0}\#W(G,n)x^n.$$

Ju's conjecture. The polynomial in the numerator of this Ehrhart series is symmetric, also known as palindromic.

The conjecture was proposed by Ju and was previously confirmed for bipartite graphs, equivalently graphs with no odd cycles. The source states that the paper solves it.