Edge-deletion gamma-nonnegativity conjecture for symmetric edge polytopes

Let $G$ be a 2-connected graph with edge set $E$, and let $P_G$ denote its symmetric edge polytope. For an edge $e\in E$, let $P_{G\setminus e}$ be the symmetric edge polytope of the graph obtained by deleting $e$. A palindromic polynomial is $\gamma$-nonnegative when its associated $\gamma$-polynomial has nonnegative coefficients. Edge-deletion gamma-nonnegativity conjecture. There exists an edge $e\in E$ such that

$$h^*_{P_G}(t)-h^*_{P_{G\setminus e}}(t)$$

is $\gamma$-nonnegative. This is described as an approach to the Ohsugi–Tsuchiya conjecture; the supplied text gives no resolution status.