The rank-unimodality conjecture for the electrical poset

Let $EP_n$ be the graded poset of electrical networks on $n$ boundary vertices, and let $EP_{n,r}$ denote its rank-$r$ elements. Its rank-generating polynomial is

$$X_n(q)=\sum_r |EP_{n,r}|q^r.$$

Rank-unimodality conjecture. $EP_n$ is rank-unimodal; equivalently, the sequence $(|EP_{n,r}|)_r$ is unimodal. The conjecture concerns the distribution of electrical networks by rank. The supplied text gives no resolution evidence.