Galashin–Pylyavskyy positivity conjecture for arborescence ratios

Let $\Gamma$ be a directed graph, let $\tilde{\Gamma}$ be a $k$-cover of $\Gamma$, let $v$ be a vertex of $\Gamma$, and let $\tilde{v}$ be a lift of $v$ in $\tilde{\Gamma}$. If the edge weights of $\Gamma$ are indeterminates, then the polynomial

$$\frac{A_{\tilde{v}}(\tilde{\Gamma})}{A_v(\Gamma)}$$

has positive coefficients. Galashin–Pylyavskyy positivity conjecture. The stated arborescence ratio has positive coefficients. This extends the known integrality result and is proved in the paper for regular covers with 2-group deck groups; the general case remains open.