Nian–Tsujie–Uchiumi–Yoshinaga limit conjecture for q-deformed graphic arrangements

Let $G=([[200~\ell], E)$ be a simple graph on $\ell$ vertices, and let $\mathcal{A}_G^q$ be its $q$-deformation of graphic arrangement. Write $\chi(\mathcal{A}_G^q,t)$ for its characteristic polynomial and $\chi(G,t)$ for the chromatic polynomial of $G$. Nian–Tsujie–Uchiumi–Yoshinaga conjecture. The characteristic polynomial $\chi(\mathcal{A}_G^q,t)$ is a polynomial in $q$ and $t$ satisfying

$$\lim_{q\to 1}\frac{\chi(\mathcal{A}_G^q,q^s)}{(q-1)^\ell}=\chi(G,s).$$

This conjecture proposes that the chromatic polynomial is recovered from the characteristic polynomial of the $q$-deformed arrangement in the limit $q\to 1$.