Degree-$n-1$ quasipolynomiality conjecture for reachable chip-firing configurations

Let $G$ be an arbitrary graph with $n$ vertices, and consider the configuration $(c,0,0,\dots,0)$, with $c$ chips on one vertex and zero chips on the remaining vertices. Reachable-configuration quasipolynomiality conjecture. The number of configurations reachable from $(c,0,0,\dots,0)$ is a quasipolynomial in $c$ of degree $n-1$ for sufficiently large $c$. The conjecture is motivated by computations for cycles $C_4$, $C_5$, and $C_6$, paths $P_2$ and $P_3$, and the complete graph $K_4$; quasipolynomiality is established in the paper for debt-reachable configurations and for reachable configurations on $C_3$, but remains conjectural for arbitrary graphs.