The uniqueness conjecture for consistent matroidal sandpile torsor algorithms

Let $M=(E,\mathcal B,\chi)$ be an oriented regular matroid, let $(\sigma,\sigma^*)$ be a pair of acyclic signatures, and let $\alpha$ and $\beta$ be matroidal sandpile torsor algorithms. Say that $\alpha$ and $\beta$ have the same structure when $\beta$ is one of $\alpha$, $\alpha'$, $\alpha”$, or $\alpha”'$, obtained by complementing the circuit and/or cocircuit signatures. Uniqueness conjecture. Every consistent matroidal sandpile torsor algorithm has the same structure as the Backman–Baker–Yuen algorithm. This is presented as an open conjecture alongside the conjecture that the Backman–Baker–Yuen algorithm itself is consistent; the authors caution that the consistency definition may require modification.