The Backman–Baker–Yuen consistency conjecture for regular matroids

Let $M=(E,\mathcal B,\chi)$ be an oriented regular matroid, let $(\sigma,\sigma^*)$ be a pair of acyclic circuit and cocircuit signatures, and let $\alpha_{(M,\sigma,\sigma^*)}$ be the Backman–Baker–Yuen matroidal sandpile torsor action on the bases $\mathcal B$. The action is called consistent if it satisfies the stated contraction and deletion compatibilities for every regular matroid, every such signature pair, every basis $B\in\mathcal B$, and every $f\in E$. Backman–Baker–Yuen consistency conjecture. The Backman–Baker–Yuen matroidal sandpile torsor algorithm is consistent. The paper notes that the proposed matroidal consistency definition may need adjustment, so this conjecture remains open in the stated framework.