Bezrukavnikov's invariant-comparison conjecture for combinatorial wall-crossing

Let $n$ be a positive integer, let $\frac{r}{s}$ be a term of the $n$-th Farey sequence, and let $\tilde{M}_{r/s}$ and $\tilde{M}^{\prime}_{r/s}$ be the compositions of generalized Mullineux involutions and the simpler involutions defined by successive walls to the left of $r/s$. For a partition, consider the total number of boxes in rows whose lengths are divisible by $s$. Bezrukavnikov's conjecture. For every partition $\lambda$ of $n$, the total number of boxes in rows divisible by $s$ is the same for $\tilde{M}_{r/s}(\lambda)$ and $\tilde{M}^{\prime}_{r/s}(\lambda^t)$. This conjecture predicts that the support-dimension invariants associated with rational Cherednik algebra wall-crossing can be computed using the simpler involutions; its resolution status is not specified in the source.