Stroppel's generalized sutured Khovanov–Hochschild homology conjecture

Let $\sigma \in {\mathfrak{B}}_{n}$, and let $m(\widehat{\sigma}) \subset A \times I$ be the mirror of its annular closure. The notation $A^{k,n-k}$ denotes the Chen–Khovanov–Stroppel algebra, and ${\mathcal{M}}_{\sigma}^{k}$ its associated categorified braid invariant bimodule. Stroppel's conjecture.

$${\text{SKh}}(m(\widehat{\sigma});n-2k) \cong HH(A^{k,n-k},{\mathcal{M}}_{\sigma}^{k}).$$

This conjecture generalizes the paper's theorem identifying sutured Khovanov homology with Hochschild homology in the Khovanov–Seidel case $k=1$; it arose from conversations with Catharina Stroppel. The supplied text gives no resolution, so its status remains open.