Grigsby's categorified wrapping number conjecture for annular links

Let $A$= $S^1\times[0,1]$ be the annulus, let $L\subset A\times I$ be an annular link, and let $\mathrm{wrap}(L)$ be the minimal geometric intersection number between $L$ and a meridional disk in $A\times I$. Let $\mathrm{AKh}(L)$ denote the annular Khovanov homology of $L$, equipped with its annular winding-number, or $k$-, grading. Categorified Wrapping Number Conjecture. The annular Khovanov homology $\mathrm{AKh}(L)$ is nontrivial in $k$-grading $\mathrm{wrap}(L)$. This conjecture seeks a categorified analogue of the wrapping-number conjecture in annular skein theory. The homology is known to be supported in $k$-gradings whose absolute values are at most $\mathrm{wrap}(L)$, but nontriviality at the extremal grading remains the conjectural assertion.