Categorified wrapping number conjecture for annular links

Determine whether the annular Khovanov homology of every annular link detects its wrapping number, namely whether \(\deg_k\operatorname{AKh}(L)=\operatorname{wrap}(L)\) for every annular link \(L\).

Background

The paper distinguishes the Kauffman-bracket annular degree from annular Khovanov homology. For every annular link $L$, the inequalities $$\deg_z\langle L\rangle\leq\deg_k\operatorname{AKh}(L)\leq\operatorname{wrap}(L)$$ hold. Although the paper gives a counterexample to the Kauffman-bracket wrapping number conjecture, it shows that its example $K$ has $$\deg_k\operatorname{AKh}(K)=\operatorname{wrap}(K)=4$$, so that example does not resolve the categorified conjecture. The general equality therefore remains the stated conjectural problem.