The higher-dimensional Heegaard Floer–Khovanov correspondence conjecture

Let $\widehat{\sigma}$ be the link associated to a braid $\sigma$, and let $Kh^{\sharp,k}(\widehat{\sigma})$ denote the degree-$k$ part of the higher-dimensional Floer homology, while $Kh^{i,j}(\sigma)$ denotes the Khovanov homology in bidegree $(i,j)$. Higher-dimensional Heegaard Floer–Khovanov correspondence conjecture. There is an isomorphism

$$Kh^{\sharp,k}(\widehat{\sigma})\simeq\bigoplus_{i-j=k\,\operatorname{mod}\,n-2}Kh^{i,j}(\sigma).$$

This conjecture proposes that the invariant constructed in the paper recovers Khovanov homology after combining its grading according to the congruence $i-j=k\,\operatorname{mod}\,n-2$. The supplied text does not state whether the conjecture has been proved or disproved.