The crosscut lower-bound conjecture for diagramless link homology

Let $k$ be the number of crosscuts, let $N$ be the number of copies of Khovanov homology in the diagramless homology of a link with $k$ crosscuts, and let the minimum crossing number of the link be the least crossing number among its link diagrams. Crosscut lower-bound conjecture. If $k$ is less than the minimum crossing number of the link, then $N=0$. This conjecture concerns the dependence of diagramless link homology on the number of crosscuts; the source gives no resolution or further evidence.