The no-gap conjecture for Khovanov homology of prime quasi-alternating links

Let $L$ be a link, and let $\mathcal{H}(L)$ denote its Khovanov homology. A link is prime if it cannot be expressed as a nontrivial connected sum, and a quasi-alternating link is a link in the class defined recursively by the quasi-alternating resolution conditions. A $(2,n)$-torus link is the torus link obtained from the $(2,n)$ torus-knot construction.

No-gap conjecture. If $L$ is a prime quasi-alternating link that is not a $(2,n)$-torus link, then the differential grading of $\mathcal{H}(L)$ has no gap.

This conjecture is supported by the paper's results for quasi-alternating Montesinos links and quasi-alternating links of braid index $3$. It is stated to imply both Conjecture 2.3 in and Conjecture 3.8 in, as well as consequences for the Jones polynomial; its general status is not resolved in the supplied text.