Rozansky's trivial tail homology conjecture for non-$A$-adequate diagrams

Let $D$ be a link diagram, and let $H^{\infty}(D)$ denote the tail homology obtained as the direct limit of the directed system of shifted categorifications of the colored Jones polynomial. A diagram is $A$-adequate when its all-$A$ state has no state graph edge joining a state circle to itself.

Rozansky's conjecture. If a diagram $D$ is not $A$-adequate, then $H^{\infty}(D)$ is trivial.

For $A$-adequate links, the tail homology categorifies the tail of the colored Jones polynomial. This conjecture predicts that the corresponding tail homology vanishes for non-$A$-adequate diagrams; the supplied source does not state whether the conjecture has been resolved.