Ladder correspondence for reduced Khovanov complexes

Let $(D',P)=\tau(D,P)$ be obtained from a connected link diagram with basepoint by component-preserving Conway mutation. Let $\widetilde{C}(D)$ denote the reduced Khovanov complex, and let an admissible activity sequence be the sequence associated with a ladder of enhanced states. Reduced ladder conjecture. For every ladder of enhanced states in $\widetilde{C}(D)$, the corresponding admissible activity sequence describes a ladder of enhanced states in $\widetilde{C}(D')$. This conjecture is presented as weaker than the full mutation-invariance conjecture, but the source explains that it would imply mutation invariance of reduced Khovanov homology.