The positive-mutation conjecture for bigraded knot Floer homology

Let $L$ and $L'$ be mutant links, and let $T$ be a tangle satisfying the hypotheses of the paper's mutation-invariance theorem for delta-graded knot Floer homology. Positive-mutation conjecture. If the mutation is positive, then there is a bigraded isomorphism

$${\rm {\widehat{HFK}}}(L)\cong {\rm {\widehat{HFK}}}(L').$$

This is proposed as a stronger form of the established result for delta-graded knot Floer homology. The paper gives motivating evidence from positive mutations of pretzel tangles, but the conjecture is not resolved in general.