Baldwin–Levine conjecture on mutation invariance of delta-graded link Floer homology

Let $L$ be a link and let $L'$ be obtained from $L$ by Conway mutation. Write $\operatorname{\widehat{HFL}}(L)$ and $\operatorname{\widehat{HFL}}(L')$ for their link Floer homologies, with the bigrading collapsed to a single $\mathbb{Z}$-grading called the $\delta$-grading. Baldwin–Levine conjecture. The $\delta$-graded groups $\operatorname{\widehat{HFL}}(L)$ and $\operatorname{\widehat{HFL}}(L')$ agree; in other words, $\delta$-graded link Floer homology is invariant under Conway mutation. This conjecture proposes a mutation-invariant version of link Floer homology, despite knot and link Floer homology not being invariant under mutation in general. The source gives no resolution status.