Manolescu's HOMFLY-PT to knot Floer homology spectral sequence conjecture

Let $L$ be a link in $S^3$. Write $coverline{H}(L)$ and $H^-(L)$ for the reduced, middle, and unreduced HOMFLY-PT homologies of $L$, and $coverline{\operatorname{HFK}}(L)$, $\operatorname{HFK}^-(L)$, and $\operatorname{HFK}(L)$ for the corresponding variants of knot Floer homology. Ignoring gradings at first, Manolescu's conjecture. There are spectral sequences with

• $E_2$ page $coverline{H}(L)$ and $E_{\infty}$ page $coverline{\operatorname{HFK}}(L)$;
• $E_2$ page $H^-(L)$ and $E_{\infty}$ page $\operatorname{HFK}^-(L)$;
• $E_2$ page $H(L)$ and $E_{\infty}$ page $\operatorname{HFK}(L)$.

Moreover, such sequences are given by the construction of Manolescu, which is known to give $E_{\infty}$ pages recovering $\operatorname{HFK}$. This conjecture would connect HOMFLY-PT homology to knot Floer homology for links. The $E_1$ page of Manolescu's construction has been identified with the appropriate sum of HOMFLY-PT complexes for singular resolutions, but identifying the $E_2$ page with HOMFLY-PT homology for links with nonsingular crossings remains open.