Manolescu's conjecture on singular-resolution knot Floer and HOMFLY-PT homology

Let $S$ be a complete resolution of a diagram $D$ in braid position. The homologies $H_{H}(S)$ and $H_{F}(S)$ are bigraded vector spaces.

Manolescu's conjecture. There is an isomorphism

$$H_{H}(S)\cong H_{F}(S)$$

as bigraded vector spaces.

The conjecture compares the singular-resolution homologies arising from the HOMFLY-PT and knot Floer cubes. In the source, it is subsequently proved by introducing additional differentials and a basepoint filtration.