Dowlin's graded sl_n to knot Floer spectral sequence conjecture

Let $L$ be a link in $S^3$, and let $n\geq 1$. Let $H_n(L)$ and $\overline{H}_n(L)$ denote the unreduced and reduced $\mathfrak{sl}_n$ homologies, with bigrading $(\mathbf{gr}_n,\mathbf{gr}_v)$, and let $\mathit{HFK}_n(L)$ and $\widehat{\mathit{HFK}}_n(L)$ denote the corresponding unreduced and reduced knot Floer homologies. The grading on $H_n(L)$ is $\mathbf{gr}_n+\frac{n}{2}\mathbf{gr}_v$.

Dowlin's graded spectral sequence conjecture. For each $n$, there are spectral sequences

$$H_n(L)\Longrightarrow\mathit{HFK}_n(L)$$

and

$$\overline{H}_n(L)\Longrightarrow\widehat{\mathit{HFK}}_n(L),$$

with each differential decreasing the grading $\mathbf{gr}_n+\frac{n}{2}\mathbf{gr}_v$ by $n$.

This conjecture is motivated by the agreement of the theories on completely singular links and predicts that the $\mathfrak{sl}_n$ and knot Floer theories are connected by grading-compatible spectral sequences. The source gives no resolution status.