Srinivas–Takagi F-nilpotent type and Hodge filtration conjecture

Let $X$ be an $n$-dimensional scheme over $\mathbb C$ and let ${\mathfrak x}$ be a normal isolated singularity of $X$. Write $X^{\mathrm{an}}$ for the analytification and $\operatorname{Gr}^0_F$ for the zeroth graded piece of the Hodge filtration. Srinivas–Takagi conjecture. The local ring at ${\mathfrak x}$ is of $F$-nilpotent type if and only if, for every $i<\dim(X)$,

$$\operatorname{Gr}^0_F\bigl(H^i_{\{\mathfrak x\}}(X^{\mathrm{an}},\mathbb C)\bigr)=0.$$

This conjecture relates reduction-modulo-primes properties of singularities to local Hodge theory; the source explicitly describes it as still open.