The depth criterion for logarithmic de Rham vanishing

Let $Z$ be a reduced closed subscheme of a smooth variety $X$ of dimension $n$, let $f:Y\to X$ be a log resolution, and let $E$ be the reduced exceptional divisor over $Z$. Depth–vanishing conjecture. If

$$\operatorname{depth}(\mathscr{O}_Z)\geq k+2,$$

then

$$R^{n-2}f_*\Omega_Y^{n-k}(\log E)=0.$$

This would extend the established vanishing for $R^{n-1}f_*\Omega_Y^j(\log E)$ and relate depth of $\mathscr{O}_Z$ to logarithmic de Rham direct-image vanishing; it remains open.