Log weak Lefschetz conjecture for log isocrystalline cohomologies

Let $Y$ be a projective SNCL scheme over the log point $s$, let $E$ be a horizontal smooth divisor on $Y$, and let $d=\dim Y$. Let $q$ be a nonnegative integer. Write $K_0=\operatorname{Frac}(\mathcal W)$ and, for a $\mathcal W$-module $M$, write $M_{K_0}=M\otimes_{\mathcal W}K_0$. The closed immersion $\iota\colon E\hookrightarrow Y$ induces

$$\iota^*_{\rm crys}\colon H^q_{\rm crys}(Y/\mathcal W(s))_{K_0}\longrightarrow H^q_{\rm crys}(E/\mathcal W(s))_{K_0}.$$

The cohomology groups carry weight filtrations $P$.

Log weak Lefschetz conjecture. Assume that $\mathcal O_Y(E)$ is ample. Then the morphism above is a filtered isomorphism with respect to $P$ if $q\leq d-2$ and strictly injective for $q=d-1$.

This is a logarithmic analogue of the weak Lefschetz theorem for log crystalline cohomology. The source introduces it as a conjecture and gives an affirmative result, but the supplied text does not specify whether the full conjecture is resolved.