Monodromy conjecture for crystalline cohomology

Let $X_K$ be a smooth scheme of finite type over $K$. Let $H^{n}_{pst}(X_K)$ be the finite-dimensional $\mathcal{H}^{ur}_1$-module equipped with its increasing weight filtration $W_{\bullet}$, together with the comparison isomorphism with de Rham cohomology described in the source; when $X_K$ admits the specified compactification, this is defined by $H^{*}_{pst}(X_K)=H^{*}_{st}(X) \otimes \mathbb{Q}_p^{ur}$, and in general by de Jong's alteration theorem. Monodromy conjecture for crystalline cohomology. The pair $(H^{n}_{pst}(X_K);W_{\bullet})$ is a mixed $\mathcal{H}^{ur}_1$-module. This is presented as the expected general mixedness statement for the weight-filtered potentially semistable crystalline cohomology; the source says that it is known to specialists but gives no resolution here.