Le Stum's conjecture on the p-adic Deligne–Kashiwara equivalence

Let $k$ be the base field and let $(X,Y)$ be a pair over $k$. Write $\mathrm{Isoc}_\mathrm{cons}(X,Y)$ for the category of constructible isocrystals and $\mathrm{DCon}(X,Y)$ for the corresponding category of constructible arithmetic $\mathscr{D}$-modules, with realization functor

$$\mathrm{sp}_!\colon \mathrm{Isoc}_\mathrm{cons}(X,Y)\rightarrow \mathrm{DCon}(X,Y).$$

Le Stum's conjecture. For any pair $(X,Y)$ over $k$, the functor $\mathrm{sp}_!$ is an equivalence of categories.

This is the proposed $p$-adic analogue of the Deligne–Kashiwara equivalence, relating constructible isocrystals to constructible $\mathscr{D}$-modules. The source presents it as a conjecture and gives no resolution.