Caro's surholonomicity conjecture for arithmetic D-modules of overconvergent F-isocrystals

Let $k$ be a field, let $Y$ be a separated smooth $k$-scheme, let $E$ be an overconvergent $F$-isocrystal on $Y$, and let $\mathrm{sp}_{Y+}(E)$ denote its specialization. An arithmetic surholonomicity conjecture. The $F$-arithmetic $\mathcal{D}_Y$-module $\mathrm{sp}_{Y+}(E)$ is surholonomic for every such $Y$ and $E$. This conjecture predicts that specialization sends overconvergent $F$-isocrystals to surholonomic arithmetic $\mathcal{D}$-modules; the supplied text recalls it from Caro's work, but gives no evidence of a resolution, so its status is left open.