Global semistable reduction conjecture for partially overconvergent F-isocrystals

Let $X$ be a smooth irreducible $k$-variety, let $\overline{X}$ be a partial compactification of $X$, and let $\mathcal{E}$ be an $F$-isocrystal on $X$ overconvergent along $\overline{X}\setminus X$. We say that $\mathcal{E}$ admits semistable reduction if there exists a quasiresolution $(f:X_1\to\overline{X},j:X_1\to\overline{X_1})$ of the pair $(\overline{X},\overline{X}\setminus X)$ such that $f^*\mathcal{E}$ is log-extendable to $X_1$. Global semistable reduction conjecture. $\mathcal{E}$ admits semistable reduction.