Dual minimal slope conjecture for overconvergent F-isocrystals

Let $X$, $K$, $\mathcal M^\dagger$, and $\mathcal N^\dagger$ be as in the minimal slope conjecture, with associated convergent $F$-isocrystals $\mathcal M$ and $\mathcal N$. Write the slope filtrations in decreasing form

$$\mathcal M=\mathcal M^0\supsetneq\mathcal M^1\supsetneq\cdots\supsetneq\mathcal M^{r-1}\supsetneq\mathcal M^r=0,$$

with slopes $s^0>s^1>\cdots>s^{r-1}$, and similarly for $\mathcal N$. The quotients $\mathcal M/\mathcal M^1$ and $\mathcal N/\mathcal N^1$ are their maximal-slope quotients. Dual minimal slope conjecture. If there is a nontrivial morphism $h:\mathcal N/\mathcal N^1\to\mathcal M/\mathcal M^1$ between the maximal-slope quotients as convergent $F$-isocrystals, then there exists a unique isomorphism $g^\dagger:\mathcal N^\dagger\to\mathcal M^\dagger$ of overconvergent $F$-isocrystals such that the induced diagram commutes in the category of convergent $F$-isocrystals on $X/K$. This is presented as the dual form of the stronger version of Kedlaya's minimal slope conjecture and is the subject studied in the paper; the supplied text gives no resolution.