Logarithmic-decay conjecture for slope filtrations

Let $M$ be an irreducible overconvergent $F$-isocrystal over $\operatorname{Spec}(F)$. Suppose its slope filtration is

$$M_0\subset M_1\subset\cdots\subset M_d=M\otimes_{\mathcal{E}^\dagger}\mathcal{E},$$

with graded pieces of slopes $\alpha_1<\alpha_2<\cdots<\alpha_d$. For each relevant $i$, set $r_i=\frac{1}{\alpha_{i+1}-\alpha_i}$. Logarithmic-decay conjecture. The subcrystal $M_i$ has strict $r_i$-log-decay; in particular, smaller differences between consecutive slopes give faster rates of decay. This conjecture predicts that, for irreducible overconvergent $F$-isocrystals, the slope gaps determine the precise logarithmic-decay rates of the slope filtration. The surrounding discussion records a related theorem giving $r_i$-log-decay, while the strictness assertion remains the conjectural strengthening.