Conjecture on the finiteness of the characteristic cycle for a unique critical slope

Let ${\mathscr F}$ be a constructible étale sheaf of flat $\Lambda$-modules on $\eta$, and let $r>1$ be a critical slope of ${\mathscr F}$. Assume that

$$({\mathscr F}_{\overline{\eta}})^{G^r}=0,\qquad ({\mathscr F}_{\overline{\eta}})^{G^{r+}}={\mathscr F}_{\overline{\eta}}.$$

Thus $r$ is the unique critical slope of ${\mathscr F}$. Finiteness conjecture for ${\tt C}_r({\mathscr F})$. The set ${\tt C}_r({\mathscr F})$ is a finite set of points of $\overline{{\bf T}}^{\tt t}_r$ that does not contain the origin. This is one of the isogeny conjectures concerning the characteristic cycle attached to a sheaf with a unique critical slope; the statement is presented in the source without a resolution.