Slope-bound conjecture for classical coherent cohomology

Let $\be X^\star(T^c)^{M_\mu,+}$ and let $:T(\mathbb{Z}_p)\to\overline{F}^{\times}$ be a finite-order character. For $w\in C^+$, set $=-w^{-1}w_{0,M}(+)-$. Let $:T^{\pm}\to\overline{F}^{\times}$ be an eigensystem occurring in the indicated finite-slope classical cohomology groups. Slope-bound conjecture. In the plus case, $v\geq-$, and in the minus case, $v\leq-w_0$. This conjectural classical slope bound is motivated by the spectral sequences and the overconvergent slope conjecture; the source does not state that it is known.