Optimal upper slope bound for the cohomology of rigid spaces

Let $X$ be a qcqs rigid space of dimension $d$ over $K$ and let $g\in G_K$ be an element projecting to $\mathrm{Fr}_{q}$. For each $i>d$, consider the eigenvalues of $g$ acting on $H^i(X_C,\mathbb{Q}_\ell)$ and their $q$-slopes.

Slope-bound conjecture. For all $i>d$, the $q$-slopes of these eigenvalues are contained in

$$[i-d,d].$$

The paper states this as a speculation that the bounds for $H^i(X_C,\mathbb{Q}_\ell)$ are optimal, motivated by examples from rigid analytifications of products of elliptic curves with multiplicative reduction. Since the source presents it as an expectation rather than an established result, its resolution is not specified here.