$p$-adic cohomological Sarnak–Xue density hypothesis

Let $G$ be a definite Gross inner form of $SO_5$ over a number field, let $p$ be a prime of the number field, let $G_p=G(\mathbb{Q}_p)$, let $\Gamma_p(q)$ be the level-$q$ $p$-arithmetic subgroup, let $\Pi(G_p)$ be the irreducible admissible representations of $G_p$, and let $r(\pi)$ and $m(\pi;q)$ denote the rate of decay of matrix coefficients and the multiplicity in $L^2(\Gamma_p(q)\backslash G_p)$, respectively. $p$-adic cohomological Sarnak–Xue density hypothesis. For any $\pi\in\Pi(G_p)$,

$$m(\pi;q)\ll\operatorname{vol}(\Gamma_p(q)\backslash G_p)^{\frac{2}{r(\pi)}}.$$

This is the proposed $p$-adic analogue for definite Gross inner forms; the source does not state whether it is resolved.