All-level torsion growth conjecture for arithmetic groups

Let $\Gamma$ be an arithmetic group, let $\Gamma_k$ range over congruence subgroups of $\Gamma$ of increasing level, and let $\delta$ denote the deficiency of the associated real semisimple group. Let $i$ be the degree at the top of the cuspidal range, and let $\mathscr{L}$ be the coefficient lattice. All-level torsion growth conjecture. When $\delta=1$, the limit

$$\lim_{k\rightarrow\infty}\frac{\log\lvert H^i(\Gamma_k;\mathscr{L})_{\operatorname{tors}}\rvert}{[\Gamma:\Gamma_k]}$$

should equal the Bergeron–Venkatesh limit for any set of congruence subgroups of increasing level. In particular,

$$\liminf_{\Gamma_k}\frac{\log\lvert H^i(\Gamma_k;\mathscr{L})_{\operatorname{tors}}\rvert}{[\Gamma:\Gamma_k]}$$

taken over all congruence subgroups should equal that limit. This strengthens the prime-level version by allowing arbitrary increasing levels; the paper offers computational evidence, while the assertion remains unproved.