Super-expander conjecture for congruence quotients of $\mathrm{SL}_3(\mathbf{Z})$

Let $\mathcal{G}_n$ be the Cayley graph of $\mathrm{SL}_3(\mathbf{Z}/n\mathbf{Z})$ with respect to the images of the elementary matrices. A sequence of bounded-degree graphs is a sequence of super-expanders if it is expanding with respect to every uniformly convex Banach space. Super-expander conjecture. The sequence $(\mathcal{G}_n)$ is a sequence of super-expanders. This is a stronger-than-Hilbertian expansion assertion related to fixed-point properties of $\mathrm{SL}_3(\mathbf{Z})$; the source gives no resolution.