Higher-dimensional coboundary expansion for infinitely many cubical Ramanujan complexes

Let $\Gamma_S$ be one of the lattices of finite characteristic not equal to $2$ constructed in the paper, let $\Gamma \subseteq \Gamma_S$ be a congruence subgroup, and let $X_\Gamma = \Gamma \backslash \mathbf{T}_{S_0}$ be the corresponding cubical Ramanujan complex. Coboundary expansion claim. Infinitely many of the Ramanujan complexes arising in this way are higher-dimensional coboundary expanders of bounded degree. This asserts an ample supply of bounded-degree higher-dimensional expanders among the arithmetic cubical Ramanujan complexes, extending the significance of the preceding Ramanujan-complex construction; the source does not provide evidence here resolving the claim.