Order-$p$ exclusion conjecture for cocompact lattices in the local pro-$p$ completion

Let $A$ be the rank-$2$ generalized Cartan matrix considered in the source, with $\max(a_{21},a_{12})\leq -2$ and without assuming $a_{21}=a_{12}$. Let $\widehat{G}$ denote the local pro-$p$ completion of the associated Kac–Moody group. A cocompact lattice is a discrete subgroup $\Gamma\leq\widehat{G}$ such that $\Gamma\backslash\widehat{G}$ is compact. The order-$p$ exclusion conjecture. A cocompact lattice in $\widehat{G}$ does not contain an element of order $p$. The source lists this among the conjectures left unresolved by the failure of the current proof in the indicated cases.