Affine-principal-minor conjecture for cocompact lattices

Let $A$ be a generalized Cartan matrix and let $\widehat{G}$ be the associated local pro-$p$ completion. An irreducible principal minor of $A$ is a principal submatrix that is irreducible; an affine-type minor is of type $\widetilde{A}_m$ when its affine Dynkin type is $\widetilde{A}_m$. The affine-principal-minor conjecture. If any irreducible principal minor of $A$ of affine type is of type $\widetilde{A}_m$, then $\widehat{G}$ admits a cocompact lattice. The conjecture is motivated by the existence of cocompact lattices for right-angled Kac–Moody groups, while the source leaves the general higher-rank assertion open.