3 problems

Haines's refinement. The assumption that one vertex of $T$ is special can be replaced by

Let $X$ be an irreducible, locally finite, exotic Euclidean building and let $\Gamma < \operatorname{Aut}(X)$ be a lattice. Bader–Caprace–Lécureux's conjecture. Then $\Gamma$ is vi…

Bruhat–Tits boundary conjecture. Then $B$ is the Tits boundary of a locally finite simplicial Bruhat–Tits building.