Bruhat–Tits boundary characterization conjecture for totally disconnected spherical buildings

Let $B$ be a compact spherical building without rank $1$ factors. Suppose that $B$ is totally disconnected and admits a chamber-transitive group of continuous automorphisms.

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

This conjecture is an analogue for locally compact Euclidean buildings of the classification of compact connected spherical buildings with chamber-transitive automorphism groups. It is wide open, even for buildings of type $A_2$, namely compact projective planes.