Generalized branched-annulus compactification conjecture for Coxeter groups

Let $W$ be a Coxeter group, let $\delta\in W$ be a Coxeter element, and let ${\normalfont\textsc{Br}}_{W,\delta}^{m}$ be the bisimplicial complex constructed with algebraic cell labels. Let $Y_W$ be the orbit configuration space. Generalized compactification conjecture. The bisimplicial complex ${\normalfont\textsc{Br}}_{W,\delta}^{m}$ is homotopy equivalent to its interior, which is homeomorphic to $Y_W$. For finite $W$, this extends the compactification result proved in the symmetric-group case; when $W$ is infinite, the complex is not compact. The source gives no general resolution status.