Homotopy equivalence conjecture for irreducible euclidean Artin groups

Let $A$ be an irreducible Artin group of euclidean type, and let $B A$ be the classifying space constructed in the paper. Let $M$ be the standard topological space with fundamental group $A$ constructed from the action of the corresponding Coxeter group on its complexified hyperplane complement. Homotopy equivalence conjecture. The classifying space $B A$ should be homotopy equivalent to $M$. A positive resolution would imply the $K(\pi,1)$ conjecture of Godelle and Paris for irreducible Artin groups of euclidean type.