The highest abelian subgroup conjecture for Coxeter, Artin, and arrangement groups

Let $G$) be either a Coxeter group, an Artin group, or the fundamental group of the complement of a complexified real simplicial arrangement of hyperplanes as in Deligne. Following the terminology in the source, a finitely generated free abelian subgroup is highest if its commensurability class is maximal. A Morse quasiflat is a quasiflat with the Morse property.

Highest abelian subgroup conjecture. Any highest abelian subgroup in $G$ is a Morse quasiflat.

This conjecture proposes that the conclusion known for highest abelian subgroups in several classes, including mapping class groups and virtually special groups, extends to Coxeter groups, Artin groups, and the indicated arrangement groups. The source provides no resolution.