Morse-element characterization for irreducible Artin–Tits groups of spherical type

Let $A$ be an irreducible Artin–Tits group of spherical type, let $Z(A)$ denote its center, and let $a\in A$. An element $a$ is Morse if its orbit in a Cayley graph of $A$ is a Morse quasi-geodesic; an element is virtually cyclic when it contains a cyclic subgroup of finite index. Morse-element characterization. The element $a$ is Morse if and only if its image in $A/Z(A)$ has virtually cyclic centralizer.

The question is open for irreducible Artin–Tits groups of spherical type other than braid groups. The authors constructed examples with strongly contracting axes, hence Morse, and this conjecture proposes that the virtually cyclic-centralizer condition captures all Morse elements.