The finite-orbit bound conjecture for the curve graph of spherical Artin–Tits groups

Let $G$ be an Artin-Tits group of spherical type with rank $n$, let $\mathcal C(G)$ be the curve graph, and let $\alpha\in G$. Consider a vertex of $\mathcal C(G)$ with a finite orbit under the action of $\alpha$. Finite-orbit bound conjecture. The size of every such finite orbit is bounded above by a number depending only on $n$. The conjecture is proved in the paper for braid groups, where every finite orbit has size at most $n+1$; its status for general spherical Artin–Tits groups is not resolved in the source.