The Cambrian lattice mutation conjecture for finite Coxeter groups

Let $Q$ be a Coxeter quiver corresponding to a finite Coxeter group, and let $\operatorname{Camb}(Q)$ denote the Cambrian lattice associated with $Q$. A lattice is mutable if every lattice obtained from it by a finite sequence of mutations is locally mutable.

Finite Coxeter Cambrian mutation conjecture. The Cambrian lattice $\operatorname{Camb}(Q)$ is mutable.

The supplied text gives no resolution of this general formulation. Its type-A and type-B cases are stated separately and the type-A/type-B conjecture is verified only in types $A_1$, $A_2$, $A_3$, $B_2$, and $B_3$.