Finite global Khovanskii basis conjecture for cluster algebras

Let $A(\Gamma)$ be a cluster algebra satisfying the assumptions of Theorem~, and suppose it has a finite global Khovanskii basis, meaning a finite set of algebra generators that is a Khovanskii basis for all valuations $G_{s;\mathcal B}$ simultaneously as $s$ ranges over all seeds. Finite global Khovanskii basis conjecture. If $A(\Gamma)$ has a finite global Khovanskii basis, then $A(\Gamma)$ is of finite cluster type. The conjecture relates finite generation of Khovanskii bases for all seed valuations to finiteness of the cluster mutation class; its resolution is not specified in the source.