Mutation invariance of maximal green sequences for surface quivers

Let $Q$ be a quiver associated to a surface, and let $Q'$ be mutation equivalent to $Q$. A maximal green sequence is a mutation sequence for which every mutation is at a green vertex and whose final seed has no green vertices.

Mutation-invariance conjecture. If $Q$ exhibits a maximal green sequence, then $Q'$ also exhibits a maximal green sequence.

The question of whether every triangulation of a surface has a maximal green sequence remains open in many cases. The authors note that mutation invariance is known to fail for general quivers, but conjecture that it may hold for quivers arising from surfaces.