The mutation-transitivity conjecture for rigid decorated representations

Let $(Q,\mathcal{S})$ be a Jacobi-finite connected quiver with potential. A decorated representation is rigid when it has no nontrivial self-extension, a negative representation is a decorated representation supported in the negative part, and $\tau$ denotes the Auslander–Reiten transform. Mutation-transitivity conjecture. Any rigid decorated representation can be obtained from a negative representation by a sequence of mutations and some power of $\tau$. The conjecture is stated as open in the paper.