Mutation compatibility conjecture for arc representations

Let $(\Sigma,M)$ be a marked surface, and let $\sigma$ and $\tau$ be tagged triangulations related by a flip at the tagged arc $i$, so that $f_i(\sigma)=\tau$. For a tagged arc $i$, let $M(\sigma,i)$ and $M(\tau,i)$ denote the associated arc representations. Mutation compatibility conjecture. The arc representations are right equivalent under mutation at $i$:

$$\mu_i(M(\sigma,i))=M(\tau,i).$$

This conjecture asserts that the arc-representation construction is compatible with mutation of quivers with potential and their representations. The source does not provide evidence of a resolution, so the conjecture remains open.