Periodic convergence conjecture for deformed F-polynomials

Let $Q$ be a framed quiver and consider the periodic mutation sequence

$$v_1,\ldots,v_p,v_1,\ldots,v_p,\ldots$$

Assume that performing the mutations $v_1,\ldots,v_p$ on the base quiver returns it to the original quiver. Periodic convergence conjecture. For every $i$, the sequence of deformed $F$-polynomials

$$S_i,S_{i+p},S_{i+2p},\ldots$$

converges. The source gives no resolution of this convergence question.