The uniqueness conjecture for non-degenerate potentials on twice-punctured positive-genus surfaces

Let $(\Sigma,\mathbb{M})$ be a positive-genus surface with empty boundary and exactly two punctures, and let $\tau$ be a tagged triangulation of $(\Sigma,\mathbb{M})$. Write $Q(\tau)$ for the associated quiver and $S(\tau)$ for its potential. A potential on $Q(\tau)$ is non-degenerate if every finite sequence of mutations produces a quiver with potential whose underlying quiver has no two-cycles. Uniqueness conjecture. Any non-degenerate potential on $Q(\tau)$ is right-equivalent to a non-zero scalar multiple of $S(\tau)$.

This asserts uniqueness, up to right-equivalence and scaling, of the non-degenerate potential associated with a tagged triangulation in the positive-genus, twice-punctured case. The supplied text does not state whether the conjecture has been proved or disproved.