The exchange-graph independence conjecture for cluster algebras

Let $\mathcal{A}(\mathbf{x},\mathbf{y},B)$ be a cluster algebra with exchange matrix $B$. Its exchange graph is the graph whose vertices are seeds and whose edges join seeds related by mutation; it carries a canonical connection matching mutations in the same cluster direction across an edge. Exchange-graph independence conjecture. The exchange graph of $\mathcal{A}(\mathbf{x}, \mathbf{y}, B)$, together with its canonical connection, depends only on $B$. This is a strengthening of the fact that the exchange graph depends only on the underlying $Y$-pattern. It is proved for cluster algebras of finite type, but the general statement remains open.