Rigidity conjecture for extended exchange matrices

Let $u$ and $v$ be vertices of the exchange graph of a cluster algebra with principal coefficients. Two extended exchange matrices are equivalent when there is a bijection of their index sets preserving the matrix entries as specified in the source. Rigidity conjecture for extended exchange matrices. The matrices ${\widetilde{B}}^u$ and ${\widetilde{B}}^v$ are equivalent if and only if $u=v$. The claim is attributed to the cited cluster-algebra literature; the source does not state a general resolution.