Rigidity conjecture for the matrices $H^v$

Let $u$ and $v$ be vertices of the exchange graph of a cluster algebra with principal coefficients, and let $H^u$ and $H^v$ denote the associated matrices. Rigidity conjecture for the matrices $H^v$. The matrices $H^u$ and $H^v$ are equivalent if and only if $u=v$. The source presents this as a strengthening of the preceding extended-matrix conjecture and gives no general resolution.