The class $\mathcal{P}$ ground-ring equality conjecture for cluster and upper cluster algebras

Let $Q$ be a quiver in the class $\mathcal{P}$, and let $\mathcal{A}$ and $\mathcal{U}$ be the cluster algebra and upper cluster algebra associated with the cluster algebra defined by $Q$. The class $\mathcal{P}$ equality conjecture. There exists some ground ring, possibly $\mathbb{ZP}$, over which $\mathcal{A}=\mathcal{U}$. The source marks the ground-ring formulation as uncertain and supplies no evidence resolving this conjecture.