Stable-discreteness and brick-discreteness for finite-dimensional algebras

Let $A$ be a finite-dimensional algebra. Say that $A$ is stably-discrete if, for each irreducible component $\mathcal{Z}\in\operatorname{Irr}(A)$ and every $\theta\in K_0(\operatorname{proj} A)$, the moduli space $\mathcal{M}^{\theta\text{-ss}}(\mathcal{Z})$ is zero-dimensional. Say that $A$ is brick-discrete if every brick in $\operatorname{brick}(A)$ has open orbit.

Stable-discreteness conjecture. An algebra $A$ is stably-discrete if and only if it is brick-discrete.

The equivalence is proved in the paper for tame algebras, following earlier work of CKW. The conjecture asks for the same equivalence for arbitrary finite-dimensional algebras.