The stable second Brauer–Thrall conjecture for τ-tilting infinite algebras

Let $A$ be a $\tau$-tilting infinite algebra. For a dimension vector $\bd\in K_0(A)^+$ and a weight $\theta\in\K_0(A)^*$, let $\operatorname{Mod}(A,\bd,\theta)^\st$ be the fine moduli space of $\theta$-stable $A$-modules of dimension $\bd$.

Stable Brauer–Thrall II' conjecture. There exist $\bd\in K_0(A)^+$ and $\theta\in\K_0(A)^*$ such that

$$\dim \operatorname{Mod}(A,\bd,\theta)^\st \geq 1.$$

This strengthens earlier brick versions by requiring a positive-dimensional moduli space of stable modules. The supplied source gives no resolution status.