Positivity conjecture for Kac polynomials of quivers with multiplicities

Let $Q$ be a quiver, let $\mathbf{r}\in\mathbb{Z}_{\geq0}^{Q_{0}}$ be a rank vector, and let $\alpha\geq1$. Let $A_{(Q,\alpha),\mathbf{r}}$ be the associated Kac polynomial for the quiver with multiplicities. Positivity conjecture.

$$A_{(Q,\alpha),\mathbf{r}}\in\mathbb{Z}_{\geq0}[q].$$

The displayed data support non-negative coefficients in examples, and the authors state that they hope to address this conjecture in future work; it generalises Kac's positivity conjecture when $\alpha=1$.