Higher-depth positivity conjecture for Kac polynomials

Let $Q$ be a quiver, let $\mathbf{r}\in\mathbb{Z}_{\geq0}^{Q_0}$ be a rank vector, and let $\alpha\geq1$. Higher-depth positivity conjecture.

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

The conjecture extends positivity from the toric case to arbitrary rank vectors and all depths. The source reports computational evidence for rank three and formulates this as a conjecture; its resolution is not established by the supplied context.