Exact formula for the stabilized Kac polynomial

Let $Q$ be the quiver, let $d$ be the dimension vector, and let $\delta$ be as in Theorem; write $\operatorname{supp}\delta$ for its support, let $d_i$ denote the components of $d$, and let $p^r(q)$ denote the $r$-colored partition generating function. The stabilized Kac polynomial conjecture. Under the assumptions of Theorem, the stabilized Kac polynomial is exactly

$$\frac{(1-q) p^{|\operatorname{supp} \delta|}(q)}{\prod_{i \notin \operatorname{supp} \delta} \prod_{k=1}^{d_i} (1 - q^k)}.$$

Computer computations for the quiver in Example support this formula. Equivalently, under the stated weak-condition hypothesis, the inclusion in the surrounding discussion should induce an isomorphism on the first $k$ cohomologies for sufficiently large $n$; the general assertion remains open.