Semistable Tutte polynomial positivity conjecture

Let $Q$ be a quiver with a stability function $Z$. For a semistable subquiver $G\in\mathcal{G}_Z(Q)$, write $\kappa(G)$ for its number of connected components and $n(G)$ for its relevant nullity, and let $\kappa(Q)$ denote the corresponding quantity for $Q$. Define the semistable Tutte polynomial by

$$T_Z(Q;t,q)=\sum_{G\in\mathcal{G}_Z(Q)}(t-1)^{\kappa(G)-\kappa(Q)}(q-1)^{n(G)}.$$

Semistable Tutte polynomial positivity conjecture. One has $T_Z(Q;t,q)\in\mathbb{N}[t,q]$. The conjecture is motivated by the positivity theorem for $a_Z(Q)$, and the source suggests that its proof should follow a similar argument; no proof or resolution is supplied.