Positivity conjecture for Donaldson–Thomas invariants of symmetric quivers with two disjoint cuts

Let $(Q,W)$ be a symmetric quiver with potential, and suppose that $(Q,W)$ admits two cuts $I$ and $I'$ such that $I\cap I'=\emptyset$. Let $\Om_\al$ denote the Donaldson–Thomas invariant for each dimension vector $\al\in\cN^{Q_0}$. Positivity conjecture. The invariants $\Om_\al$ are polynomials in $\cL^{\pm\frac12}$, and $\Om_\al(-\cL^{\frac12})$ is a polynomial with integer, non-negative coefficients. This conjecture predicts a strong positivity property for motivic Donaldson–Thomas invariants under the stated cut hypotheses; its resolution is not supplied here.