Purity conjecture for additive character varieties

Let $Y$ be the additive character variety associated to a reductive group $G$, a genus $g$, and a tuple of $G$-orbits in the Lie algebra, under the additive genericity assumptions. Purity conjecture. The variety $Y$ is pure; consequently, its point-counting polynomial $|Y(\mathbb{F}_q)|$ has non-negative coefficients. This would generalize the corresponding non-negativity result known for additive character varieties when $G=\mathrm{GL}_n$, where the varieties are isomorphic to quiver varieties; the source reports only computer evidence in the reductive setting.