Non-negativity conjecture for the coefficients of $A_g(n,q)$

For integers $g\ge 2$ and $n\ge 1$, let $A_g(n,q)$ be the polynomial associated in the paper with the counting of tuples of nilpotent matrices under simultaneous conjugation. Write

$$A_g(n,q)=\sum_s a_{n,s}q^s,$$

where the coefficients $a_{n,s}$ are integers. Non-negativity conjecture. For every $g\ge 2$ and $n\ge 1$, all coefficients $a_{n,s}$ are non-negative integers. This predicts positivity for the counting polynomial and is not accompanied here by a resolution, so its status remains open.