Conjecture on the CSM classes of Dynkin quiver orbits

Let $Q$ be a Dynkin quiver with vertex set $Q_0$, and let $\beta$ be a positive root of $Q$. For each vertex $i\in Q_0$, write $\alpha_{i,1},\ldots,\alpha_{i,\beta(i)}$ for the corresponding variables. The $c^o_\beta$ conjecture. For any positive root $\beta$ we have

$$c^o_\beta=\prod_{i\in Q_0}\prod_{u=1}^{\beta(i)}\prod_{v=1}^{\beta(i)}(1+\alpha_{i,u}-\alpha_{i,v}).$$

The conjecture gives an explicit product formula for the CSM class $c^o_\beta$, one of the main building blocks in the CSM/MC theory of Dynkin quiver orbits and in the cohomological and K-theoretic Hall algebras. The surrounding text reports that many calculated examples support it, but provides no proof or resolution.