Neguț's Kac-polynomial formula for the graded dimension of the shuffle algebra

Let $Q$ be a quiver, let ${\mathcal B}_{\b0}$ be the slope-zero algebra graded by dimension vectors, and write

$$A_Q(t,\boldsymbol{z})=\sum_{\boldsymbol{n}\in {\mathbb N}^I\setminus\b0}A_{Q,\boldsymbol{n}}(t)\boldsymbol{z}^{\boldsymbol{n}},$$

where $A_{Q,\boldsymbol{n}}(t)$ is the Kac polynomial. Define

$$\chi_{{\mathcal B}_{\b0}}(\boldsymbol{z})=\sum_{\boldsymbol{n}\in {\mathbb N}^I}\dim {\mathcal B}_{\b0|\boldsymbol{n}}\boldsymbol{z}^{\boldsymbol{n}}$$

and $\operatorname{Exp}[\sum_{\boldsymbol n\ne\b0}d_{\boldsymbol n}\boldsymbol z^{\boldsymbol n}]=\prod_{\boldsymbol n\ne\b0}(1-\boldsymbol z^{\boldsymbol n})^{-d_{\boldsymbol n}}$. Neguț's Kac-polynomial dimension conjecture. For every quiver $Q$,

$$\chi_{{\mathcal B}_{\b0}}(\boldsymbol{z})=\operatorname{Exp}[A_Q(1,\boldsymbol{z})].$$

Equivalently, ${\mathcal B}_{\b0}$ should be isomorphic as a graded vector space to the symmetric algebra of a graded vector space with graded dimension $A_Q(1,\boldsymbol z)$. The text motivates this as an interpretation of the positivity of Kac polynomials, but gives no resolution status.