The virtual Hodge polynomial generating-function conjecture for stable-bundle moduli spaces

Let $X$ be a curve over $\mathbb{C}$, let $\Gamma$ denote the set of characters $\alpha=(n,d)$, and let $\mathcal{M}(\alpha)$ be the moduli space of stable bundles on $X$ with character $\alpha$. For each $\alpha\in\Gamma$, let $A_\alpha\in\mathbb{Q}[u,v]$ be the virtual Hodge polynomial of $\mathcal{M}(\alpha)$, and let $R_\alpha$ be the rational functions defined above. For $\mat{\mutemp}\in\mathbb{Q}$, set

$$A_\mat{\mutemp}=\sum_{\mat{\mutemp}(\alpha)=\mat{\mutemp}}A_\alpha x^\alpha,\qquad R_\mat{\mutemp}=1+\sum_{\mat{\mutemp}(\alpha)=\mat{\mutemp}}R_\alpha x^\alpha.$$

Virtual Hodge polynomial conjecture. One has

$$R_\mat{\mutemp}\circ\operatorname{Exp}\left(\frac{A_\mat{\mutemp}}{1-uv}\right)$$

in $\mathbb{Q}(u,v)^{\rm tw}[[x_1,x_2]]$, where the twisted multiplication is determined by $x^\alpha\circ x^\beta=(uv)^{-\langle\alpha,\beta\rangle}x^{\alpha+\beta}$. This conjectural identity gives a generating-function relation between the virtual Hodge polynomials of stable-bundle moduli spaces and the functions obtained from the stack-counting formula; the supplied text does not state whether it has been proved or remains open.