The Donaldson-number formula conjecture for moduli spaces of degree-d sheaves

Let $\pi:\mathrm{M}(d,1)\to |\mathcal{O}_{\mathbb{P}^{2}}(d)|$ be the Fitting map, and let

$$\alpha_d:=\pi^{*}\mathcal{O}_{|\mathcal{O}_{\mathbb{P}^{2}}(d)|}(1).$$

Here $g$ denotes the dimension of a general fiber of $\pi$. Donaldson-number formula conjecture. For the indicated moduli space and every relevant integer $m$,

$$\chi(\mathrm{M}(d,1),m\alpha_d)=\binom{m+3d-1}{m}=\binom{m+\dim|\mathcal{O}_{\mathbb{P}^{2}}(d)|-g}{m}.$$

The formula predicts the K-theoretic Donaldson numbers of multiples of the pullback of the hyperplane class from the linear system. The source does not state a resolution status.