Nekrasov's conjecture for Quot schemes of affine space

Let $Y=\mathbb{C}^d$, let $E=\bigoplus_{i=1}^{r+1}\mathcal{O}_Y\langle y_i\rangle$ and $V=\bigoplus_{i=1}^{r}\mathcal{O}_Y\langle v_i\rangle$. Nekrasov's conjecture for Quot schemes. When $d=2$, or when $d=4$ with some choice of signs $o(\mathcal{L})$,

$${\mathcal{C}}_Y(E,V;q)=\exp\left(q\int_Yc_{d-1}(Y)\right).$$

This generalizes the formulation attributed to Nekrasov by Cao and Kool. The source states that the four-dimensional case follows from Nekrasov–Piazzalunga's conjecture together with a cohomological-limit result, while the two-dimensional case is checked only in several finite ranges; the conjecture is therefore not established in full in the source.