MNOP dimension-zero Donaldson–Thomas conjecture for smooth projective threefolds

Let $X$ be a smooth projective threefold. For a curve class $\beta$ and integer $n$, let $I_X(\beta,n)$ be the Hilbert scheme of one-dimensional subschemes $Z\subset X$ with $[Z]=\beta$ and $\chi(\mathcal O_Z)=n$. Define the dimension-zero Donaldson–Thomas series by

$$\mathcal{DT}_{X,0}(q)=\sum_n \deg[I_X(0,n)]^{\mathrm{virt}}q^n.$$

Let

$$M(q)=\prod_n\frac{1}{(1-q^n)^n}$$

and let $c_3(T_X\otimes K_X)$ denote the third Chern class, viewed as a Chern number.

MNOP dimension-zero Donaldson–Thomas conjecture. For any smooth projective threefold $X$, the dimension-zero Donaldson–Thomas series has the form

$$\mathcal{DT}_{X,0}(q)=M(-q)^{c_3(T_X\otimes K_X)}.$$

This conjecture predicts a universal MacMahon-function formula for the virtual counts of zero-dimensional subschemes on any smooth projective threefold. It is attributed here to Maulik, Nekrasov, Okounkov and Pandharipande; the supplied text gives no evidence resolving it.