Oblomkov–Okounkov–Pandharipande stationary DT rationality conjecture

Let $X$ be a nonsingular threefold, let $\beta$ be a curve class, let $\alpha_i\in H^{>0}(X)$, and let $k_i$ be positive integers. Define the renormalized DT series by

$$\mathrm{Z}^{\prime,X}_{\rm DT,\beta}(\mathrm{ch}_{k_1}(\alpha_1),\dots,\mathrm{ch}_{k_m}(\alpha_m))=\frac{\mathrm{Z}^X_{\rm DT,\beta}(\mathrm{ch}_{k_1}(\alpha_1),\dots,\mathrm{ch}_{k_m}(\alpha_m))}{\mathrm{Z}^X_{\rm DT,0}(1)}.$$

Oblomkov–Okounkov–Pandharipande conjecture. If all insertions are stationary, meaning $\alpha_i\in H^{>0}(X)$, then the renormalized invariant is a rational function of $q$ regular away from the roots of unity. The conjecture is proven for complete toric varieties.