The Klemm–Pandharipande integrality conjecture for Calabi–Yau fourfolds

Let $Z$ be a smooth projective complex Calabi–Yau variety of dimension four, let $d\in\operatorname{H}_2(Z,\mathbb{Z})$, and let $\gamma\in\operatorname{H}^4(Z,\mathbb{Z})$. Define $\mathrm{GW}_{0,d;\gamma}(Z)$ by the one-point genus-zero invariant and define $\mathrm{KP}_{0,d;\gamma}(Z)$ through

$$\mathrm{GW}_{0,d;\gamma}(Z)=\sum_{k\mid d}\frac{\mathrm{KP}_{0,d/k;\gamma}(Z)}{k^2}.$$

Klemm–Pandharipande integrality conjecture.

$$\mathrm{KP}_{0,d;\gamma}(Z)\in\mathbb{Z}.$$

This is the proposed higher-dimensional analogue of the Aspinwall–Morrison integrality prediction for rational curves. Its resolution is not stated in the supplied text.