The algebraic Cheeger–Gromoll splitting conjecture

Let $((X,D),L)$ be an open K-polystable polarized dlt log Calabi–Yau pair, with exactly two connected components of $\operatorname{Supp}(\lfloor D\rfloor)$, interpreted as having two ends. Algebraic Cheeger–Gromoll conjecture. There exist a klt log Calabi–Yau variety $(B,D_B)$ and a numerically trivial line bundle $N$ such that

$$X\simeq\mathbb P(\mathcal O\oplus N),$$

with $D$ the union of the two natural sections, and every complete Ricci-flat weak Kähler metric on $X^{o}$ is complex-analytically locally a product of a lower-dimensional Ricci-flat weak Kähler metric and a flat metric. This is intended as an algebraic analogue of the Cheeger–Gromoll splitting phenomenon; the source gives no resolution.