Mirror symmetry of variations of Hodge structures for Fano varieties

Let $X$ be a Fano variety, and let $Y\to\mathbb{C}$ be a one-parameter family. The Picard--Fuchs $\mathcal D$-module of $Y$ is the differential $\mathcal D$-module governing the periods of the family, while the regularized quantum $\mathcal D$-module is the regularized differential system associated with the quantum cohomology of $X$.

Mirror symmetry of variations of Hodge structures. For any Fano variety $X$ there exists a one-parameter family

$$Y\to\mathbb{C}$$

whose Picard--Fuchs $\mathcal D$-module is isomorphic to a regularized quantum $\mathcal D$-module for $X$.

This conjecture proposes a mirror-symmetric realization of the quantum differential system of every Fano variety as the Picard--Fuchs system of a one-parameter family. The source provides no evidence of resolution, so the conjecture remains open.