The Doran-Harder-Thompson reconstruction conjecture via gluing

Let $\widecheck{\frZ}_0 \to \AA^1$ and $\widecheck{\frZ}_1 \to \AA^1$ be Landau–Ginzburg models, and suppose that the fibres of $\widecheck{\frZ}_0 \to \AA^1$ have one dimensional complex moduli. The fibres are the fibres over $\CC^* \subset \CC$, and $t \mapsto t^{-1}$ denotes the inversion map on the base. Doran-Harder-Thompson reconstruction conjecture via gluing. The Calabi-Yau $\widecheck{\frX_{gen}}$ is obtained by gluing the Landau–Ginzburg models $\widecheck{\frZ}_0$ and $\widecheck{\frZ}_1$ along their fibres over $\CC^* \subset \CC$ under a deformation of the map $t \mapsto t^{-1}$. The source says that reconstruction of this form is known in cases where the fibres have at most one-dimensional complex moduli, and presents the proposed holomorphic gluing as a second part of the conjecture.