LG/CY correspondence conjecture for tt* geometries

Let $M_{mar}$ be the marginal-deformation subspace of the deformation space $M$. Let ${\mathscr E}^{\operatorname{LG}}=({H}^{\operatorname{LG}}\to M_{mar},\kappa^{\operatorname{LG}},\eta^{\operatorname{LG}},D^{\operatorname{LG}},C^{\operatorname{LG}},\bar{C}^{\operatorname{LG}})$ and ${\mathscr E}^{\operatorname{CY}}$ denote the corresponding Landau–Ginzburg and Calabi–Yau $tt^*$ structures. LG/CY correspondence for $tt^*$ geometries. There exists an isomorphism $\Phi:{\mathscr E}^{\operatorname{LG}}\to{\mathscr E}^{\operatorname{CY}}$ between the two $tt^*$ geometry structures. This conjectures an isomorphism of the Landau–Ginzburg and Calabi–Yau $tt^*$ structures over the marginal deformation space; the source gives no evidence of resolution.