Strong mirror symmetry conjecture for Fano manifolds and toric Landau–Ginzburg models

Let $X$ be a smooth Fano manifold and let $D$ be a divisor on $X$. A toric Landau–Ginzburg model is a Laurent-polynomial model associated with $X$ and $D$.

Strong mirror symmetry conjecture. Every pair consisting of a smooth Fano manifold and a divisor on it has a toric Landau–Ginzburg model.

This is the strong version of the mirror-symmetry conjecture for variations of Hodge structures discussed in the source. The existence is not proved in the stated generality.