Landau–Ginzburg mirror symmetry for Hodge numbers

Let $(Y,w)$ be a Landau–Ginzburg model of Fano type arising, together with a tame compactification, as a mirror of a projective Fano manifold $X$ of dimension $n=\dim Y$. Let $f^{p,q}(Y,w)$ denote the Landau–Ginzburg Hodge numbers and let $h^{p,q}(X)$ denote the usual Hodge numbers of $X$. Landau–Ginzburg mirror Hodge-number conjecture. For each $p,q$,

$$f^{p,q}(Y,w)=h^{p,n-q}(X).$$

This is one of the mirror-symmetry conjectures relating Landau–Ginzburg invariants to the Hodge numbers of the mirror Fano variety. The source does not establish the assertion in general; it discusses results for mirrors of del Pezzo surfaces.