The equality of Landau–Ginzburg Hodge invariants

Let $(Y,w)$ be a Landau–Ginzburg model admitting a tame compactification. Let $f^{p,q}(Y,w)$ be the Hodge-theoretic invariants defined from the Hodge filtration on relative cohomology, and let $h^{p,q}(Y,w)$ be those defined from the monodromy filtration. A Landau–Ginzburg Hodge invariants conjecture asserts that

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

This is the equality predicted by the Katzarkov–Kontsevich–Pantev framework; in the source it is subsequently known under additional hypotheses, but no unconditional resolution is supplied here.