The unconditional weak Landau–Ginzburg model formula for cyclic covers

Let $Y$ be a smooth Fano variety of index $r$, let $D\subseteq Y$ be a smooth anti-canonical divisor, and let $X$ be the corresponding cyclic cover. A graded exact Lagrangian torus in $Y\backslash D$ is the hypothesis used in the preceding construction. Unconditional cyclic-cover formula. The weak Landau–Ginzburg model formula for cyclic covers holds without assuming that $Y\backslash D$ contains a graded exact Lagrangian torus. This would make the cyclic-cover construction purely algebro-geometric rather than dependent on the existence of such a Lagrangian torus; the source does not state whether the claim has been resolved.