The Weinstein skeleton conjecture for toric hypersurface mirrors

Suppose $\triangle$ is vertex-simplicial and $\triangle^\vee$ is facet-simplicial. Let $Z^\vee_\infty$ be the large volume limit and let $\Lambda^\infty$ be the associated Legendrian boundary. Toric hypersurface skeleton conjecture. There is a Weinstein structure on $Z^\vee_\infty$ whose Lagrangian skeleton is homeomorphic to $\Lambda^\infty$. The sheaf of Fukaya categories on this skeleton is equivalent to the Kashiwara–Schapira sheaf on $\Lambda^\infty$. This conjecture identifies the proposed Legendrian skeleton with a Weinstein skeleton and predicts compatibility of their categorical sheaves; the supplied source gives no evidence of resolution.