Dual Monge–Ampère structure conjecture for maximal Calabi–Yau degenerations

Let $Y$ be the smooth part of the limiting base of a maximal degeneration of a Calabi–Yau family, equipped with its Monge–Ampère metric and integral affine structure, and let $Y^{\vee}$ denote the dual Monge–Ampère manifold. Dual Monge–Ampère structure conjecture. Smooth parts of maximal degenerations of dual families of Calabi–Yau manifolds are dual Monge–Ampère manifolds with dual integral affine structures. This is the geometric counterpart of mirror symmetry and identifies the limiting differential-geometric structures on the two sides; the source gives no resolution.