Kontsevich–Soibelman conjecture on dual integral Monge–Ampère limits

Let a dual pair of Calabi–Yau families have Gromov–Hausdorff limits, and let the smooth parts of these limits carry the induced integral Monge–Ampère structures. A Monge–Ampère manifold is a smooth Riemannian manifold $(Y,g)$ with a flat connection defining an affine structure, such that locally $g_{ij}=\partial^2F/\partial x_i\partial x_j$ and $\det(\partial^2F/\partial x_i\partial x_j)=const$. Kontsevich–Soibelman conjecture. The smooth parts of Gromov–Hausdorff limits of dual families of Calabi–Yau manifolds are dual integral Monge–Ampère manifolds. This is a real-affine formulation of the Strominger–Yau–Zaslow mirror-symmetry picture; its general validity remains open.