Kontsevich–Soibelman conjecture on the non-archimedean collapse map

Let ${X}^{an}$ be the smooth analytic space associated with the Calabi–Yau variety over $K={{\bf C}}((t))$, and let $\pi_{mer}$ map meromorphic points to their limiting points in the Gromov–Hausdorff limit $B$. Let $B^{sm}$ be the maximal open subset where the limiting metric is smooth. Kontsevich–Soibelman conjecture. The map $\pi_{mer}$ is well-defined and extends continuously to $\pi:{X}^{an}\to B$; $B^{sm}$ is exactly the set of $\pi$-smooth points; and the ${\bf Z}$-affine structures on $B^{sm}$ arising from the collapse and non-archimedean pictures coincide. The conjecture seeks to identify the metric and non-archimedean descriptions of the limiting affine base; it remains open in general.