The folklore conjecture generalizing Kontsevich–Soibelman's conjecture on collapsing boundaries

Let $\overline{\mathcal{M}}^{GH, diam}$ be the metric compactification at fixed-diameter scale, and let $\partial_{collaps}\overline{\mathcal{M}}^{GH, diam}$ denote its collapsing boundary. Let $Sk(\mathcal{X})$ be the essential skeleton of an algebraic degeneration, such as the dual complex of a dlt degeneration. A large complex structure limit (LCS limit) is the type of degeneration referred to in the source, and a singular tropical metric space is a tropical metric space that may have singularities.

Folklore conjecture generalizing Kontsevich–Soibelman's conjecture. The collapsing boundary densely parametrizes singular tropical metric spaces homeomorphic to essential skeleta $Sk(\mathcal{X})$ of algebraic degenerations. The generic boundary points correspond to LCS limits. The space $\overline{\mathcal{M}}^{GH, diam}$ is far from being an algebraic object; indeed, the collapsing boundary itself is a tropical object.

This conjecture describes collapsing metric degenerations at fixed-diameter scale, in contrast with non-collapsing limits that can retain complex-algebraic or singular Calabi–Yau structure. The source presents it as a guiding conjecture generalizing Kontsevich–Soibelman's conjecture away from LCS limits, without giving a resolution status.