Odaka's conjecture on minimally non-collapsing limits

In a polarized flat punctured holomorphic family $\pi^*:(\mathcal X^*,\mathcal L^*)\to\Delta^*$ of $n$-dimensional polarized klt projective varieties with continuous Kähler metrics $g_t$, choose points $p_i\in\mathcal X_{t_i}$ with $t_i\to0$, and use the equivalence relation on rescaling sequences defined by boundedness of $\{\log(r_i'/r_i)\}_i$. Existence of minimally non-collapsing limits. There is a unique equivalence class of minimal non-collapsing orders. Moreover, for sufficiently general sequences of points, the pointed Gromov–Hausdorff limits are complete Ricci-flat weak Kähler spaces. The conjecture is motivated by degeneration theory and has partial confirmation in the smooth case apart from metric completeness; the source gives no resolution.