Minimal log canonical center parametrization conjecture

Let $M\subset\overline{M}^{\mathrm{SBB}}$ be one of the conjectural compactifications, and define

$$\mathcal{M}_{\mathrm{CY}(d)}=\{d\text{-dimensional klt log Calabi–Yau pairs}\}/\sim,$$

where $\sim$ is generated by log crepant birational maps. Minimal log canonical center parametrization conjecture. There is a natural map

$$\psi_{\mathrm{mlcc}}\colon\partial\overline{M}^{\mathrm{SBB}}\to\bigsqcup_{0\le d<n}\mathcal{M}_{\mathrm{CY}(d)}$$

such that, for a polarized dlt minimal model $(\mathcal{X},\mathcal{L})\to C$ with klt fibers parametrized by $M$ away from $0$, the image of the limiting point $\varphi(0)$ is represented by the minimal log canonical center of $(\mathcal{X},\mathcal{X}_0)$ with its natural different. The preceding birational-uniqueness proposition supports well-definedness under the permitted changes of models and base change, but the parametrization itself remains conjectural.