Satake–Baily–Borel type compactification conjecture for Calabi–Yau moduli

Let $M$ be a moduli space of polarized log-terminal Calabi–Yau varieties satisfying the assumptions specified in the source. Satake–Baily–Borel compactification conjecture. There should be a compactification $M\subset\overline{M}^{\mathrm{SBB}}$ whose underlying space is the log canonical model of $M$, with the stated quotient description, a natural morphism from every weak K-moduli compactification, and an ample $\mathbb{Q}$-line bundle pulling back to the CM line bundle. For strict Calabi–Yau varieties, it should also admit the stated finite morphism to the conjectural compactification associated with the period map, with the corresponding pullback property for the Hodge line bundle. This generalizes the Satake–Baily–Borel picture; beyond the Hermitian symmetric cases, the proposed construction is explicitly presented as conjectural and is connected to the absence of a general Torelli theorem.