Odaka's K-moduli conjecture for K-polystable polarized varieties

Let a polarized variety mean a projective variety equipped with a polarization, and consider the moduli space of K-polystable polarized varieties. K-moduli conjecture. A set of K-polystable polarized varieties forms a separated scheme. Furthermore, each connected component is a quasi-projective scheme with the ample CM line bundle. This conjecture is a foundational expectation for the algebraic construction of K-moduli spaces and the positivity of the CM line bundle. The source states that, including the intermediate Kodaira-dimension case $ba=1$, it remains a long-standing open problem.