  For moduli of polarized smooth K-trivial a.k.a., Calabi-Yau varieties in a
general sense, we revisit a classical problem of constructing its "weak
K-moduli" compactifications which parametrizes K-semistable (i.e.,
semi-log-canonical K-trivial) degenerations. Although weak K-moduli is not
unique in general, they always contain a unique partial compactification
(K-moduli).
  Our main theorem is the log minimality of their normalizations, under some
conditions. Partially to confirm that known examples satisfy the conditions, we
also include an appendix on the algebro-geometric reconstruction of Kulikov
models via the MMP, which has been folklore at least but we somewhat
strengthen.
