Fully factorized mean-field inference

Identity Notes & Concept Scope This is the complete-factorizability mean-field construction, not a claim that the target variables are actually independent. It is the singleton-factor limit of structured mean field and differs from block or chain factors that retain dependencies. The approximation family and variational objective do not prescribe BBVI’s score-function estimator, amortized recognition, a training algorithm or any particular probabilistic model. Factorization depends on the declared variable units; treating a whole chain as one variable would be a different, structured partition at the state-variable level. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 382 preceding native IDs/names/aliases for the four researched candidates. Both full-checkout fixed-string searches included ignored and hidden files, with 45 and 45 matching lines. All 31 unique matched contents were read: prior specialized inference records, source/review context and pending leads, not exact records for the three new identities. Expanded titles, source IDs, plural forms and complete/partial-factorizability terminology were included. All 68 semantic label/synonym hits and 23 exact fully annotated AIO CLASS nodes with outgoing edges were read. Their generated YAMLs and seven native neighbors were read or byte-verified unchanged after prior complete reading, totaling 30 contextual records. The broader phrase structured variational inference is searched but not asserted as an unconditional alias of structured mean field. Boltzmann trees remains an unresolved full-text lead. Absence is bounded to the pinned vocabulary and inspected neighborhood.