  The factorizable vectors of a complete Boolean algebra of type I factors,
acting on a separable Hilbert space, are shown to be total, resolving a
conjecture of Araki and Woods. En route, the spectral theory of noise-type
Boolean algebras of Tsirelson is cast in the noncommutative language of
"factorizations with unit" for which a muti-layered characterization of being
"of Fock type" is provided.
