LASSI[r,q] assigns q fragment statelets to all fragments in all Hilbert spaces, but only in the Hilbert spaces in which the given fragment gained or lost an electron or flipped its spin is this necessary, according to Table . This is a confirmation and a refinement of the observation made in Ref. 19 that led to the development of what we called "LASSI[r,q CT ]": only fragments that "change" in some way relative to the LASSCF reference state require more than one fragment statelet.