  Consider a projector matrix P, representing the first order reduced density
matrix in a basis of orthonormal atom-centric basis functions. A mathematical
question arises, and that is, how to break P into its natural component kernel
projector matrices, while preserving N-representability of P. The answer relies
upon 2- projector triple products, P'jPP'j. The triple product solutions,
applicable within the quantum crystallography of large molecules, are
determined by a new form of the Clinton equations, which - in their original
form - have long been used to ensure N-representability of density matrices
consistent with X-ray diffraction scattering factors.
