It is shown that the nuclear Hamiltonian can be separated rigorously as ${\cal H}={\cal H}_m+{\cal H}_M.$ For sufficiently smooth forces the monopole part ${\cal H}_m $is entirely responsible for Hartree-Fock selfconsistency and hence saturation properties. The multipole part ${\cal H}_M$ contains the "residual'' terms - pairing, quadrupole, etc. - that will be analyzed in a companion paper. We include a review of the basic results often needed when working with multipole decompositions and average monopole properties.