Seniority-zero states are mean-field wavefunctions.

We use symbolic computation, numerical experiments, and mathematical arguments to establish that every seniority-zero state can be expressed as a (number-symmetry-broken) antisymmetric product of interacting geminals (APIG). Moreover, for bosons, the configuration interaction coefficients are exactly parameterized by matrix permanents. This establishes that bosonic wavefunctions can be exactly described by a mean field, specifically the (number-symmetry-broken) symmetric product of boson orbitals. While exact parameterization is extremely costly, we present numerical evidence showing that the APIG wavefunction approaches the true wavefunction exponentially quickly as the number of interacting geminals increases.