  We show that the Nambu-Goldstone formalism of the broken gauge symmetry in
the presence of the $T=1$ pairing condensate offers a quantitative description
of the binding-energy differences of open-shell superfluid nuclei. We conclude
that the pairing-rotational moments of inertia are excellent pairing
indicators, which are free from ambiguities attributed to odd-mass systems. We
offer a new, unified interpretation of the binding-energy differences
traditionally viewed in the shell model picture as signatures of the valence
nucleon properties. We present the first systematic analysis of the
off-diagonal pairing-rotational moments of inertia and demonstrate the mixing
of the neutron and proton pairing-rotational modes in the ground states of
even-even nuclei. Finally, we discuss the importance of mass measurements of
neutron-rich nuclei for constraining the pairing energy density functional.
