Unraveling Topological Crystalline Materials with Spin-Resolved Topology in Insulators and Dual Charge-Resolved Topology in Superconductors

3D topological crystalline insulators (TCIs) are abundant in nature, but exhibit bulk responses, classification groups, surface anomalies, and fermion-doubling exceptions that are poorly understood compared to those of standard topological insulators. It was recently shown that the spin-resolved topology of the projected U(1)-spin spectrum can be used to overcome these issues in nonmagnetic TCIs, specfically revealing the existence of bulk partial axion angles and anomalous surface half quantum spin Hall states. Building on this progress, we here introduce a ``dual'' framework of U(1)-charge resolved topology in topological (crystalline) superconductors (SCs). Combining spin- and charge-resolved topology with a refined notion of second-quantized-embedded SC symmetry groups, we formulate complementary real- and momentum-space invariants for nodeless SCs with arbitrary numbers of spin, orbital, and sublattice degrees of freedom, and arbitrarily complicated pairing terms beyond the weak-coupling regime. Our study reveals new hierarchies of and relationships between normal-state TCIs and topological crystalline SCs, whose surface anomalies expand upon and recontextualize the celebrated Fu-Kane proximity effect.