Spinful Dirac Fermion Quadrupling and Surface Anomalies from Topological Crystalline Insulator and Superconductor Hierarchies

3D topological insulators (TIs) carry a Z₂-nontrivial bulk axion angle θ=π that is quantized by spinful time-reversal symmetry T and gives rise to unpaired surface Dirac fermions through the parity anomaly. However, this neat picture of Z₂ bulk topology and surface anomalies in 3D TIs has been upended over the past decade through the exhaustive classification of band structures and free-fermion TIs and topological crystalline insulators, which surprisingly revealed that there do not exist free-standing 2D T-invariant semimetals with fewer than four spinful Dirac fermions, and that 3D TIs with bulk inversion symmetry are Z₄-classified. Recent studies have provided a partial solution, showing that two symmetry-protected spinful Dirac fermions (or one fourfold Dirac fermion) act as the quantum critical point between anomalous "half" 2D TI states via a novel variant of the parity anomaly. Using a link between topological superconductors and TIs discovered through charge-resolved topology, we complete the problem by showing that a single spinful Dirac fermion is in fact a quantum multicritical point with a second anomaly - distinct from the standard parity anomaly - that places the odd and even Dirac fermion cases on the same footing.