Gauged CRT and the Topological Solution to the Strong CP Problem

We show that the gauging of CRT symmetry in quantum gravity uniquely selects Pin⁺ structure on 4-dimensional spacetime, and that this selection provides a topological constraint strongly favoring θ = 0 at the fermion path integral level. Although CRT² = 1 (Harlow-Numasawa) does not directly distinguish Pin⁺ from Pin⁻, Pin⁺ is uniquely determined by the conjunction of Kramers theorem (T̂² = (−1)F) and bordism classification (Ω⁴Pin⁺ = ℤ₁₆ versus Ω⁴Pin⁻ = 0), with GR compatibility providing independent support. On a Pin⁺ spacetime, the CRT gauge symmetry identifies the two degenerate Dashen vacua at θ = π as gauge-equivalent at the fermion path integral level, eliminating the degeneracy and leaving θ = 0 as the unique stable vacuum. We establish the CPT Transparency Theorem: the η-invariant is a bordism invariant with no local density, so CPT modification cannot produce local CPT-violating operators in the Standard Model Extension (a_L^μ = 0). This yields dual-channel falsifiability: (i) positive detection of CMB TB/EB polarization from Pin⁺ topology, and (ii) null result for neutrino CPT violation—both channels must be simultaneously satisfied. We note that Yonekura’s result on CP gaugeability applies to simply-connected gauge groups; the Standard Model’s U(1) factor requires GUT embedding for direct application. We emphasize that the conclusion θ = 0 is established at the fermion path integral level; whether non-perturbative bosonic effects could destabilize this conclusion remains an open question.