7.10 Strong CP Resolution

Abstract

The standard formulation of the strong CP problem is: the -term in the QCD Lagrangian violates CP symmetry, yet the experimental bound is far smaller than the natural expectation . The standard solution (Peccei-Quinn mechanism) introduces the axion, but the axion has not been discovered to date. This paper provides a geometric resolution of the strong CP problem: is algebraically locked by the determinant reality of Birkhoff double stochasticity. This locking is algebraic, rigid, and non-dynamical — requiring no axion, no Peccei-Quinn symmetry, and no anthropic explanation. **Core Conclusions**: 1. **Theorem 7.1 (Strong CP Resolution)** : is algebraically locked by the determinant reality of Birkhoff double stochasticity 2. **No axion exists**: the algebraic locking of implies the axion is not required — the standard QCD axion and Peccei-Quinn symmetry do not exist 3. **Coexistence with CKM phase**: (absolute phase locking) and (relative phase) can coexist