Why CKM and PMNS Angles Are Not Free Parameters

Why CKM and PMNS Angles Are Not Free Parameters A Geometric Rigidity Principle within the Temporal Theory of the Universe (TTU) In the Standard Model, the CKM and PMNS mixing matrices are introduced as independent empirical inputs, a "free‑angle paradigm" that lacks a dynamical explanation. We challenge this assumption within the framework of the Temporal Theory of the Universe (TTU), where fermions are identified as localized temporal solitons (chronons) in a compact hyper‑time dimension Θ. We demonstrate that mixing matrices are not fundamental entities but emerge as overlap integrals of solitonic wavefunctions u_f(Θ) in hyper‑time. This mechanism establishes a rigorous rigidity principle: since the same temporal constants {α, κ, χ} determine both the spectral hierarchy (masses) and the mode shapes (localization), the mixing angles cannot vary independently of the mass spectrum. Keywords: CKM matrix, PMNS matrix, mixing angles, overlap integrals, temporal solitons, flavor physics, hyper-time geometry, dynamical rigidity.