The Lepton Spectrum as a Phase-Stability Ladder: Universal Temporal Functionals and the Exponential Mass Hierarchy

Abstract

The Lepton Spectrum as a Structural Consequence of Hyper-Temporal Dynamics: Nonlinear Localization and the Emergence of the Flavor Hierarchy

The Standard Model remains descriptive in its treatment of the fermion flavor hierarchy, utilizing over twenty empirical Yukawa couplings to parameterize observed masses without providing a dynamical origin for their values. This paper proposes a reformulation of the leptonic sector within the Temporal Theory of the Universe (TTU)—a deductive framework that recovers the mass spectrum from the first principles of 5D temporal dynamics on an M^4 × S^1 manifold. We suggest that leptons are not fundamental points, but stable, phase-locked resonant modes (chronons) of a universal temporal field τ.

By implementing a Consistency Enforcement Loop (CEL), we demonstrate that the fundamental parameters established in the hadronic sector—specifically temporal stiffness (χ) and the hyper-time radius (R_Θ)—necessitate the observed lepton hierarchy with significant Parameter Rigidity. The ≈3500‑fold mass disparity between the electron and the tau lepton is recovered as a result of Nonlinear Localization: as the topological winding number n increases, the medium’s saturation threshold (τ_crit) induces an exponential surge in phase inertia.

The PMNS mixing matrix is derived through the Overlap Geometry of delocalized temporal profiles, providing a causal explanation for the large mixing angles observed in neutrinos relative to the narrow CKM quark mixing. Numerical realizations, obtained via a self-consistent iterative scheme (SCTF), achieve a predictive accuracy exceeding 99.9% for charged lepton masses, serving as a proof-of-principle for the framework's deductive capacity. Furthermore, the model suggests a topological prohibition of a fourth generation due to phase decoherence at the saturation limit. This approach indicates that the algebraic "bookkeeping" of the Standard Model may be successfully reformulated as a deterministic map of temporal geometry, where matter emerges as a stable harmonic resonance of the M^4 × S^1 manifold.