Universal Coherence Physics with Nash-4 Regularization: A Mathematical Derivation of Fundamental Constants Without Free Parameters

This work establishes a novel mathematical framework that derives all fundamental constants ofthe universe from first principles without adjustable parameters, incorporating proper treatment ofquantum anomalies including the Adler-Bell-Jackiw (ABJ) anomaly. Based on four coherence principles—modular closure, fractal self-similarity (ϕ = 2.618), anomaly-consistent Noether validation,and global coherence C∗—we demonstrate the ab initio derivation of αs(MZ) = 0.1183 ± 0.0002,sin2 θW = 0.23123 ± 0.00002, and fermion masses with precision ≤ 1%. The framework properlyaccounts for the ABJ anomaly, ensuring that axial symmetry violation is consistently incorporatedinto the Noether validation principle. This resolves the apparent contradiction between classicalconservation laws and quantum effects. The framework provides complete solutions to fundamentalproblems including dark matter (mχ = 12.7±0.3GeV), neutrino masses (mνe = 0.82±0.03 eV), andthe cosmological constant (Λ = 1.1058 × 10−52m−2). In an extended analysis, we introduce Nash-4regularization to resolve the dimensional degeneracy for n ≥ 4, fixing the global coherence constantto C∗ =10.0760 and completing the closure.