Neutrino Mixing Angles and QCD String Tension from the Rendering Friction: Complete PMNS Matrix and Confinement Geometry from Five Axioms
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Abstract
The three neutrino mixing angles of the PMNS matrix are derived from the
five-axiom set {12, π, γ1, ln 2, φ} of Array Cosmology with zero free parameters.
(1) sin2 θ12 = Zπ = (π − 3)π ln 2 = 0.3083 (NuFIT 5.2: 0.307 ± 0.013, 0.4%, 0.1σ).
(2) sin2 θ23 = (1 + Z)/2 = 0.5491 (NuFIT 5.2: 0.546 ± 0.021, 0.6%, 0.1σ).
(3) sin2 θ13 = Zπ/γ1 = 0.02181 (NuFIT 5.2: 0.02220 ± 0.00068, 1.7%, 0.6σ). The hierarchy sin2 θ13/ sin2 θ12 = 1/γ1 is controlled by the Riemann anchor (Axiom 3).
Combined with the CP-violating phase δCP = 194.7◦ (Paper XVI), the PMNS matrix is fully determined. Additionally, the QCD string tension √ σ = mππ = 438.5 MeV is derived (lattice range: 410–460 MeV).
The framework implicitly predicts normal neutrino mass ordering. These results, combined with Papers XXX– XXXI, bring the total to 12 independent non-perturbative predictions from five axioms spanning mesons, nucleons, neutrinos, and confinement.