Neutrino Mixing Angles and QCD String Tension from the Rendering Friction: Complete PMNS Matrix and Confinement Geometry from Five Axioms
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.
Related
- Single-Field Inflation from the Rendering Algebra: Complete Derivation via Icosahedral Geometry
- The Strong CP Angle as an Index Phase, the Quark Mass Determinant, and the Neutrino Mass Sector from the Rendering Algebra R12
- PMNS Mixing, Cauchy Duality, Unified CP Phases, Neutrino Mass Splitting, and the Higgs Mass Ratio from the Rendering Algebra R12
- The Barbero–Immirzi Parameter, Black-Hole Entropy, and the Area Gap from the R12 Rendering Algebra: McKayFolding, the SU(2)4 Horizon Category, and the Complete Entropy Expansion
- Spacetime Existence, Structure, and Expansion Rate from the R12 Rendering Algebra: A Complete Top-Down Derivation with Zero External Physics
BibTeX
@misc{lim2026neutrino,
title = {{Neutrino Mixing Angles and QCD String Tension from the Rendering Friction: Complete PMNS Matrix and Confinement Geometry from Five Axioms}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23604045},
url = {https://zenodo.org/records/23604045},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Neutrino Mixing Angles and QCD String Tension from the Rendering Friction: Complete PMNS Matrix and Confinement Geometry from Five Axioms
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23604045
UR - https://zenodo.org/records/23604045
AB - 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.
ER -