QCD Structure from the Generative Triple Evolution Substrate: Asymptotic Freedom, Confinement, and Hadron Spectroscopy from F21 subset SU(3)

The group F21 = Z7 semidirect Z3, a finite subgroup of SU(3), is identified as the Sigma(21) Frobenius group; under restriction to F21, the SU(3) adjoint decomposes as 8 = 1' + 1'' + 3 + 3-bar, reproducing the GTE colour-octet structure. This identification is forced by Frobenius norm ratios and MDL minimality, with no free parameters, and is machine-certified in Lean 4 with zero sorry. The F21 embedding reproduces all QCD colour factors (C_F = 4/3, C_A = 3, T_F = 1/2) and structure constants to machine precision. One-loop beta-function coefficient b0 = 7 and two-loop coefficient b1 = 26 follow from the F21 species count (zero sorry). Running gives alpha_s(M_Z) = 0.1201 (+1.78% vs PDG 2024) at two loops and 0.1193 (+1.10%) at three loops. Three independent group-theoretic arguments force theta_QCD = 0 without a Peccei-Quinn axion (machine-certified). The Phi_MDL kink condensate provides hadron spectroscopy from zero PDG inputs: f_pi = 91.35 MeV (-0.81% vs PDG) under lattice calibration, improving to f_pi = 92.34 MeV (+0.30%) under the Self-Consistency Condition m_phi = m_tau; pion mass = 136.49 MeV (+1.11%); eta-eta' mixing angle in PDG range; QFT mass gap unconditionally established from orbit arithmetic in Lean 4 (zero sorry, zero axioms).

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-27
DOI
https://doi.org/10.5281/zenodo.20417565
Primary Topic
Quantum Chromodynamics and Particle Interactions
Type
preprint
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preprint

QCD Structure from the Generative Triple Evolution Substrate: Asymptotic Freedom, Confinement, and Hadron Spectroscopy from F21 subset SU(3)

Nova Spivack
Zenodo (CERN European Organization for Nuclear Research)
Quantum Chromodynamics and Particle Interactions
preprint

QCD Structure from the Generative Triple Evolution Substrate: Asymptotic Freedom, Confinement, and Hadron Spectroscopy from F21 subset SU(3)

Nova Spivack
preprint en

Abstract

The group F21 = Z7 semidirect Z3, a finite subgroup of SU(3), is identified as the Sigma(21) Frobenius group; under restriction to F21, the SU(3) adjoint decomposes as 8 = 1' + 1'' + 3 + 3-bar, reproducing the GTE colour-octet structure. This identification is forced by Frobenius norm ratios and MDL minimality, with no free parameters, and is machine-certified in Lean 4 with zero sorry. The F21 embedding reproduces all QCD colour factors (C_F = 4/3, C_A = 3, T_F = 1/2) and structure constants to machine precision. One-loop beta-function coefficient b0 = 7 and two-loop coefficient b1 = 26 follow from the F21 species count (zero sorry). Running gives alpha_s(M_Z) = 0.1201 (+1.78% vs PDG 2024) at two loops and 0.1193 (+1.10%) at three loops. Three independent group-theoretic arguments force theta_QCD = 0 without a Peccei-Quinn axion (machine-certified). The Phi_MDL kink condensate provides hadron spectroscopy from zero PDG inputs: f_pi = 91.35 MeV (-0.81% vs PDG) under lattice calibration, improving to f_pi = 92.34 MeV (+0.30%) under the Self-Consistency Condition m_phi = m_tau; pion mass = 136.49 MeV (+1.11%); eta-eta' mixing angle in PDG range; QFT mass gap unconditionally established from orbit arithmetic in Lean 4 (zero sorry, zero axioms).

Zenodo (CERN European Organization for Nuclear Research)
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Quantum Chromodynamics and Particle Interactions
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