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
- Nova Spivack
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