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

Programme status: This record belongs to an active research programme. It is not a finished or final theory. The framework is currently undergoing a systematic audit, together with corrections and improvements prompted by reader feedback. Several significant issues have been identified, and some claims, derivations and interpretations in the current version may be revised, qualified or withdrawn in future versions. Revised versions will be released when this work is complete. See PROGRAM_STATUS.md. Status as of October 2026.

The group = _3, identified as the (21) Frobenius group, is a finite subgroup of SU(3) forced by Frobenius norm ratios and MDL minimality (no free parameters, machine-certified in Lean 4, zero sorry). Under restriction to , the SU(3) adjoint decomposes as 8 = 1' 1'' 3 3, reproducing the GTE colour-octet structure. All QCD colour factors (C_F = 4/3, C_A = 3, T_F = 1/2) and structure constants f^abc are reproduced to machine precision (). The one-loop (b_0 = 7) and two-loop (b_1 = 26) -function coefficients follow from the species count (both ). Three-loop running gives _s(M_Z) = 0.1193 (+1.10\% vs.\ PDG 2024). Three independent arguments force theta_QCD = 0 without a Peccei-Quinn axion (, ROBUST). The QFT mass gap is established unconditionally from orbit arithmetic (, zero axioms). From zero PDG inputs: f_^SCC = 92.34\,MeV (+0.30\%, ); m_^GTE = 139.57\,MeV (-0.001\%, 0.00, via pion\_mass\_from\_gor); -' mixing _P = -13.08^ 3.74^ (within PDG range); _top^1/4 = 166.5\,MeV (-6.4\% ); and baryon spin J = 1/2 (seven zero-sorry Lean theorems). The framework is an EFT below the seven-kink threshold _GTE = 7\,M_kink 2.0\,GeV (tree (8/7)\,m_ = 2030.70 0.14\,MeV, ; quantum-corrected 1.970 0.146\,GeV, ); the SU(3) UV completion is conjectural.