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

The group = _3, identified as the Σ(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 ). 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) β-function coefficients follow from the species count (both ). Three-loop running gives α_s(M_Z) = 0.1193 (+1.10\% vs.\ PDG~2024). Three independent arguments force θ_ 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_π^ SCC = 92.34MeV (+0.30\%,~ ); m_π^ GTE = 139.57MeV (-0.001\%, 0.00σ,~ via \_mass\_from\_gor); η–η' mixing θ_P = -13.08^ ± 3.74^ (within PDG range); χ_ top^1/4 = 166.5MeV (-6.4\%~ ); and baryon spin J = 1/2 (seven zero-sorry Lean theorems). The framework is an EFT below Λ_ GTE ≈ 2.01GeV; the → SU(3) UV completion is conjectural.