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

The group = Z_7 _3, a finite subgroup of SU(3), is identified as the (21) Frobenius group; under restriction to , the SU(3) adjoint decomposes as 8 = 1' 1'' 3 3, 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. We present the complete QCD consequences as a standalone record complementary to the electroweak capstone . The embedding reproduces all QCD colour factors (C_F = 4/3, C_A = 3, T_F = 1/2) and structure constants f^abc to machine precision. One-loop -function coefficient b_0 = 7 and two-loop coefficient b_1 = 26 follow from the species count, both machine-certified (zero sorry). The three-loop coefficient b_2 = 180.91 (N_f = 5) is forced by the same Casimir invariants. Running at two loops gives _s(M_Z) = 0.1201 (+1.78 three-loop running gives _s(M_Z) = 0.1193 (+1.10 Three independent group-theoretic arguments force = 0 without a Peccei–Quinn axion (machine-certified, ROBUST). The kink condensate provides hadron spectroscopy from zero PDG inputs: f = m kink/ = 91.35 MeV (-0.81 lattice calibration; replacing the calibrated m kink by the Self-Consistency Condition (SCC) m = m (Section ) yields f_^ SCC = 92.34 MeV (+0.30 improvement, with no free parameters); pion mass m_^ = 136.49 MeV (+1.11 GOR inversion with GTE-derived B_0^ NLO and quark masses (zero PDG input), –' mixing angle _P = -13.08^ 3.74^ (within PDG range [-14.3^, -10.7^], entire chain zero PDG input), and top^1/4 = 166.5 MeV (-6.4 The baryon spin J = 1/2 is machine-certified from the [D]/ chain via seven zero-sorry Lean theorems; the positive-parity assignment () follows from kink topology and is not yet independently Lean-certified. The two-sector gauge architecture requires three abelian fields A_, A'_, A_^ EM with equal Cartan couplings e' = e (machine-certified). Non-abelian Berry holonomy on the orbit space supplies emergent SU(3) colour structure; 5/5 independent holonomy tests pass. The QFT mass gap is established unconditionally from orbit arithmetic in Lean 4 (zero sorry, zero axioms). The framework is an effective field theory (EFT) below 2.01 GeV; the proposal that flows to SU(3) Yang–Mills above is conjectural.