What question did this study set out to answer?

The aim is to explore the structure of Quantum Chromodynamics (QCD) using a novel mathematical framework based on SU(3) symmetries and Frobenius groups.

June 18, 2026Open Access

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

Key Points

The aim is to explore the structure of Quantum Chromodynamics (QCD) using a novel mathematical framework based on SU(3) symmetries and Frobenius groups.
Utilized the Frobenius norm ratios and minimal description length in computing aspects of SU(3) structure.
Employed a three-loop running approach to derive coupling constants and function coefficients related to QCD.
Examined the mass gap and baryon characteristics through theoretical constructs without empirical inputs.
Three-loop running yields alpha_s(M_Z) = 0.1193 (+1.10% vs. PDG 2024).
Derived mass values: f_SCC = 92.34 MeV (+0.30%), m_GTE = 139.57 MeV (-0.001%), and baryon spin J = 1/2.
Established theta_QCD = 0 without needing a Peccei-Quinn axion, confirming QFT mass gap unconditionally.

Abstract

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 (CF = 4/3, CA = 3, TF = 1/2) and structure constants fᵃbc are reproduced to machine precision (). The one-loop (b₀ = 7) and two-loop (b₁ = 26) -function coefficients follow from the species count (both). Three-loop running gives ₛ (MZ) = 0. 1193 (+1. 10\% vs. \ PDG 2024). Three independent arguments force thetaQCD = 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) ; ₜop¹/4 = 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\, Mₖink 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.

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