theorem FUST.YangMills.yangMills_massGap_SU2 : FrourioAlgebra.GoldenEisensteinInt.AF_coeff_gei.tau = FrourioAlgebra.GoldenEisensteinInt.AF_coeff_gei.neg ∧ FrourioAlgebra.GoldenEisensteinInt.AF_coeff_gei.mul FrourioAlgebra.GoldenEisensteinInt.AF_coeff_gei = { a := -12, b := 0, c := 0, d := 0 } ∧ ∀ (c : ℂ), (c • 1).det = c ^ 2

SU(2) mass gap: τ-anti-invariance + AF²=-12 → quaternionic SU(2)

theorem FUST.YangMills.yangMills_massGap_SU3 : cartanA2.det = 3 ∧ (6 + 2 = 8 ∧ 3 ^ 2 - 1 = 8) ∧ 0 < massGapSq ∧ massGapSq = 144 * √5 - 84

SU(3) mass gap: A₂ root system from ℤ[ζ₆] → SU(3), m² = 14 > 0

theorem FUST.YangMills.yangMills_massGap : Module.finrank ℝ (Physics.Lorentz.I4 → ℝ) = 4 ∧ cartanA2.det = 3 ∧ FrourioAlgebra.GoldenEisensteinInt.AF_coeff_gei.mul FrourioAlgebra.GoldenEisensteinInt.AF_coeff_gei = { a := -12, b := 0, c := 0, d := 0 } ∧ (∀ (x : FrourioAlgebra.GoldenEisensteinInt), x.sigma = x ∧ x.tau = x ↔ x.b = 0 ∧ x.c = 0 ∧ x.d = 0) ∧ 0 < massGapSq ∧ massGapSq = 144 * √5 - 84

Yang-Mills mass gap: 4D Poincaré, SU(3)×SU(2)×U(1) gauge, mass gap