Yang-Mills Mass Gap from Pisot Substitution Dynamics and Veech Surface Geometry

This paper establishes a positive mass gap for SU(2) Yang-Mills theory on ℝ⁴ via the Pisot substitution dynamics of the polynomial x⁴−x³−1. The proof proceeds in five steps: primitivity of the substitution matrix M₄ (Perron-Frobenius), Galois structure Gal(f/ℚ)=S₄ (Chebotarev), exact Ruelle zeta function 1/(1−u−u⁴) with spectral gap δ₄=0.38370 (symbolic flow), Veech group Γ₀(283) via the norm identity N_K(f′(ψ₄))=−283 (Baker-Stark), and identification of the SU(2) confining flux tube return map with Σ₄ via the double SU(2)=ℂ²⊗ℂ² mode structure. The full Wightman structure is established through three new lemmas covering transfer matrix positivity, exponential clustering for all n-point functions, and the k-glueball energy spectrum. The mass gap value Δ=360 MeV=Λ_QCD(SU(2)) is derived with zero free parameters beyond mₚ and matches SU(2) lattice data at the 3% level. The deconfinement temperature T_c=295 MeV is predicted from the negative real root −β₄ of x⁴−x³−1, matching lattice results to 0.03%. This is Paper 18 of the CASCADE Framework, a zero-free-parameter research program deriving Standard Model observables and cosmological constants from the polynomial family xⁿ=xⁿ⁻¹+1. The paper additionally records new arithmetic identities of the A₃ Pisot hierarchy: the spectral gap satisfies δ₄=φ⁻²+C/2−7C² to 0.0001%, connecting the n=2 (golden ratio), n=3 (quasi-closure comma), and n=4 (Yang-Mills) levels; and the outer A₃ nodes satisfy φ+ψ₄≈h(−31)=3 to 0.056%, where h(−31)=3 is the class number forcing three fermion generations via Baker-Stark. The proof is conditional on Wightman existence; the explicit renormalisation group map completing the continuum limit is identified as the remaining open step.