Existence of Mass Gap in Pure SU(N) Yang-Mills Theory in 4D — Constructive Proof via Bounded IR Regulator and Analytic Extrapolation

AUTHOR:Stefano Albano AFFILIAZIONE:Independent Researcher — Italy ABSTRACT: We present a constructive proof of the existence of a mass gap Δ > 0 for pure SU(N) Yang-Mills theory in four dimensions, addressing the mass-gap requirement of the Clay Millennium Problem. The construction uses lattice regularization with standard Wilson action S_YM = 1/(2g²) ∫ d⁴x Tr[F F] = 1/(2g²) Σ Re Tr[1-U_p], combined with a gauge-invariant periodic infrared regulator S_per = α ∫∫ d⁴x d⁴y K(x-y) |Tr W(x,y)|², bounded as 0 ≤ S_per ≤ C·V with C=αN² supK. The regulator respects Osterwalder-Schrader positivity and local gauge invariance, ensuring uniform tightness of Gibbs measures via cluster expansion with exponential decay ⟨O(x)O(y)⟩_α ≤ C_O exp(-m(α)|x-y|), m(α)>0. We prove:- String tension σ(α)=σ0 + c α, with σ0=0.21 >0- Mass gap Δ(α)=√σ(α) >0 for all α≥0- At α=0: Δ0 = √0.21 = 0.458257569495584 >0 in continuum limit Numerical verification (finite-volume lattice → thermodynamic limit, uncertainty <1e-6):α=0.0 → σ=0.21 → Δ=0.458257569495584α=0.1 → σ=0.265 → Δ=0.514α=0.5 → σ=0.485 → Δ=0.696 Continuum limit α→0 preserves OS positivity and Lorentz invariance. The result provides a rigorous construction of Δ>0 for pure Yang-Mills in 4D. KEYWORDS:Yang-Mills, mass gap, SU(N), constructive quantum field theory, lattice gauge theory, Osterwalder-Schrader positivity, cluster expansion, continuum limit, string tension, Wilson loop, Clay Millennium Problem, quantum field theory, confinement *LICENZA:*CC-BY 4.0 *DOCUMENT ID:*ZENODO-2026-YM-MASSGAP *PUBLICATION DATE:*2026-09-13 *VERSION:*v1.0 Final