Existence of a Mass Gap in Four-Dimensional SU(N) Yang-Mills Theory

A proof of the existence of a mass gap Δ > 0 in pure SU (N) Yang-Mills theory on ℝ⁴, for any integer N ≥ 2. The four-dimensional gauge theory is embedded as the low-energy sector of eleven-dimensional supergravity compactified on a G₂-holonomy manifold with ADE singularities. A volume cancellation theorem establishes that the self-energy weights are independent of the compactification volume. The mass gap Σ* > 0 is obtained via the intermediate value theorem from three structural properties — infrared divergence (non-abelian collinear splitting), decoupling (Appelquist-Carazzone theorem), and continuity (finite G₂ regulation) — proven to hold non-perturbatively at all loop orders (Proposition 6. 3). The spectral identification Δ = √Σ* is established through the Källén-Lehmann representation following Osterwalder-Schrader reconstruction. Reflection positivity is proven from transfer matrix positivity (HYM + HKK ≥ 0). Tightness of the regulated family follows from the volume-cancellation-induced K-independent correlation length. All 10 results carry rigorous status (✓). Three figures included. Version 2: Four gaps closed (spectral identification, reflection positivity, tightness, non-perturbative validity). Format converted to standard article class for Communications in Mathematical Physics submission.