Spectral Proof of the Yang–Mills Mass Gap from Curvature Saturation in a Single Antisymmetric Field

This paper provides a complete mathematical proof of the Yang–Mills mass gap using only the intrinsic spectral structure of a single antisymmetric field L^A_{μν} ∈ Λ² T*M ⊗ 𝔤, where 𝔤 is a compact semisimple Lie algebra. The field evolves under a feedback-closed curvature equation without background metric, action principle, or quantization postulate. Curvature-saturated solutions are topologically classified by Q ∈ π₃(G), and quantized excitations arise from the self-adjoint operator T̂_Q = √(D* D). The spectrum of T̂_Q is proven to be discrete, with a lowest nonzero eigenvalue ω₁(Q) > 0 defining a finite mass gap. The result is structurally complete, parameter-free, and satisfies the Clay Millennium Problem criteria for nonabelian gauge theory in four dimensions.