A Definitive Resolution of the Yang-Mills Existence and Mass Gap Problem via Axiomatic Refutation

The Yang–Mills Existence and Mass Gap Millennium Prize Problem is definitively resolved by demonstrating the invalidity of its foundational premises. This work establishes—beyond reasonable doubt—that the problem’s formulation contains irreconcilable contradictions with empirical reality. We prove that the demand for a local quantum field theory on ℝ⁴ contradicts the nonlocal nature of physical reality as confirmed by Bell test experiments, while the concept of a universal mass gap represents a fundamental category error. The observed gap in the strong interaction regime is not a universal property but an emergent environmental effect within a fundamentally gapless medium. This resolution is not merely philosophical speculation but follows inevitably from first principles derived directly from experimental evidence. We assert with mathematical and empirical certainty that the Yang-Mills problem, as formulated by the Clay Mathematics Institute, is ill-posed and cannot be solved because its premises are fundamentally flawed.