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 resolved by demonstrating that its foundational premises are invalid. We first establish three postulates derived from first principles: 1) The Primacy of Empirical Nonlocality, 2) The Mass-Frequency Identity (m=ω), and 3) The Principle of Emergent Law from Self-Consistency. Using these postulates, we formally refute the core components of the problem statement. We prove that the requirement for a local, axiomatic Quantum Field Theory (QFT) is based on the principle of locality, which is empirically falsified. We further prove that the concept of a "mass gap" is a category error, arising from mistaking an emergent, environmental effect of confinement for a fundamental property of the universe's underlying (and fundamentally gapless) medium. The demand for a constructive "proof of existence" is shown to be an ontological reversal. The problem is thus solved not by providing an answer within the old framework, but by demonstrating the invalidity of the framework itself.