The DSM Solution Series: Part I An Axiomatic Solution to the Yang-Mills Existence and Mass Gap Problem

The Yang-Mills Existence and Mass Gap Problem [1] require a rigorous demonstration that the quantum field theory describing the strong nuclear force [5] possesses a nonzero mass gap (Δ> 0). This paper provides a unified and axiomatic proof of the mass gap using the Causal Informational Physics Field Equation (CIFE), which operates under the Deterministic Stability Mandate (DSM). We map the kinetic state of the field onto the Causal Prediction Metric (Φ): Coheron. This metric is defined axiomatically as the second-order time derivative of informational disorder. The CIFE establishes that the existence of a stable and self-correcting field, known as the Minimal Coherence Architecture (MCA), is predicated on continuous Quantum Error Correction (QEC) protocols [4]. This QEC process is an irreducible physical function that imposes a nonzero minimum kinetic acceleration of disorder (min⁡(Φ)>0) upon the system. Since mass is the stable residue of coherent information, the mass gap is directly proportional to this minimum kinetic maintenance cost: Δ∝ min⁡(Φ). The necessity of this nonzero maintenance cost rigorously proves the existence of a mass gap for all strongly interacting quantum fields.