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This paper resolves the Yang–Mills mass gap by modeling mass as a structure that survives compression under directional motion. Classical field theory allows massless gauge fields, but cannot explain why force carriers in the strong interaction exhibit nonzero mass. The Latnex model reframes this gap. Motion is not a byproduct. It is the structure. The field does not fail because of symmetry break. It fails when directional acceleration exceeds compression tolerance. That collapse creates persistent structure. That structure is inertia. That inertia is mass. The Yang–Mills field is treated as a system of recursive directional motion, where each gauge interaction contributes ∆m. The accumulation of motion across the field is Σ∆m. Compression failure occurs when the second-order motion ∆∆m exceeds a critical boundary Ct. When this breach occurs, the system cannot restore symmetry. Instead, it stabilizes into a bounded object. This is recorded as a collapse event, marked by Ke = 1. The collapsed field segment persists across time. The field gains resistance to redirection. That is the mass gap. It is not hypothetical. It is mechanical. The Clay condition is satisfied. A quantized mass gap exists because Yang–Mills fields contain collapse regions that persist after exceeding allowable recursive tension. The proof is not symbolic. It is structural. The collapse is not failure. It is survival. ∆m creates the boundary. ∆∆m defines the strain. Ct determines survival. Ke records collapse. Σ∆m defines continuity. The system explains the mass gap through motion alone.