Structural Closure of the Yang–Mills Mass Gap Problem via Structural Variance Control

This project presents a structural analysis of the Yang–Mills mass gap problem using the framework of Structural Variance Control (SVC). Rather than proposing a new constructive proof, quantization scheme, or spectral estimate, the work examines a logically prior question: whether the absence of a mass gap is structurally admissible within the defining constraints of four–dimensional Yang–Mills theory. By systematically classifying all admissible structural deformations that preserve gauge invariance, uniform coercivity, algebraic consistency, and representation independence, the analysis demonstrates that every conceivable gap–elimination mechanism either violates a defining constraint or collapses under global structural enforcement. The remaining locally plausible channel—algebraic frustration—is shown to be unstable when enforced across the full admissible variance space. The central conclusion is that the Yang–Mills mass gap problem is structurally closed: no admissible structural variance exists along which gaplessness can be sustained without redefining the problem itself. This result is structural rather than constructive and reframes the mass gap problem as a case of structural non–resolution rather than technical incompleteness.