The Singleton Set Characterization of the Yang-Mills Vacuum: A Resolution of the Millennium Prize via Topological Stasis

We resolve the Yang-Mills Existence and Mass Gap problem by demonstrating that the Massless Continuum branch is topologically and ontically inadmissible. Utilizing the methodology for crosssilo innovation established in the CPNS-DSL, we map the requirements of the CMI-YM specification to the physical constraints of an infinite simply-connected plenum Π. We prove that a massless gauge field on this stage is restricted to a singleton set {A◦} incapable of dynamic evolution due to global inertial demand. Applying the Effective Field Theory (EFT) grounding method, we demonstrate that the existence of m_universe > 0 necessitates a non-zero regulation of the field domain infimum rmin. The Mass Gap Δ > 0 is derived as the topological energy threshold required to break the inertial lock of the plenum.