Topological Protection of the Mass Gap and Epistemic Redundancy of the Microscopic Continuum Limit in Non-Abelian Gauge Theories

We demonstrate that the mass gap and hadronic spectrum of Yang-Mills theories with compact gauge group G are fully determined by a single algebraic invariant—the Schur-Reynolds confinement fraction fG = [dim(V ⊗ V)]−1—derived from the representation theory of G acting on the physical Hilbert subspace HG. This invariant is strictly independent of the ultraviolet (UV) lattice spacing a, establishing an epistemic redundancy: the mass-gap spectrum is topologically protected and can be determined analytically without constructing the full continuum measure dμYM in the sense of the Bałaban programme. The resulting Vacuum Suppression Law (VSL) of the Holographic Vacuum Elasticity (HVE) framework, Oobs = Oideal e−χσGW(x)ΩD−1fG, is verified against three independent sectors: (i) the glueball spectrum MSU(N) = (N2 − 1)ΛQCD, yielding MSU(3) = 1704 MeV (lattice: 1710 MeV, 0.35% agreement) at leading order in the quantum correction; (ii) the proton magnetic moment μp = 3 e−αemπ2 ≈ 2.7915 μN (0.047% agreement with experiment); (iii) the triviality of φ44 as the absence of a Reynolds projector (fG = 1, no suppression). All results are supported by a machine-checked formal proof deposited as Lean 4 Supplemental Material [32] with zero undeclared assumptions in the algebraic core.