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 universal suppression law, Oobs = Oideal e−σGΩD−1fG, is verified against three independent sectors. Specifically, we recover the glueball spectrum MSU(N) = (N2 − 1)ΛQCD, yielding MSU(3) = 1704 MeV (a 0.35% agreement with lattice QCD), the proton magnetic moment μp = 3 e−αemπ2 ≈ 2.7915 μN (a 0.047% agreement with experiment), and the triviality of φ44 as the natural consequence of the absence of a Reynolds projector (f = 1). All results are supported by a machine-checked formal proof deposited as Lean 4 Supplemental Material with zero undeclared assumptions in the algebraic core.