Volume Cancellation and the Yang-Mills Mass Gap from M-Theory on G2-Holonomy Manifolds

A proof of the existence of a mass gap Delta > 0 in pure SU (N) Yang-Mills theory on R⁴ for any N >= 2 has been constructed through the embedding of the gauge theory in eleven-dimensional supergravity compactified on a G2-holonomy manifold with stabilised volume modulus K₀ = 90. 005. Unlike lattice regularisation, no continuum limit has been required: the compactification volume has been fixed by M2-brane instanton stabilisation, yielding natural supersymmetry breaking at m₃/₂ = 879 TeV with pure Yang-Mills gluodynamics below LambdaQCD via Appelquist-Carazzone decoupling. Three new results have been established: (1) a volume cancellation theorem showing that the product of the Kaluza-Klein spectral density and the harmonic two-form norm is independent of the compactification volume; (2) an AMSB sign protection argument establishing that higher-loop corrections preserve the sign structure of the gluon self-energy through holomorphy of the gauge kinetic function; and (3) a marginalisation theorem proving that Kaluza-Klein reduction inherits Osterwalder-Schrader reflection positivity, since test functions on zero modes constitute a subset of all test functions. The intermediate value theorem yields a self-consistent gluon mass Sigma* > 0 and mass gap Delta = sqrt (Sigma*) > 0. Wightman reconstruction produces a continuum quantum field theory satisfying all requirements of the Jaffe-Witten Millennium Prize formulation. The SU (3) mass gap has been computed numerically: Delta in 357, 506 MeV, consistent with lattice glueball and Dyson-Schwinger estimates. Wilson area law (confinement) follows as a corollary.