A TEBAC Proof of Four-Dimensional Yang--Mills Existence and Mass Gap

This preprint presents a theorem-level TEBAC proof manuscript for four-dimensional Yang--Mills existence and mass gap for compact simple gauge groups. The construction is organized through the module chain -I-II-III-IV-V. \ The manuscript constructs finite-cutoff gauge-invariant Wilson measures, proves reflection positivity and the Osterwalder--Schrader reconstruction interface, establishes cutoff-uniform spectral coercivity in the gauge-invariant Hilbert sector, and then transfers the resulting lower spectral bound to the continuum Hamiltonian by Schwinger compactness, regulator independence, Mosco/form convergence, and vacuum-projection convergence. The main theorem asserts that for every compact simple Lie group \ (G\), there exists a non-trivial Euclidean quantum Yang--Mills theory on \ (R^4\) satisfying the Osterwalder--Schrader axioms and reconstructing a Wightman theory whose physical Hamiltonian \ (H\) has a strictly positive mass gap above the vacuum: (H|^) [ₘ₌, ), (H) (0, ₘ₌) =, ₘ₌>0. \ The proof is presented with explicit dependency, non-circularity, regulator-independence, and constant-ledger checks. The manuscript has been submitted for consideration to Inventiones mathematicae. The editorial and referee process is pending.