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 \[{YM-I}{YM-II}{YM-III}{YM-IV}{YM-V}.\] 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 \(R⁴\) satisfying the Osterwalder--Schrader axioms and reconstructing a Wightman theory whose physical Hamiltonian \(H\) has a strictly positive mass gap above the vacuum: \[Spec(H|Ω^⊥)⊆ [ΔYM,∞),(H)∩(0,ΔYM)=,ΔYM>0.\] 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.