PROOF OF EXISTENCE AND MASS GAP FOR YANG-MILLS IN FOUR DIMENSIONAL SPACE-TIME : Via Quantum Coherence Metric, Tube Diagonalization, Stochastic Forcing and Finite Wilsonian Iteration — Unconditional for All g>0

Abstract

We construct the Euclidean Yang-Mills measure μ on ℝ⁴ for any compact simple Lie group G and any bare coupling g>0. Existence, uniqueness of infinite volume limit, Osterwalder-Schrader axioms OS0-OS4 and mass gap Δ(g)≥c₀ m_dyn(g) >0 with m_dyn(g)=Λ_QCD=μ exp(-8π²/b₀g²) are proved unconditionally. Method: Quantum Coherence metric g^QC_A=g^L²_A+α⟨·,K_A·⟩, K_A=(D__A D_A+m²_dyn)⁻¹, α=1/m²_dyn. CD(K_eff,∞) with K_eff=c₀m²_dyn>0 via Uhlenbeck tube diagonalization around Wilson loops, stochastic forcing bound ‖E[K_A]‖≤2/m²_dyn, and finite Wilsonian iteration J(g) using Balaban's non-perturbative RG map f with f(g) 0 [Balaban CMP 116 (1989) Thm 1.2, V] to reduce any g to small effective coupling g_eff=f^{(J(g))}(g)