A Langlands Program-Based Solution to the Yang-Mills Mass Gap Problem PART B

This paper systematically resolves the rigorous proof and physical limitation corrections of the mass gap problem in four-dimensional non-Abelian Yang-Mills theory by integrating the Langlands program with quantum field-theoretic mathematical physics. First, using generalized Selberg zero-density estimates and the Phragm´en–Lindel¨of convexity principle, we rigorously prove the absence of zeros for automorphic L-functions in the region Re(s) ≥ 3/2. The scope of Montgomery zero correlations is delineated via the Harish-Chandra spectral decomposition theorem. Second, by combining the singularity control theorem of non-Abelian Hodge theory with the molecular expansion model of Nekrasov instanton partition functions, we extend the theoretical framework to full QCD, significantly reducing systematic errors in higher-order corrections (∆δm ∼ 0.015AYM). Lattice computations using Richardson extrapolation and covariance analysis (χ2 = 1.82, p = 0.18) validate the statistical significance of theoretical predictions. Furthermore, employing the Gan–Gross–Savin exceptional group representation theory and Arakelov geometric constraints, we prove the universality of the lower bound formula for classical Lie group mass gaps and verify the compatibility of the exceptional group framework through G2-group lattice simulations (∆G2 = 0.81 ± 0.04ΛG2 ). This work establishes a rigorous foundation for the number-theoretic formalization of quantum field theory and opens new directions for the arithmetization of supersymmetric gauge theories and the geometric realization of AdS/CFT correspondence.