Topological crystallization of the non-Abelian vacuum: a physical foundation for the Yang–Mills mass gap via triangulation of QCD anomalies

Abstract We propose a physical foundation for the existence of the mass gap Δ > 0 in pure Yang–Mills gauge theory based on the concept of topological crystallization of the non-Abelian vacuum. Employing an anomaly triangulation methodology -a coherent analysis of three independent empirical phenomena in quantum chromodynamics (QCD) -we demonstrate that the Yang–Mills vacuum is not an amorphous fluctuating field but rather a hierarchical topological lattice. The primary analytical tool is the Lund plane decomposition of hadronic jets, in which we predict a discrete “zebra-stripe” resonance structure as a direct experimental consequence of topological charge quantization. Starting from the Adler–Bell–Jackiw anomaly equation, we derive a quantized radiation condition linking jet kinematics to topological invariants of the vacuum. From the BPST instanton form factor we further derive an effective topological potential that analytically forbids zero modes. The numerical coefficient c in the mass-gap formula is computed from the one-loop instanton fluctuation determinant, yielding c ≈ 1.18 and a predicted mass gap Δ ≈ 350 MeV, in quantitative agreement with lattice QCD estimates for the scalar glueball mass m(0++) ≈ 1.73 ± 0.10 GeV without free parameters.