The HDG Three-Gluon Vertex from Ward–Takahashi Identity and Topological Memory (HDG_XXXV)

Paper XXXV of the History-Dependent Gravity (HDG) series, part of the 'Temporal Nonlocality and Fundamental Physics' community. This work addresses the long-standing spectral inversion problem in non-perturbative QCD calculations, where scalar-kernel truncations of the gluon Bethe-Salpeter equation artificially predict the pseudoscalar glueball (0⁻⁺) to be lighter than the tensor glueball (2⁺⁺), contradicting lattice QCD results. KEY RESULTS:1. We construct a complete three-gluon vertex satisfying the Ward-Takahashi identity with a topological transverse component.2. We prove that in the minimal tensor basis, interference between symmetric and antisymmetric structures vanishes identically.3. The pure topological contribution γ₂² alone resolves the no-go theorem, lifting M(0⁺) above M(2⁺⁺).4. We derive a functional renormalization group flow showing that channel mixing is inevitably generated by HDG nonlocality.5. The mixing parameter emerges as an infrared fixed point (c_mix* ≈ 0.125), not a fitted parameter.6. Projector-derived spectral shifts yield exact agreement with lattice QCD: M(0⁻⁺)/M(2⁺⁺) ≈ 1.08. PHYSICAL INSIGHT:"Topology sets the scale; the RG flow sets the value." This repository includes:- Complete LaTeX source of the paper (paper_35.tex, paper_35.pdf)- All Python code for numerical calculations and figure generation- Reproducible workflows for BSE solving, RG flow integration, and spectrum analysis RELATED WORK:This is Paper XXXV in the HDG series, extending Paper XXXIV (DOI: 10.5281/zenodo.21425214) which introduced the infrared-enhanced gluon propagator.