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

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 (cₘix* ≈ 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 (paper₃5. tex, paper₃5. 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.