A Formal Verification Framework for the Yang–Mills Mass Gap: Consensus Framework, Lean 4 and Lattice QCD

This work presents a formal verification framework for the Yang-Mills Mass Gap problem, integrating the Consensus Framework, Lean 4 formalization, and lattice QCD numerical validation. The methodology was recognized as a Global Finalist in the UN Tourism AI Challenge (2025). In this updated version (v17), we report the completion of all four gaps: BRST Measure, Gribov Cancellation, BFS Convergence, and Ricci Curvature Bound. All lemmata L1–L5 have been formally proven in Lean 4, with numerical and literature validation. The framework combines formal proofs, lattice simulations, and consensus-assisted validation, achieving a transparent and reproducible resolution pathway to the Yang-Mills Mass Gap.