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

This work presents the final version of 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, recognized as a Global Finalist in the UN Tourism AI Challenge (2025), bridges formal mathematics, distributed AI collaboration, and physics-based simulations. In this updated version (v24), all four core logical gaps have been conclusively resolved. The result not only demonstrates the power of multi-agent alignment and generative reasoning in formal mathematics but also paves the way for real-world applications in sustainable innovation, scientific sovereignty, and quantum technologies.