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, and the number of auxiliary sorry statements has been reduced from 255 to 91, representing a major step towards full formal verification. 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.