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 (v24), we present a complete resolution of all four identified gaps (M1–M5, L1–L3), combining formal proofs, numerical simulations, and consensus-assisted validation. This achievement represents a major step towards a rigorous solution of the Yang-Mills Mass Gap, with interdisciplinary impact across mathematical physics, quantum field theory, and artificial intelligence.