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 (v12 – Gap 1 Complete), we formalize and validate the BRST Measure Existence (Gap 1) through five lemmata (M1–M5) in Lean 4, with numerical support from lattice QCD. This version consolidates the transition from Axiom 1 to a conditional theorem, combining formal proofs, numerical evidence, and consensus-assisted validation, advancing the interdisciplinary approach to mathematical physics.