Published October 24, 2025
| Version v7
Publication
Open
A Formal Verification Framework for the Yang–Mills Mass Gap: Consensus Framework, Lean 4 and Lattice QCD
Description
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.
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YangMills_v24_FINAL_2025-10-24.pdf
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Additional details
Identifiers
- URL
- https://github.com/smarttourbrasil/yang-mills-mass-gap
- Other
- ttps://orcid.org/0009-0004-6047-2306
Dates
- Updated
-
2025-10-20
Software
- Repository URL
- https://github.com/smarttourbrasil/yang-mills-mass-gap
- Programming language
- Python
- Development Status
- Active
References
- Gribov, V. N. (1978). Quantization of Non-Abelian Gauge Theories. Nuclear Physics B, 139(1), 1–19. https://doi.org/10.1016/0550-3213(78)90175-X
- Uhlenbeck, K. (1982). Connections with 𝐿 𝑝 L p Bounds on Curvature. Communications in Mathematical Physics, 83(1), 31–42. https://doi.org/10.1007/BF01947069
- Glimm, J., & Jaffe, A. (1987). Quantum Physics: A Functional Integral Point of View. 2nd Edition. Springer. ISBN: 978-0387964775
- Osterwalder, K., & Schrader, R. (1973). Axioms for Euclidean Green's Functions I. Communications in Mathematical Physics, 31(2), 83–112. https://doi.org/10.1007/BF01645738
- C. Alexandrou, A. Athenodorou, K. Cichy, A. Dromard, E. Garcia-Ramos, K. Jansen, U. Wenger, and F. Zimmermann Artigo: "Comparison of topological charge definitions in Lattice QCD" Publicação: Eur. Phys. J. C 80, 424 (2020) DOI: https://doi.org/10.1140/epjc/s10052-020-7984-9