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Published October 21, 2025 | Version v2
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A Formal Verification Framework for the Yang–Mills Mass Gap: Consensus Framework, Lean 4 and Lattice QCD

Authors/Creators

  • 1. Smart Tour Brasil

Contributors

Project leader:

  • 1. smart tour brasil

Description

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 Artificial Intelligence Challenge (2025). The framework combines formal proof, numerical simulation, and AI-assisted consensus validation, fostering interdisciplinary approaches in mathematical physics. This version includes the first validated formulation of Lemma L3 (Topological Pairing), refined after numerical analysis, which establishes its validity across non-trivial topological sectors, marking a critical step towards transforming Axiom 2 into a theorem.

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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