There is a newer version of the record available.

Published October 25, 2025 | Version v8
Publication Open

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 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 115, 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.

Files

TowardsaFormalVerificationoftheYang-MillsMassGapinLean4.pdf

Files (1.2 MB)

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