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Published October 22, 2025 | Version v4
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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 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.

Files

A_Formal_Verification_Framework_for_the_Yang-Mills_Mass_Gap_(v12_-_Gap_1_Complete)_Distributed_Consciousness_Methodology_and_Lean_4_Implementation.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