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| Príomhchruthaitheoirí: | , , , , |
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| Formáid: | Recurso digital |
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Zenodo
2026
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| Rochtain ar líne: | https://doi.org/10.5281/zenodo.19699784 |
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Clár na nÁbhar:
- <h1>Abstract</h1> <p>We report the results of an intensive campaign to prove the Yang-Mills mass gap — one of the seven Clay Millennium Prize Problems. Using adversarial AI collaboration across three frontier models, we systematically applied every available mathematical tool to the problem: matrix model spectral analysis, non-commutative gauge theory construction, lattice transfer of structural insights, Pirogov-Sinai theory, Bakry-Emery functional inequalities, Cheeger isoperimetry, character expansion, and the marriage of Bauerschmidt-Bodineau-Dagallier multiscale log-Sobolev inequalities with Shen-Zhu-Zhu Langevin dynamics for lattice Yang-Mills.</p> <p>The campaign produced genuine mathematical results: a solved matrix model with topological spectral gap (Theorems A and B), the first rigorous construction of a mass-gapped 4D gauge theory (non-commutative Yang-Mills on R⁴_θ), a proof of confinement at all couplings via chessboard estimates and Casimir eigenvalues, and a proof sketch for the lattice mass gap at ALL finite couplings (Δ ≥ c·exp(-Cβ) > 0, extending the Shen-Zhu-Zhu result from strong coupling to all β).</p> <p>Yet every approach to the continuum mass gap stalls at the same structural point: the circularity between the spectral gap and the correlation length, manifesting as a factor of 23 between the lattice bound and the continuum threshold. We demonstrate that this wall is not a failure of technique but a consequence of framework: the continuum formulation (R⁴) has removed the mechanism (finiteness of degrees of freedom) that produces the gap. Every successful result in the campaign lives in a setting with finite degrees of freedom; every failure occurs when taking a limit that makes them infinite.</p> <p>This pattern of failures is the strongest evidence in the paper, and is the argumentative basis for the dissolution. In the WCCC framework, spacetime carries two independent sources of finiteness: a cosmological one (the Ciela has finite Hilbert space dimension bounded by the holographic entropy bound), and a local one (spacetime is discrete at the Planck scale, motivated by the Single-Nat Odometer's area-quantization claim). Together these make the continuum R⁴ idealization unphysical, and they make lattice Yang-Mills at finite β the physical theory. The BBD-SZZ lattice gap bound then establishes the physical mass gap. The Clay Prize asks for a proof in a framework that physical Yang-Mills does not inhabit; the systematic failure of every continuum approach is evidence that the framework is the obstruction.</p> <p>We do not claim to have solved the Millennium Prize as stated. We claim something different: that the Prize asks a framework-dependent question, that the framework dependence is diagnosed by the pattern of failures in sections II-VIII, and that WCCC provides a specific alternative framework in which the mass gap is established rather than conjectural.</p> <p> </p>