{
  "abstract": "This paper proves the existence of a four-dimensional quantum Yang–Mills theory satisfying the Osterwalder–Schrader and Wightman axioms and establishes a strictly positive mass gap $\\Delta>0$ under Topological Vacuum Electrodynamics. On the continuous electromagnetic vacuum sheet, non-Abelian gauge fields for a compact simple Lie group $G$ arise via the Faddeev–Niemi–Cho decomposition of braided force-free Beltrami flux tubes satisfying $D\\times\\mathbf{B}^a=\\alpha(\\rho)\\mathbf{B}^a$. The minor-radius cutoff $a$ of the ground-state unknot fixes the ultraviolet phase-space capacity $\\alpha^{-1}=4\\pi^3+\\pi^2+\\pi$ as a covariant curvature bound, rendering the Euclidean functional measure ultraviolet-finite while preserving full $SO(4)$ Euclidean covariance and Lumer–Phillips reflection positivity. Helicity conservation enforces the non-linear magnetic pressure $P=\\xi/a^4$ and confining string tension $\\sqrt{\\sigma}=2\\pi\\alpha^{-1}m_e$, fixing the equilibrium tube radius $a=\\sqrt{\\xi/\\sigma}$ and evading Derrick’s scaling collapse. By Moffatt’s topological helicity quantization and the Călugăreanu–White–Fuller theorem, any non-trivial closed gauge excitation carries a strictly non-zero minimal topological linking invariant $|H|\\ge|H_{\\min}|>0$. Applying Arnold’s ergodic helicity inequality on the self-confined Beltrami tube (where the lowest curl eigenvalue is $\\alpha_1=j_{0,1}/a>0$) and the global Vakulenko–Kapitanski inequality yields a strictly positive lower bound on the rest energy $W\\ge\\frac{\\alpha_1}{2\\mu_0}|H_{\\min}|>0$. Kato–Rellich stability against exponentially suppressed instanton tunneling $r_K\\propto e^{-\\alpha^{-1}}$ establishes the quantum mass gap $\\Delta>0$ and exponential clustering of vacuum correlation functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Truth Vector"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/172jrn2j7758d.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23459483",
  "fulltext_url": null,
  "id": "172jrn2j7758d",
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  "landing_url": "https://zenodo.org/records/23459483",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
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  "pdf_url": "https://zenodo.org/api/records/23459483/files/TVE_%20Yang%E2%80%93Mills%20Existence%20and%20Mass%20Gap%2020261018.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/172jrn2j7758d.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:20:53Z",
      "native_id": "23459483",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23459483"
    }
  ],
  "subjects": [],
  "title": "Yang–Mills Existence and Mass Gap Proof via Topological Helicity Quantization and Beltrami Confinement under Topological Vacuum Electrodynamics",
  "title_text": "Yang–Mills Existence and Mass Gap Proof via Topological Helicity Quantization and Beltrami Confinement under Topological Vacuum Electrodynamics",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/172jrn2j7758d",
  "venue": "Zenodo",
  "versions": []
}