{
  "abstract": "We formalize in Lean 4 the gauge closure of the Feynman functional integral for the free field without Wick rotation. First, the restriction to box divisions is removed via a direction bound and a uniform Riemann-sum estimate for all $δ$-fine cylindrical divisions. Second, the coordinate measure on $\\mathbb{R}^k$ is identified with the standard Gaussian one. Third, the Saks-Henstock lemma and additivity are proved. Fourth, the Fresnel formula $\\int_{\\mathbb{R}} e^{i a x^2/2} dx = \\sqrt{2π/a} e^{iπ/4}$ is proved as an improper (gauge) integral. This yields the projective consistency of the oscillating Gaussian premeasure and the existence of the free-field integral. The free field is completely closed: we prove the Fresnel formula for an arbitrary symmetric positive-definite action $A$, compute the generating functional and the two-point function $\\langle y_p y_q \\rangle = i(A^{-1})_{pq}$, and prove Wick's theorem. The interacting field $λφ^4$, unbounded generators, and renormalisation remain open. All results are machine-verified with no sorry or new axioms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37346",
  "author_total": 1,
  "authors": [
    {
      "name": "Yu. N. Berdinsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6k7x01z1m7ryj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37346",
  "fulltext_url": null,
  "id": "6k7x01z1m7ryj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37346",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Mathematical and Theoretical Analysis"
    ]
  ],
  "openalex": "W7224102021",
  "pdf_url": "https://arxiv.org/pdf/2610.37346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6k7x01z1m7ryj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.37346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37346"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Algebraic Completeness of Feynman Premeasures: The Henstock-Kurzweil Path Integral and Operator Wick Calculus in Lean 4",
  "title_text": "Algebraic Completeness of Feynman Premeasures: The Henstock-Kurzweil Path Integral and Operator Wick Calculus in Lean 4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/6k7x01z1m7ryj",
  "venue": "arXiv",
  "versions": []
}