{
  "abstract": "We develop a machine-checked construction of non-Gaussian functional integrals using the Henstock--Kurzweil gauge integral and Chernoff product approximations. The central object is a finite family of bosonic modes with action S(phi) = (1/2) phi^T A phi + lambda * sum_i phi_i^4, where A is positive definite. We prove that the one-mode integral I(omega, j, lambda) is finite, strictly positive, monotone and infinitely differentiable in the coupling lambda on [0, infinity). Its derivatives are given by convergent integrals of phi^{4k} with the same weight, not by the divergent perturbative series. The M-mode influence functional factorises into one-mode integrals and is bounded by its Gaussian value. A Chernoff / Lie--Trotter splitting handles the non-commutativity of the free and non-Gaussian generators. All statements are formalised in Lean 4 with Mathlib; the accompanying file HkNonGaussian.lean is free of sorry and uses only the standard axioms propext, Classical.choice, Quot.sound. Four illustrative applications are worked out at the level of explicit formulas: the Duffing oscillator, local volatility (CEV) in finance, Wilson--Cowan neural fields, and non-Gaussian quantum reservoirs. The construction is completely direct and does not use Wick rotation, Wiener measure, zeta-regularisation or analytic continuation back from imaginary time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10793",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuri N. Berdinsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bqvjb2xh9p9n7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10793",
  "fulltext_url": null,
  "id": "bqvjb2xh9p9n7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10793",
  "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": "W7212255491",
  "pdf_url": "https://arxiv.org/pdf/2609.10793",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bqvjb2xh9p9n7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.10793",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10793"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Henstock--Kurzweil Gauge Integral in the Non--Gaussian Regime: A Machine--Verified Construction",
  "title_text": "Henstock--Kurzweil Gauge Integral in the Non--Gaussian Regime: A Machine--Verified Construction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/bqvjb2xh9p9n7",
  "venue": "arXiv",
  "versions": []
}