{
  "abstract": "This is the fourteenth paper of a programme constructing the Feynman functional integral without a Wick rotation, on the basis of the non-absolutely convergent Henstock–Kurzweil (HK) integral and of Kuelbs–Steadman spaces. It attacks the question left open by the previous work: does the normalized CutOut ratio r_N(epsilon) of the quasi-abelian two-mode class of SU(2) on T^4 tend to zero at a fixed coupling epsilon > 0? All results of the previous works are used as black boxes and none is re-proved. The question is not resolved here, and none of the three possible outcomes is asserted; what the paper establishes is a precise description of the boundary of the present methods, together with two negative results which close two of the three proposed routes.\n\n(I) The monotonicity mechanism of the direct-comparison route is impossible: for a continuous perturbation weight h_N and an open Gribov region meeting the box B_R without filling it, one always has inf_{B_R cap Omega} h_N <= sup_{B_R setminus Omega} h_N, because the two regions share a boundary point interior to the box; the proposed suppression factor exp(-epsilon^2 [inf_Omega h_N - sup_{B setminus Omega} h_N]) is therefore always >= 1.\n\n(II) The premise of the oscillation route is false: the unperturbed truncated determinant does not alternate in sign, since the retained modes come in pairs {n, -n} and each factor is even in n, whence Delta_0^{(N)}(A) >= 0 for all A and N; a sign-reversing involution acting through the determinant can exist only on the null set {Delta_0^{(N)} = 0}. Two conditional criteria of that route survive and are proved in full: an exact measure-preserving sign-reversing involution makes the numerator vanish, and a polynomially decaying numerator with a denominator bounded below gives the CutOut.\n\n(III) The estimates (K4)–(K7) of the previous works do not decide the question: for every admissible tuple of constants there are data satisfying all of them with r_N -> 0, data with r_N bounded away from 0, and data with r_N unbounded. In particular the obstruction of the previous work — the failure of the error budget to be o(N) — is compatible with the CutOut, which settles the fallback statement (ii) of the programme; the fallback statement (i) is proved in conditional form only. Every theorem is proved in full in the main text and machine-verified in Lean 4 with no sorry, no admit and no new axiom, and a deterministic numerical script illustrates the two negative results at small N.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Yu. N. Berdinsky",
      "orcid": "0009-0003-1858-004X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6af2kf1g5c1ry.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23578376",
  "fulltext_url": null,
  "id": "6af2kf1g5c1ry",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23578376",
  "language": "eng",
  "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": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23578376/files/InfiniteHK14_ru.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6af2kf1g5c1ry.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:20:20Z",
      "native_id": "23578376",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23578376"
    }
  ],
  "subjects": [],
  "title": "Fixed-epsilon CutOut in the quasi-abelian class of the non-abelian Henstock–Kurzweil functional integral: direct comparison, oscillation, and the classification of regimes",
  "title_text": "Fixed-epsilon CutOut in the quasi-abelian class of the non-abelian Henstock–Kurzweil functional integral: direct comparison, oscillation, and the classification of regimes",
  "type": "preprint",
  "updated_at": "2026-11-05T12:20:20Z",
  "url": "https://research.draconitic.com/paper/6af2kf1g5c1ry",
  "venue": "Zenodo",
  "versions": []
}