{
  "abstract": "SUPERSEDED VERSION — DO NOT CITE THE NUMERICAL VALUES BELOW. This is version 1.0. It is superseded by version 1.2 (10.5281/zenodo.20481592). Please cite the concept DOI 10.5281/zenodo.20455089, which always resolves to the current version. Three assertions in the text below are incorrect and have been corrected in later versions: The Stokes constant is wrong. This version reports S ≈ 0.43770528. The correct value is S = 2πK = 0.45790662316901763611…. The error was an incorrect Dingle prefactor, Γ(βexp) = −6.00599, used in place of the universal resurgence factor 2π = 6.28319. The two agree to 4.4%, which is why the error was not caught sooner. The connection parameter is wrong. This version reports σconn ≈ 0.06087689. The corrected value is 0.06335272. Theorem 4.1 is not a theorem. The identification of the isomonodromic deformation as Painlevé V on the Sakai surface of type D5(1) is stated below as Theorem 4.1. It is not proved. It is restated as Conjecture 4.1 in version 1.2. The late-term amplitude K = 0.07287810255…, the Gevrey/Borel branch-point structure, the Wallis-discriminant exclusion argument, and the closed-form non-identification are unchanged and are not affected by these corrections. Notice added 2026-08-29 by the author. We study the resurgence and isomonodromic structure of a constant V_quad ≈ 1.19737… arising as the limit of a quadratic polynomial continued fraction (PCF). The convergent denominators satisfy a Wallis-type recurrence whose continuum limit yields an exact second-order ODE of the form a(x)y'' + a'(x)y' + c(x)y = 0, with a(x) = 3x²+x+1 and c(x) = −x². This exact-ODE structure forces both finite singularities to be apparent and explains, via monodromy, the failure of CM-period and hypergeometric identification strategies. The CM discriminant disc(a) = 1 − 12 = −11 that appears throughout the analysis is the discriminant of the Wallis characteristic polynomial, not a deep CM structure; this explains why exhaustive PSLQ searches against CM period bases at discriminant −11 return null by a structural argument independent of precision. The isomonodromic deformation of the underlying connection is governed by the fifth Painlevé equation with parameters α=1/6, β=γ=0, δ=−1/2 (δ≠0); its space of initial conditions is the Sakai surface D5^(1) with affine Weyl symmetry W(A3^(1)). Since δ≠0 the equation does not reduce to Painlevé III, and the constant is expected to be a generic, non-classical PV transcendent. The formal asymptotic series at infinity is Gevrey-1 divergent; its Borel transform has a branch-point singularity at ξ0=2/√3 (the Stokes gap) with branch exponent β_exp=−1/(3√3), confirmed to eight significant figures by Domb–Sykes analysis and Richardson³ extrapolation. The Stokes constant S ≈ 0.43770528… is computed to eight digits by the Dingle late-term formula. An exhaustive search over 245 variants of the Jimbo (1982) connection formula establishes that S is not a simple combination of Gamma values at the WKB parameters; its closed-form identification requires the connection parameter σ_conn, which is transcendental in the accessory parameter q=(5+i√11)/54. The structure b(x)=a'(x) identified here is a general feature of PCF-derived ODEs: for any polynomial continued fraction, the Wallis recurrence produces an exact ODE whose apparent singularity positions are the roots of the Wallis characteristic polynomial and whose CM discriminant is disc(a). ## additional_notesProvenance note. This manuscript classifies the V_quad isomonodromic deformation as Painlevé V on the Sakai surface of type D5^(1) (Theorem 4.1). This supersedes an earlier Painlevé III(D6) framing of the same constant used in companion deposits — PCF-1 (concept DOI 10.5281/zenodo.19931635) and Channel Theory (concept DOI 10.5281/zenodo.19941678) — where V_quad was described as a PIII(D6) prototype/reduction. The present PV/D5^(1) classification is the corrected determination; Remark 4.3 records why the PV→PIII confluence is not taken (delta = -1/2 != 0) and why PIII(D7) is excluded.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Papanokechi",
      "orcid": "0009-0000-6192-8273"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9qbvje7tgapew.bib",
  "cited_by": 7,
  "doi": "10.5281/zenodo.20455089",
  "fulltext_url": null,
  "id": "9qbvje7tgapew",
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  "landing_url": "https://doi.org/10.5281/zenodo.20455089",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7162863602",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-30",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/9qbvje7tgapew.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W7162863602",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.20455089"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Mathematical functions and polynomials",
      "subfield": "general"
    }
  ],
  "title": "A non-classical Painlevé V transcendent from a quadratic polynomial continued fraction: surface classification and resurgent Stokes data",
  "title_text": "A non-classical Painlevé V transcendent from a quadratic polynomial continued fraction: surface classification and resurgent Stokes data",
  "type": "preprint",
  "updated_at": "2026-11-06T13:20:22Z",
  "url": "https://research.draconitic.com/paper/9qbvje7tgapew",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}