{
  "abstract": "Positive-diagonal D-stability asks whether stability persists under every positive diagonal left scaling. We replace the classical Hurwitz half-plane by the Matignon sector for commensurate Caputo systems and solve the resulting real three-dimensional problem on the full-dimensional strict-P(−A) stratum. Four scale-invariant quantities (β12,β13,β23,κ) reduce the complete positive-diagonal orbit to an open simplex, and for 2/3<α<1 we prove the exact criterion κ<Tα(β). At α=1, Tα collapses to Cain’s classical threshold, while Tα>T1 for every 2/3<α<1, producing an explicit genuinely fractional band. The threshold objective is strictly convex in logit coordinates, has a unique nondegenerate optimizer, and yields the minimum-dimension result: three is the minimum dimension in which the genuinely fractional multiplicative-D-stable class has nonempty full-dimensional interior. We then construct a nonlinear three-species Caputo Kolmogorov realization with double-Allee basal growth and intraguild predation. A natural competing-consumer architecture is proved unable to enter the fractional-only band, whereas the intraguild-predation architecture realizes an open biological subset of it. Varying only the Allee threshold moves the fixed biological system transversally across Cain’s classical D-stability boundary into the fractional-only Matignon region. A reproducible integration of the full nonlinear model at a certified orbit point displays decaying Caputo transients at α=0.9, while the same parameters, rate scaling and initial perturbation leave a fixed local neighborhood at α=1.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ibrahim Alraddadi",
      "orcid": "0000-0002-0094-7937"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c04gq73tczx70.bib",
  "cited_by": 0,
  "doi": "10.3390/math14214087",
  "fulltext_url": null,
  "id": "c04gq73tczx70",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/4087",
  "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": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-07",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/c04gq73tczx70.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T00:21:18Z",
      "native_id": "10.3390/math14214087",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/4087"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "From Cain to Matignon: Exact Positive-Diagonal Stability in Dimension Three and a Nonlinear Caputo Ecological Realization",
  "title_text": "From Cain to Matignon: Exact Positive-Diagonal Stability in Dimension Three and a Nonlinear Caputo Ecological Realization",
  "type": "peer-reviewed",
  "updated_at": "2026-11-10T00:21:18Z",
  "url": "https://research.draconitic.com/paper/c04gq73tczx70",
  "venue": "Mathematics",
  "versions": []
}