{
  "abstract": "FINDING: The search results are a scattered mix — no direct paper on \"Jacobi polynomials in two-mode squeezed thermal states with photon addition\" was retrieved. The closest mathematical anchors are: (a) a 2025 GPU elastodynamics paper using Jacobi/Gauss-Seidel (JGS2), (b) a lecture on Jacobi/Gegenbauer/Chebyshev polynomials, (c) an MIT lecture on two-photon excitation, (d) a Wolfram demo on Jacobi collocation, (e) a dual-rail photon quantum computation lecture, and (f) a hexaquark decay paper. No unified quantum-optical result emerges.\n\nMATH: - Jacobi polynomials \\(P_n^{(\\alpha,\\beta)}(x)\\) — orthogonal on \\([-1,1]\\) with weight \\((1-x)^\\alpha(1+x)^\\beta\\). - Gegenbauer: \\(C_n^{(\\lambda)}(x) = \\frac{(2\\lambda)_n}{(\\lambda+1/2)_n} P_n^{(\\lambda-1/2,\\lambda-1/2)}(x)\\). - Chebyshev: \\(T_n(x) = P_n^{(-1/2,-1/2)}(x)\\) (scaled). - JGS2: iterative solver — no closed-form constants given. - Hexaquark: SU(3) antidecuplet — group theory, no explicit ratios in abstract. - No occurren\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/15tf2vrg1n3x5.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23446922",
  "fulltext_url": null,
  "id": "15tf2vrg1n3x5",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23446922",
  "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": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/15tf2vrg1n3x5.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:50Z",
      "native_id": "23446922",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23446922"
    }
  ],
  "subjects": [],
  "title": "Gap Analysis: No Direct Study on Jacobi Polynomials in Two-Mode Squeezed Thermal States with Photon Addition — E8 Intelligence Research",
  "title_text": "Gap Analysis: No Direct Study on Jacobi Polynomials in Two-Mode Squeezed Thermal States with Photon Addition — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:50Z",
  "url": "https://research.draconitic.com/paper/15tf2vrg1n3x5",
  "venue": "Zenodo",
  "versions": []
}