{
  "abstract": "FINDING: The search results are a mix of generic recurrence-solving pedagogy and one substantive research paper linking interpolated Apéry numbers to critical L-values of modular forms. The core mathematical insight is that Zagier's interpolation of Apéry numbers (for ζ(3)) is not an isolated combinatorial curiosity but a critical L-value of a weight-4 modular form, and this extends to all six of Zagier's sporadic sequences.\n\nMATH: - Apéry numbers: \\( a_n = \\sum_{k=0}^n \\binom{n}{k}^2 \\binom{n+k}{k}^2 \\), satisfying recurrence \\( (n+1)^3 a_{n+1} = (2n+1)(17n^2+17n+5) a_n - n^3 a_{n-1} \\). - Characteristic polynomial of the recurrence (in the limit of large n, after scaling): roots are \\( \\lambda = 17 + 12\\sqrt{2} \\approx 33.97 \\) and its reciprocal \\( 17 - 12\\sqrt{2} \\approx 0.0294 \\). Note \\( 17 + 12\\sqrt{2} = (1+\\sqrt{2})^4 \\), and \\( (1+\\sqrt{2}) \\) is the silver ratio. - Modular form connection: The interpolated Apéry numbers \\( A_t(n) \\) (Zagier's t-deformation) are shown to\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/b81aj29akn6s5.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635248",
  "fulltext_url": null,
  "id": "b81aj29akn6s5",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23635248",
  "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": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b81aj29akn6s5.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:56Z",
      "native_id": "23635248",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23635248"
    }
  ],
  "subjects": [],
  "title": "Modular L-Values Link Zagier's Sporadic Sequences to Apéry Numbers — E8 Intelligence Research",
  "title_text": "Modular L-Values Link Zagier's Sporadic Sequences to Apéry Numbers — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:56Z",
  "url": "https://research.draconitic.com/paper/b81aj29akn6s5",
  "venue": "Zenodo",
  "versions": []
}