{
  "abstract": "FINDING: Zagier's interpolation of Apéry numbers for ζ(3) is a critical L-value of a weight-4 modular form; this extends to all six sporadic sequences, linking number-theoretic recurrences to modular symmetries. | MATH: Apéry numbers \\(a_n = \\sum_{k=0}^n \\binom{n}{k}^2 \\binom{n+k}{k}^2\\) satisfy \\(a_n = \\sum_{k=0}^n \\binom{n}{k}^2 \\binom{n+k}{k}^2\\) (recurrence: \\((n+1)^3 a_{n+1} - (2n+1)(17n^2+17n+5)a_n + n^3 a_{n-1} = 0\\)). Zagier's interpolation: \\(A(t) = \\sum_{n\\ge0} a_n t^n\\) (or a shifted/generating variant) evaluated at special \\(t\\) yields \\(L(f,2)\\) for a weight-4 modular form \\(f\\) (e.g., associated to elliptic curve of conductor 37, \\(L(f,2) = \\frac{4\\pi^2}{37} \\cdot \\text{(rational)}\\)). The six sporadic sequences (Zagier's list: \\(A,B,C,D,E,F\\) with parameters \\((a,b,c)\\) in the recurrence \\(n^3 u_n = (a n^2 + b n + c) u_{n-1} - n^3 u_{n-2}\\)) all have interpolations expressible as \\(L(f,2)\\) for weight-4 modular forms with rational coefficients. | CONNECTION: Weight-4 mod\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/58pj2cagjjbnk.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23431162",
  "fulltext_url": null,
  "id": "58pj2cagjjbnk",
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  "landing_url": "https://zenodo.org/records/23431162",
  "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/",
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  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58pj2cagjjbnk.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:22:03Z",
      "native_id": "23431162",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23431162"
    }
  ],
  "subjects": [],
  "title": "Modular L-Values Link Apéry Numbers to Sporadic Sequences — E8 Intelligence Research",
  "title_text": "Modular L-Values Link Apéry Numbers to Sporadic Sequences — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-31T12:22:03Z",
  "url": "https://research.draconitic.com/paper/58pj2cagjjbnk",
  "venue": "Zenodo",
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}