{
  "abstract": "FINDING: The E8 lattice's kissing number (240) and its theta series are governed by modular forms, specifically the Eisenstein series E₄(τ), whose coefficients are the divisor function σ₃(n) — linking exceptional root systems to SL(2,Z) symmetry and multiple zeta values. | MATH: E8 theta series: Θ_E8(τ) = E₄(τ) = 1 + 240 Σ_{n≥1} σ₃(n) qⁿ, where q = e^{2πiτ}, σ₃(n) = Σ_{d|n} d³. Kissing number = 240 = coefficient of q¹. E₄ transforms under SL(2,Z): E₄((aτ+b)/(cτ+d)) = (cτ+d)⁴ E₄(τ). Multiple Eisenstein series generalize this to higher weight and depth, with regularized values connecting to multiple zeta values (MZVs) at weight 2k. | CONNECTION: 240 = 2⁴·3·5; ratio 240/360 = 2/3 (base-60 compatible). The E8 root system has 240 roots, each with norm² = 2; the Weyl group order is 696,729,600. The golden ratio φ = 1.618 appears in E8's Coxeter plane projection (vertices project to rings with φ-related radii). The kissing number 240 relates to the 8-dimensional sphere packing density π⁴/384\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/apyg8gz2z3tnn.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23464895",
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  "id": "apyg8gz2z3tnn",
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  "landing_url": "https://zenodo.org/records/23464895",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/apyg8gz2z3tnn.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:51Z",
      "native_id": "23464895",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23464895"
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  "subjects": [],
  "title": "E8 Lattice's Kissing Number and Theta Series Linked to Modular Forms and SL(2,Z) Symmetry — E8 Intelligence Research",
  "title_text": "E8 Lattice's Kissing Number and Theta Series Linked to Modular Forms and SL(2,Z) Symmetry — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:51Z",
  "url": "https://research.draconitic.com/paper/apyg8gz2z3tnn",
  "venue": "Zenodo",
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}