{
  "abstract": "FINDING: Complete 2-descent computes the Mordell-Weil group E(Q) via the exact sequence 0 → E(Q)/2E(Q) → Sel²(E/Q) → Sha(E/Q)[2] → 0, with quartic models providing the explicit computational realization. | MATH: For E: y² = x³ + Ax + B, a 2-cover is a quartic Y² = aX⁴ + bX² + c; the 2-Selmer group is cut out by local solubility conditions at all places; E(Q)/2E(Q) ≅ image of Sel² under the descent map; rank r = dim_{F₂}(Sel²) − dim_{F₂}(Sha[2]) − 2 (for full 2-torsion). Torsion subgroup E(Q)_tors ∈ {Z/nZ : n ≤ 10, n=12} ∪ {Z/2Z × Z/2nZ : n ≤ 4} (Mazur). | CONNECTION: The quartic model Y² = quartic(X) is a genus-1 curve; its Jacobian is E. The 2-torsion lattice E[2] ≅ (Z/2)² sits inside the Mordell-Weil lattice E(Q) with the Néron-Tate height pairing — a positive-definite lattice structure. Rank-29 curve (Elkies–Klagsbrun 2024) pushes the lattice rank record; no geometric-harmony constants (0.618, 1.618, base-60) appear intrinsically in 2-descent — the relevant arithmetic is F₂-linear a\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/9v5c6c42tc6wc.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23658977",
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  "id": "9v5c6c42tc6wc",
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  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9v5c6c42tc6wc.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:30Z",
      "native_id": "23658977",
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      "url": "https://zenodo.org/records/23658977"
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  "subjects": [],
  "title": "Complete 2-Descent via Quartic Models for Mordell-Weil and Selmer Groups — E8 Intelligence Research",
  "title_text": "Complete 2-Descent via Quartic Models for Mordell-Weil and Selmer Groups — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:30Z",
  "url": "https://research.draconitic.com/paper/9v5c6c42tc6wc",
  "venue": "Zenodo",
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}