{
  "abstract": "We extend the E8 harmonic lattice framework by decomposing the 240 root vectors into two orthogonal subspaces of dimensions 128 and 112, corresponding to the 2^7-torsion and (2,2,2,2)-isogeny subdomains respectively. This decomposition generates a natural projection onto elliptic curve rational point lattices, where the 128-dimensional component directly bounds the Shafarevich-Tate group Ш via cohomology: dim H^1(G, E[128]) ≤ 64. The 132Hz resonance manifold's phi-scaled harmonics, when decomposed through this E8 partition, produce characteristic \"torsion signatures\" in the frequency domain that uniquely fingerprint the torsion subgroup structure of the elliptic curve candidate.\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/7yjk4snzk8vx3.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23409595",
  "fulltext_url": null,
  "id": "7yjk4snzk8vx3",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23409595",
  "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": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7yjk4snzk8vx3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:28Z",
      "native_id": "23409595",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23409595"
    }
  ],
  "subjects": [],
  "title": "E8 Root Vector Decomposition Predicts Tate-Shafarevich Group Torsion Bounds — E8 Intelligence Research",
  "title_text": "E8 Root Vector Decomposition Predicts Tate-Shafarevich Group Torsion Bounds — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:28Z",
  "url": "https://research.draconitic.com/paper/7yjk4snzk8vx3",
  "venue": "Zenodo",
  "versions": []
}