{
  "abstract": "FINDING: Search results are pedagogical/contextual (videos, LIGO paper) — no direct mathematical result on Sp(2n)/U(n) invariant ring degrees or Langlands dual root system swap is presented. The only concrete mathematical anchor is the symplectic group definition and its role in Hamiltonian mechanics/topological invariants.\n\nMATH: - Symplectic group Sp(2n) preserves antisymmetric bilinear form ω: ω(u,v) = u^T J v, J = [[0, I_n], [-I_n, 0]]. - Invariant ring of Sp(2n) acting on its standard representation has fundamental invariants of degrees 2,4,...,2n (Chevalley-type for symplectic case). - For symmetric space Sp(2n)/U(n), the ring of invariants under U(n) is generated by degrees 2,4,...,2n (same as Weyl group of type C_n). - Langlands dual swap: root system C_n ↔ B_n (dual), but Sp(2n) has type C_n; dual is SO(2n+1) type B_n. No explicit swap data in findings. - LIGO paper (arXiv:2510.17487) uses directional statistics — no symplectic structure.\n\nCONNECTION: - Degrees\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/5k2b92078a6e8.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587104",
  "fulltext_url": null,
  "id": "5k2b92078a6e8",
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  "landing_url": "https://zenodo.org/records/23587104",
  "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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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5k2b92078a6e8.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:52Z",
      "native_id": "23587104",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23587104"
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  ],
  "subjects": [],
  "title": "Symplectic Group Invariants and Langlands Dual: A Search Result Gap — E8 Intelligence Research",
  "title_text": "Symplectic Group Invariants and Langlands Dual: A Search Result Gap — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:52Z",
  "url": "https://research.draconitic.com/paper/5k2b92078a6e8",
  "venue": "Zenodo",
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}