{
  "abstract": "FINDING: The search results are pedagogically shallow (YouTube tutorials on linear Diophantine equations and orbit-stabilizer) with one substantive research paper on Diophantine properties of nilpotent Lie groups — no direct result on \"Weyl group orbit termination\" or \"minimal pair\" is found.\n\nMATH: - Linear Diophantine: \\( ax+by=c \\) solvable iff \\( \\gcd(a,b) \\mid c \\). General solution: \\( x = x_0 + \\frac{b}{g}t,\\; y = y_0 - \\frac{a}{g}t \\), \\( g=\\gcd(a,b) \\). - Orbit-Stabiliser (finite): \\( |G| = |\\mathrm{Orb}(x)| \\cdot |\\mathrm{Stab}(x)| \\). - Diophantine Lie group (arXiv:1307.1489): For finitely generated \\( \\Gamma \\subset G \\), exists \\( \\beta>0 \\) such that for non-trivial \\( \\gamma \\in B_\\Gamma(n) \\), \\( d(\\gamma, e) > |B_\\Gamma(n)|^{-\\beta} \\). The group is Diophantine if this holds for all \\( k \\) (likely all generating sets).\n\nCONNECTION: - The Diophantine property for Lie groups is a metric analogue of *lattice spacing* — it quantifies how far discrete subgroups\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/3vv6n8q2mwyy5.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23410009",
  "fulltext_url": null,
  "id": "3vv6n8q2mwyy5",
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  "landing_url": "https://zenodo.org/records/23410009",
  "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,
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  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3vv6n8q2mwyy5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:23Z",
      "native_id": "23410009",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23410009"
    }
  ],
  "subjects": [],
  "title": "Weyl Group Orbits and Minimal Pairs: A Literature Gap — E8 Intelligence Research",
  "title_text": "Weyl Group Orbits and Minimal Pairs: A Literature Gap — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:20Z",
  "url": "https://research.draconitic.com/paper/3vv6n8q2mwyy5",
  "venue": "Zenodo",
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}