{
  "abstract": "FINDING: The search returned no primary source establishing a \"quantum parameter modular inversion q → q⁻¹ ↔ affine simple reflection s₀\" theorem; results are adjacent (Q-systems, quantum affine/loop algebras, affine quantization, geometric Langlands) but none directly prove the claimed correspondence. | MATH: The relevant algebraic skeleton is: quantum parameter q ∈ ℂ*, inversion q ↦ q⁻¹; affine Weyl group generated by simple reflections s_i (i=0,…,n); Langlands dual Ǧ with root system Φ^∨; the affine reflection s₀ acts on the affine root lattice by w(α) = w(α) − ⟨α, α_i^∨⟩α_i. The q ↔ q⁻¹ symmetry is the standard *bar involution / Chevalley involution* on U_q(ĝ), not a new identity. | CONNECTION: Root systems (A_n, D_n, E_6,7,8) and affine extensions are crystallographic — their Cartan matrices have integer entries and admit the Coxeter/reflection structure. The q ↔ q⁻¹ map is an involution of the Dynkin diagram (a graph automorphism), which for simply-laced types is trivial, for B_n\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/335h9wz9jhysn.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23658667",
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  "id": "335h9wz9jhysn",
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  "landing_url": "https://zenodo.org/records/23658667",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/335h9wz9jhysn.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:33Z",
      "native_id": "23658667",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23658667"
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  ],
  "subjects": [],
  "title": "No Primary Source for Quantum Parameter Inversion ↔ Affine Simple Reflection Correspondence — E8 Intelligence Research",
  "title_text": "No Primary Source for Quantum Parameter Inversion ↔ Affine Simple Reflection Correspondence — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:33Z",
  "url": "https://research.draconitic.com/paper/335h9wz9jhysn",
  "venue": "Zenodo",
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}