{
  "abstract": "FINDING: Sine-Gordon model appears across superconductors, spin ladders, pendulums, and integrable defects — but the search results are pedagogical/demonstrative, not a specific new research breakthrough on zigzag ladders with unequal exchange. | MATH: Core equation: \\(u_{tt} - u_{xx} + \\sin u = 0\\) (1+1D sine-Gordon). Bosonization maps spinful Tomonaga-Luttinger liquid to sine-Gordon with coupling \\(g \\propto \\cos(\\sqrt{2}\\phi)\\) for backscattering; spin-charge separation yields charge boson \\(\\phi_c\\) and spin boson \\(\\phi_s\\), with zigzag ladder frustration producing a gap via \\(\\cos(\\sqrt{8}\\phi_s)\\) terms. Defect construction uses quantum affine \\(sl_2\\) representations (q-oscillators), generalising Q-operators. | CONNECTION: The sine-Gordon potential \\(\\cos u\\) has period \\(2\\pi\\) — a root-system periodicity of \\(A_1\\). Soliton/kink solutions interpolate between vacua \\(u=0\\) and \\(u=2\\pi\\), with kink mass \\(M = 8\\sqrt{\\lambda}\\) (for \\(\\lambda=1\\)). Breather frequency \\(\\omega =\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/eexs0drd0q18b.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587048",
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  "id": "eexs0drd0q18b",
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  "landing_url": "https://zenodo.org/records/23587048",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eexs0drd0q18b.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:53Z",
      "native_id": "23587048",
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  "subjects": [],
  "title": "Sine-Gordon Universality Across Physical Systems: A Pedagogical Review — E8 Intelligence Research",
  "title_text": "Sine-Gordon Universality Across Physical Systems: A Pedagogical Review — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:53Z",
  "url": "https://research.draconitic.com/paper/eexs0drd0q18b",
  "venue": "Zenodo",
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}