{
  "abstract": "FINDING: Spontaneous symmetry breaking (SSB) and topological order are distinct paradigms; SSB involves a reduced matrix element scaling with inverse volume, while topological order is robust to local perturbations and lacks local order parameters. | MATH: SSB order parameter \\(\\langle \\phi \\rangle \\neq 0\\) in thermodynamic limit; reduced matrix element \\(\\langle \\Omega | \\phi(x) | \\Omega \\rangle \\sim V^{-1/2}\\) for finite volume \\(V\\), vanishing as \\(V \\to \\infty\\). Topological ground state degeneracy \\(D\\) on genus-\\(g\\) surface scales as \\(D = k^g\\) (e.g., \\(\\mathbb{Z}_k\\) gauge theory). | CONNECTION: Topological order connects to modular data and anyonic braiding — fusion rules and \\(S,T\\) matrices satisfying \\(S^2 = (ST)^3 = C\\), with \\(S\\)-matrix elements containing \\(e^{2\\pi i / k}\\) (root-of-unity phases, base-60 compatible via cyclotomic fields). Crystallographic analog: fractional quantum Hall states have filling fractions \\(\\nu = p/q\\) (e.g., 1/3, 2/5) — ratios not golden, b\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": [
    {
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        0
      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/czczykmaedrke.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587025",
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  "id": "czczykmaedrke",
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  "landing_url": "https://zenodo.org/records/23587025",
  "language": "eng",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/czczykmaedrke.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:53Z",
      "native_id": "23587025",
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  "subjects": [],
  "title": "Distinguishing Spontaneous Symmetry Breaking from Topological Order via Volume Scaling — E8 Intelligence Research",
  "title_text": "Distinguishing Spontaneous Symmetry Breaking from Topological Order via Volume Scaling — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:53Z",
  "url": "https://research.draconitic.com/paper/czczykmaedrke",
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