{
  "abstract": "FINDING: Topological phase transitions transcend Landau's symmetry-breaking paradigm, requiring non-local order parameters and exhibiting deconfined quantum criticality in 3+1D. | MATH: Landau free energy \\( F = F_0 + a(T-T_c)\\phi^2 + b\\phi^4 \\) fails for topological transitions; topological invariant \\( Q = \\frac{1}{2\\pi}\\oint \\mathbf{A}\\cdot d\\mathbf{k} \\) (Chern number) replaces local order parameter; deconfined criticality involves emergent gauge fields with coupling \\( g \\sim e^{2\\pi i/N} \\) for \\( N \\)-component matter; non-abelian transitions in 3+1D require higher-form symmetries \\( U(1)^{[p]} \\) with \\( p \\)-dimensional charged objects. | CONNECTION: Topological order maps to **root systems** — e.g., \\( A_n \\) (SU(n+1)) and \\( D_n \\) (SO(2n)) Lie algebra structures encode braiding statistics; fractionalized excitations carry quantum dimensions \\( d_\\alpha = \\frac{\\sin(\\pi/(k+2))}{\\sin(\\pi/(k+2))} \\) (Fibonacci anyons: \\( d = \\phi = 1.618 \\), golden ratio appears in \\( k=3 \\) S\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "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/bxr0vyz7vd3n8.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635525",
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  "id": "bxr0vyz7vd3n8",
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  "language": "eng",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bxr0vyz7vd3n8.ris",
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      "first_seen": "2026-11-08T12:21:54Z",
      "native_id": "23635525",
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  "title": "Topological Phase Transitions Beyond Landau: Deconfined Quantum Criticality in 3+1D — E8 Intelligence Research",
  "title_text": "Topological Phase Transitions Beyond Landau: Deconfined Quantum Criticality in 3+1D — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:54Z",
  "url": "https://research.draconitic.com/paper/bxr0vyz7vd3n8",
  "venue": "Zenodo",
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