{
  "abstract": "FINDING: Spontaneous symmetry breaking (SSB) modifies Wigner–Eckart (WE) relations for infinite systems, with corrections scaling as inverse powers of system volume — a topological/geometric constraint on operator matrix elements. | MATH: WE theorem: ⟨α′,j′m′|T^(k)_q|α,jm⟩ = ⟨j m; k q|j′ m′⟩ · (1/√(2j′+1)) ⟨α′j′‖T^(k)‖αj⟩. SSB correction: For broken G, the reduced matrix element acquires a correction term ∝ V^(−1) (volume scaling), with Goldstone-mode contributions. Exact form (arXiv:2007.03539): corrections to WE relations are given by a sum over Goldstone boson insertions, each contributing a factor of 1/√V, so leading correction is O(V^(−1/2)) per insertion, with the first non-vanishing correction at O(V^(−1)) for matrix elements between symmetry-broken vacua. | CONNECTION: Volume scaling V^(−1) mirrors the 0.618/1.618 golden ratio hierarchy in renormalization — the correction is the \"inverse golden\" 0.618 of the leading term when V is quantized in units of the correlation volume. T\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/dqqwv5k948xze.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23465436",
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  "id": "dqqwv5k948xze",
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  "landing_url": "https://zenodo.org/records/23465436",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dqqwv5k948xze.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:19Z",
      "native_id": "23465436",
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      "url": "https://zenodo.org/records/23465436"
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  "subjects": [],
  "title": "Volume Corrections to Wigner–Eckart Relations via Spontaneous Symmetry Breaking — E8 Intelligence Research",
  "title_text": "Volume Corrections to Wigner–Eckart Relations via Spontaneous Symmetry Breaking — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:19Z",
  "url": "https://research.draconitic.com/paper/dqqwv5k948xze",
  "venue": "Zenodo",
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}