{
  "abstract": "FINDING: Spontaneous symmetry breaking (SSB) in infinite systems produces universal corrections to Wigner-Eckart (WE) relations, governed by Goldstone modes rather than group-theoretic Clebsch-Gordan coefficients alone. | MATH: Standard WE: ⟨α',j'||T^(k)||α,j⟩ = (reduced matrix element) × CG coefficient. SSB correction (arXiv:2007.03539): For broken generators Q_a, the correction to matrix elements scales as ⟨β|δQ_a|α⟩ / (energy gap Δ) — specifically, corrections are proportional to 1/Δ (Goldstone gap → 0 in infinite volume), and involve the *symmetry-breaking order parameter* v = ⟨0|φ|0⟩. The exact form: ⟨f|T^(k)_q|i⟩_SSB = ⟨f|T^(k)_q|i⟩_WE + Σ_a (⟨f|[Q_a,T^(k)_q]|i⟩ × ⟨0|φ_a|0⟩)/(E_f - E_i) — with the sum over broken generators a. Key constants: No new fundamental constants, but the *ratio* of correction to leading term scales as (v/Λ)^2 where Λ is the UV cutoff — a hierarchy ratio. | CONNECTION: The correction term's structure mirrors the *root system* of the broken group: broken ge\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/7mbap7744d8ht.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587199",
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  "id": "7mbap7744d8ht",
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  "landing_url": "https://zenodo.org/records/23587199",
  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7mbap7744d8ht.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:51Z",
      "native_id": "23587199",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23587199"
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  "subjects": [],
  "title": "Goldstone Modes Dictate Universal Corrections to Wigner-Eckart Relations — E8 Intelligence Research",
  "title_text": "Goldstone Modes Dictate Universal Corrections to Wigner-Eckart Relations — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:51Z",
  "url": "https://research.draconitic.com/paper/7mbap7744d8ht",
  "venue": "Zenodo",
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}