{
  "abstract": "FINDING: The CHSH-3 inequality extends the standard CHSH framework to three measurement settings per party, with quantum violations computable via semidefinite programming; the Hilbert space structure underpinning these violations is the tensor product of local Hilbert spaces, with singular values of the correlation matrix determining maximal violation bounds. | MATH: Standard CHSH: \\(S = \\langle AB \\rangle + \\langle AB' \\rangle + \\langle A'B \\rangle - \\langle A'B' \\rangle \\leq 2\\) (local), \\(S_{\\text{quantum}} \\leq 2\\sqrt{2} \\approx 2.828\\). CHSH-3 generalizes to three settings per party, with the quantum bound given by the maximal singular value of the correlation tensor \\(T_{ij} = \\langle A_i \\otimes B_j \\rangle\\), i.e., \\(\\|T\\|_\\infty \\leq \\sqrt{3}\\) for the specific CHSH-3 form (Tsirelson-type bound). The Hilbert space is \\(\\mathcal{H}_A \\otimes \\mathcal{H}_B\\), and the singular value decomposition of the \\(3 \\times 3\\) correlation matrix yields singular values \\(\\sigma_1 \\geq \\si\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/33eyw8whpz79t.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23431333",
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  "id": "33eyw8whpz79t",
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  "landing_url": "https://zenodo.org/records/23431333",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
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  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/33eyw8whpz79t.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:22:00Z",
      "native_id": "23431333",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23431333"
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  ],
  "subjects": [],
  "title": "Quantum Violations of CHSH-3 Inequality via Tensor Product Hilbert Spaces — E8 Intelligence Research",
  "title_text": "Quantum Violations of CHSH-3 Inequality via Tensor Product Hilbert Spaces — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-31T12:22:00Z",
  "url": "https://research.draconitic.com/paper/33eyw8whpz79t",
  "venue": "Zenodo",
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}