{
  "abstract": "The contextuality degree of a set of Pauli contexts is the least number of contexts that every noncontextual $\\pm1$ assignment violates. For the four-qubit hyperbolic quadric $\\mathcal{Q}^{+}(7,2)$, with $135$ points and $1575$ lines as contexts, Muller et al. conjectured from heuristic searches that the degree is $315$ and that the violated contexts of every optimal assignment form a dual polar space $DW(5,2)$. We prove both conjectures. The lower bound has a short proof by hand: every doily ($GQ(2,2)$) of the quadric contains ten Peres-Mermin grids covering each of its lines four times, so every assignment violates at least three of its fifteen lines, and averaging over the doilies gives $1575/5=315$. The equality case is local: an assignment is optimal exactly when it violates one ruling of one grid in every doily. Using this as a SAT encoding, we show that there are exactly $240$ optimal violated sets, one orbit of $\\mathrm{O}^+(8,2)$, each isomorphic to $DW(5,2)$. The same argument gives the first lower bounds $\\lceil L/5\\rceil$ for all quadrics with $L$ lines in $N\\ge4$ qubits. The degree theorem is kernel-checked in Lean 4, and the completeness of the enumeration is certified by a DRAT proof checked by the verified checker cake_lpr.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26465",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhengyu Li"
    },
    {
      "name": "Amandeep Gupta"
    },
    {
      "name": "Vijay Ganesh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/762vg2929131k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26465",
  "fulltext_url": null,
  "id": "762vg2929131k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26465",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7223041481",
  "pdf_url": "https://arxiv.org/pdf/2610.26465",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/762vg2929131k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.26465",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26465"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Four-Qubit Hyperbolic Quadric Has Contextuality Degree 315",
  "title_text": "The Four-Qubit Hyperbolic Quadric Has Contextuality Degree 315",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/762vg2929131k",
  "venue": "arXiv",
  "versions": []
}