{
  "abstract": "Intertwined complete projective experiments share outcomes, motivating the search for a common spectral labeling across contexts. Strong coloring tests whether complete contexts admit one context-independent nondegenerate spectrum; when that labeling exists, chromatic separability tests which event distinctions it preserves. We distinguish these questions from ordinary Kochen--Specker statelessness, geometric realizability, event-order representation, and Born-probability models. A state extends to a strong d-coloring exactly when deletion of its support leaves a (d-1)-colorable graph. Faithful real 17- and 21-ray restrictions of completed Yu--Oh have separating ordinary states but forced color identities; one quantum preparation requires exactly 1/9 nonextendable weight despite admitting an ordinary-state model. Independent Hermitian projection arguments correct earlier inferences from a chromatic gap to statelessness or nonrealizability. Hesse's complex 37-ray example separates real and complex geometry and has exact state-family minima 6/7/18 for three representation requirements. A rational two-plane construction gives a linear real 65-ray example with 393,216 states and explicit event-order and probability failures. General and specified ancestry results distinguish geometric KS extensions from abstract chromatic-to-stateless constructions. Detailed enumerations, regenerated state certificates, and extended proofs are supplementary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.04289",
  "author_total": 1,
  "authors": [
    {
      "name": "Karl Svozil"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdf82ct31hqna.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.04289",
  "fulltext_url": null,
  "id": "cdf82ct31hqna",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.04289",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7167639611",
  "pdf_url": "https://arxiv.org/pdf/2607.04289",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdf82ct31hqna.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2607.04289",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.04289"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Chromatic Constraints on Quantum Observables: Gaps, Contextuality, and Separability",
  "title_text": "Chromatic Constraints on Quantum Observables: Gaps, Contextuality, and Separability",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/cdf82ct31hqna",
  "venue": "arXiv",
  "versions": []
}