{
  "abstract": "We prove that, for any $f:S^2\\to S^1$ and any $\\varepsilon>0$, there exist orthogonal vectors $x,y\\in S^2$ such that the length of the shortest arc between $f(x)$ and $f(y)$ is at most $π/2 +\\varepsilon$. This proves a conjecture of Ghebleh from 2007 that the circular chromatic number of the real orthogonality graph is equal to four.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22680",
  "author_total": 1,
  "authors": [
    {
      "name": "Jonathan A. Noel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7c97bw02k3kf9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22680",
  "fulltext_url": null,
  "id": "7c97bw02k3kf9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22680",
  "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",
      "math.MG"
    ],
    [
      "openalex",
      "2608|Mathematics and Applications"
    ]
  ],
  "openalex": "W7214007936",
  "pdf_url": "https://arxiv.org/pdf/2609.22680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7c97bw02k3kf9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22680"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Orthogonal Pairs in Maps from the Sphere to the Circle",
  "title_text": "Orthogonal Pairs in Maps from the Sphere to the Circle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/7c97bw02k3kf9",
  "venue": "arXiv",
  "versions": []
}