{
  "abstract": "We construct a smooth Riemannian metric with strictly positive sectional curvature on \\(S^3\\times S^3\\). Since \\(S^3\\times S^3\\) is even-dimensional and has Euler characteristic zero, our result disproves the positive-curvature case of Hopf's sign conjecture. The metric and the proof were discovered by the Odin Automatic AI Research Agent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11980",
  "author_total": 3,
  "authors": [
    {
      "name": "Shengtao Guo"
    },
    {
      "name": "Ethan X. Fang"
    },
    {
      "name": "Junwei Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e4yxymvde6jg6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11980",
  "fulltext_url": null,
  "id": "e4yxymvde6jg6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11980",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7212693265",
  "pdf_url": "https://arxiv.org/pdf/2609.11980",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e4yxymvde6jg6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.11980",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11980"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Metric with Positive Sectional Curvature on $S^3\\times S^3$",
  "title_text": "A Metric with Positive Sectional Curvature on S^3× S^3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/e4yxymvde6jg6",
  "venue": "arXiv",
  "versions": []
}