{
  "abstract": "Amplituhedra are semi-algebraic sets of fundamental importance in particle physics. Their discovery initiated the field of Positive Geometry. We settle a central conjecture in this field: we show that the $m=2$ amplituhedron is a positive geometry. Our main new tool is a Hodge-theoretic criterion for being a positive geometry, connecting the work of Brown--Dupont with the original setup of Arkani-Hamed--Bai--Lam.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27903",
  "author_total": 3,
  "authors": [
    {
      "name": "Joris Koefler"
    },
    {
      "name": "Dmitrii Pavlov"
    },
    {
      "name": "Rainer Sinn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c11t9c3qvr1th.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27903",
  "fulltext_url": null,
  "id": "c11t9c3qvr1th",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27903",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223159099",
  "pdf_url": "https://arxiv.org/pdf/2610.27903",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c11t9c3qvr1th.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27903",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27903"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The $m=2$ amplituhedron is a positive geometry",
  "title_text": "The m=2 amplituhedron is a positive geometry",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/c11t9c3qvr1th",
  "venue": "arXiv",
  "versions": []
}