{
  "abstract": "Three general plane conics admit $184$ complex tangent circles, and it had been conjectured that at most $136$ of them could be real. We construct an explicit strongly general triple of smooth conics over $\\mathbb{Q}$ with exactly $160$ real tangent circles; the same count therefore occurs on a nonempty Euclidean chamber. The construction combines a fourfold splitting theorem for two flagged double-line degenerations with exact Sturm--Tarski, elimination, and interval certificates. We also show that the Grothendieck--Witt-valued count is $92\\mathbb{H}$ and express its real local signs, up to a fixed orientation convention, in terms of curvature differences, residual intersection divisors, and contact normals. The exact-arithmetic code and certificate data are archived in the accompanying repository.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26285",
  "author_total": 4,
  "authors": [
    {
      "name": "Haoyang Liu"
    },
    {
      "name": "Tianle Liu"
    },
    {
      "name": "Guorui Xu"
    },
    {
      "name": "Fan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b22q3pbgdb73t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26285",
  "fulltext_url": null,
  "id": "b22q3pbgdb73t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26285",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214100254",
  "pdf_url": "https://arxiv.org/pdf/2609.26285",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b22q3pbgdb73t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26285",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26285"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Two-flag degenerations and real circles tangent to three conics",
  "title_text": "Two-flag degenerations and real circles tangent to three conics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/b22q3pbgdb73t",
  "venue": "arXiv",
  "versions": []
}