{
  "abstract": "The moving sofa problem asks for the largest planar set that can pass through a unit-width right-angled hallway. Gerver's 1992 construction remains the largest explicit example, but its defining switching parameters, continuum of supporting hallways, and contact topology involve transcendental equations and global inequalities. We give a reproducible exact-rational certification of the construction. A strict four-dimensional Krawczyk inclusion encloses the reduced switching system, while an independent twenty-two-dimensional Krawczyk calculation verifies Romik's full matching and contact equations in an explicit rational box. Exact interval propagation through the five analytic phases proves the support identities, global half-plane constraints, inner-wall separation, niche topology, oriented contacts, injectivity, and area bounds. From the certified support functions we identify every supporting hallway as L_t=x(t)+R_tL. For G=K_0\\setminus\\mathcal N(K_0) we prove directly that G is nonempty, closed, and connected and that Φ_t(q)=R_{-t}(q-x(t)) is a continuous path in SE(2) carrying G through the hallway, with the correct initial and final arms. We further identify G with Romik's reconstruction of Gerver's classical eighteen-piece sofa. The deterministic companion verifier uses only Python's standard library and exact rational arithmetic. As a consequence, the Gerver-specific geometric hypotheses in Baek's recent variational framework are rigorously certified; we also clarify the one-sided tangent-speed convention at two contact-curve junctions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13955",
  "author_total": 1,
  "authors": [
    {
      "name": "Dawid Trela"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/61p66rg63m1bn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13955",
  "fulltext_url": null,
  "id": "61p66rg63m1bn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13955",
  "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",
      "cs.CG"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2608|Mathematics and Applications"
    ]
  ],
  "openalex": "W7221802207",
  "pdf_url": "https://arxiv.org/pdf/2610.13955",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/61p66rg63m1bn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.13955",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13955"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Certified Geometry and Admissible Motion of Gerver's Sofa",
  "title_text": "Certified Geometry and Admissible Motion of Gerver's Sofa",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/61p66rg63m1bn",
  "venue": "arXiv",
  "versions": []
}