{
  "abstract": "Let $K_M \\subset \\mathbb{R}^3$ be the \"snaky\" corridor with unit-square cross-section: an infinite entry arm parallel to the $x$-axis, a middle arm parallel to the $y$-axis whose clear straight section has length $M$, and an infinite exit arm parallel to the $z$-axis, with the two turns lying in the $x$-$y$ and $y$-$z$ planes. Let $V^*(K_M)$ be the supremum of the volumes of connected bodies that can be moved continuously (by rigid motions) from the entry arm to the exit arm while remaining inside $K_M$. We prove $V^*(K_M) \\le 7.8691$ for every $M \\ge 3.53$ (Theorem A); by a sharper analysis of the same mechanism, $V^*(K_M) \\le 4.2862$ for every $M \\ge 2.61$ (Theorem B); and, by replacing the final analytic caps with a certified branch-and-bound computation over the compact family of entry tubes compatible with the forced events, $V^*(K_M) \\le 3.4083$ for every $M > 2.2$ (Theorem C; computer-assisted, in double precision with conservative slack). In particular all three bounds apply to the corridor with $M = 4$ used in Problem 6.64 of Georgiev, Gómez-Serrano, Tao and Wagner (arXiv:2511.02864), and uniformly to every \"turns far apart\" reading of that problem. To the best of our knowledge, this is the first upper bound for the snaky-corridor 3D moving sofa problem; previously not even finiteness of $V^*$ had been recorded. This note proves upper bounds only; combined with the certified lower bound 1.8558404 from the author's separate certification work via the problem's own evaluation pipeline, the state of the problem becomes $1.8558404 \\le V^*(K_4) \\le 3.4083$. Theorems A and B are elementary and self-contained: a first-crossing (elbow) event forces a definite tilt of the body's own entry tube, and Fubini-type chord estimates for tilted tubes cap the volume. Theorem C certifies, by the same forced-event skeleton, the largest corridor volume that any admissible entry tube can carry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14050",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuzhe Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6e78j3zwv88rz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14050",
  "fulltext_url": null,
  "id": "6e78j3zwv88rz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14050",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CG"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7221829095",
  "pdf_url": "https://arxiv.org/pdf/2610.14050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6e78j3zwv88rz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "An upper bound for the three-dimensional moving sofa problem in a snaky corridor",
  "title_text": "An upper bound for the three-dimensional moving sofa problem in a snaky corridor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/6e78j3zwv88rz",
  "venue": "arXiv",
  "versions": []
}