{
  "abstract": "Consider the \"snaky\" corridor $K_4 \\subset \\mathbb{R}^3$ from Problem 6.64 of arXiv:2511.02864: a tube of unit-square cross-section whose two right-angle turns lie in perpendicular planes, with a straight middle section of clear length $4$. We exhibit explicit rigid motions of connected bodies through $K_4$ and certify their volumes with the problem's own evaluation pipeline, unmodified, at the tight motion tolerances of its final scoring stage (translation $0.005$, rotation $0.05$ degrees). The certificates give $V^*(K_4) \\ge 1.8355162$ at grid fineness $0.002$ and $V^*(K_4) \\ge 1.8558404$ at grid fineness $0.001$, against the previously reported $1.81$; rerunning the pipeline's published best path under the identical configuration yields $1.8179428$, so every comparison is path against path under one fixed certifier. Three stages produce the record motion: a simple \"staggered twist\" backbone in which the whole 90-degree twist about the tube axis happens inside the second turn; evolutionary (CMA-ES) refinement, including a mixed-fidelity scheme that re-scores each generation's leading candidates on a grid twice as fine and lets those ranks steer recombination; and a gradient polish carried out directly at the finer carve resolution, guarded by periodic rebuilding of the frozen interpolation structure and by a penalty on control-pose spacing. These guards close three documented failure modes in which an optimizer inflates its own objective: frozen-structure inflation, spacing stretch, and exploitation of a coarse grid by optimizing and selecting on it. A staircase-based predictor with two grid bases, anchored by matching grid sensitivity, forecast the certificates to about $0.001$ before the runs. With the companion note's upper bound $V^*(K_4) \\le 3.4083$, the problem now sits in the bracket $1.8558404 \\le V^*(K_4) \\le 3.4083$. All paths, notebooks and certified results are public.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14051",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuzhe Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3488b5rr2han3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14051",
  "fulltext_url": null,
  "id": "3488b5rr2han3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14051",
  "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",
      "1704|Computational Geometry and Mesh Generation"
    ]
  ],
  "openalex": "W7221775654",
  "pdf_url": "https://arxiv.org/pdf/2610.14051",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3488b5rr2han3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14051",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14051"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "New certified lower bounds for the moving sofa problem in a three-dimensional snaky corridor",
  "title_text": "New certified lower bounds for the moving sofa problem in a three-dimensional snaky corridor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/3488b5rr2han3",
  "venue": "arXiv",
  "versions": []
}