{
  "abstract": "Snooker folklore holds that no single stroke can pocket all twenty-one object balls. We examine the claim in an explicit model: twenty-two equal disks on a rectangle with six pocket points, under constant rolling deceleration, frictionless collisions with normal restitution, and lossy specular cushions. We exhibit a configuration and a stroke, and prove in interval arithmetic that every stroke in an explicit box around it pockets all twenty-one object balls, so the set of successful strokes has positive measure. That set is a ribbon: every speed from 9.3213 to 12 m/s works, while the certified window of directions is 9.4813e-43 radians wide, a number explained by a first-order analysis of twenty near-grazing collisions. A second configuration, a near-frozen cluster, has a certified window 9.4e-4 radians wide, thirty-nine orders of magnitude wider; its certificate uses Taylor models of degree six. The strokes with a given list of events form a semialgebraic set, and the endpoints of the windows are algebraic numbers. For the regulation opening position we state the corresponding conjecture, and show that if it holds with a regular witness then a finite certified search establishes it.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.12995",
  "author_total": 1,
  "authors": [
    {
      "name": "Avner Kantor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/34rf7agbgb1wp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.12995",
  "fulltext_url": null,
  "id": "34rf7agbgb1wp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.12995",
  "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",
      "cs.CG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7168410051",
  "pdf_url": "https://arxiv.org/pdf/2607.12995",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/34rf7agbgb1wp.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:58Z",
      "native_id": "2607.12995",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.12995"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "One Shot, Twenty-One Balls: A Computer-Assisted Proof of a Single-Stroke Total Clearance in an Idealized Model of Snooker",
  "title_text": "One Shot, Twenty-One Balls: A Computer-Assisted Proof of a Single-Stroke Total Clearance in an Idealized Model of Snooker",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/34rf7agbgb1wp",
  "venue": "arXiv",
  "versions": []
}