{
  "abstract": "We determine the minimum number of directional commands needed to solve alevel of Order of the Sinking Star, modeled as a crystal-exchangepuzzle on an 11*11 board. A command swapsthe player with the nearest crystal in the selected row or column, regardlessof distance; only an empty ray permits an ordinary unit walk. Two gates admitthe player to the exit exactly while all sixteen crystals occupy their targetcells. We give an explicit 93-command solution and exclude every shortersolution by an exact, cost-bounded breadth-first search. The search representsa position by its seventeen occupied cells and one active cell. Its admissibleheuristic partitions command costs between a compressed core abstraction andresidual motion, strengthened by a necessary activation detour and a cornervisit condition. The completed computation retained 605,349,215 occupied setsand 1,863,925,136 states. We prove the reductions and pruning conditions,describe the exact storage scheme, and provide source code, execution logs,and a reproduction driver. The result is a computer-assisted proof for thespecified instance, with an explicit implementation trust boundary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29493",
  "author_total": 1,
  "authors": [
    {
      "name": "Zilai Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bd1vbze7nr2dx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29493",
  "fulltext_url": null,
  "id": "bd1vbze7nr2dx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29493",
  "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.AI"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1702|Artificial Intelligence in Games"
    ]
  ],
  "openalex": "W7223197973",
  "pdf_url": "https://arxiv.org/pdf/2610.29493",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bd1vbze7nr2dx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29493",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29493"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An Exact 93-Move Solution to a Nonlocal Crystal-Exchange Puzzle",
  "title_text": "An Exact 93-Move Solution to a Nonlocal Crystal-Exchange Puzzle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/bd1vbze7nr2dx",
  "venue": "arXiv",
  "versions": []
}