{
  "abstract": "We describe a finite computational verification of Markov Uniqueness Conjecture for normalized positive integer solutions of $x^2+y^2+z^2=3xyz$ with $z \\leq 10^{500000}$. The archived run reports $239\\,536\\,376\\,556$ triples with distinct maximal coordinates.The method combines a disjoint tree decomposition, certified fixed-point range bounds, a deterministic 48-bit candidate screen,and replay modulo $2^{128}$. We give the mathematical justification and a reproducibility procedure covering package checks,retained-data auditing, and a full rerun. The conclusion depends on correct execution of the exhaustive screen and replay; the retained audit does not regenerate the deleted screening buckets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01007",
  "author_total": 2,
  "authors": [
    {
      "name": "Hu Tan"
    },
    {
      "name": "Ying Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/841ta33978gd3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01007",
  "fulltext_url": null,
  "id": "841ta33978gd3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01007",
  "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",
      "math.GM"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01007",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/841ta33978gd3.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01007",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01007"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "A Computational Verification of the Markov Uniqueness Conjecture for $z\\leq 10^{500000}$",
  "title_text": "A Computational Verification of the Markov Uniqueness Conjecture for z≤ 10^500000",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/841ta33978gd3",
  "venue": "arXiv",
  "versions": []
}