{
  "abstract": "We construct a deterministic Farey-boundary algorithm converting a cyclic prefix table for an element of $\\mathsf T$ into a word in addressed boundary flips. The reduction uses rational boundary pairs and cyclic order, with a marked edge determining the residual modular correction. Its unmarked stage uses at most twice the minimum number of diagonal exchanges. For input size $s$, the complete output has $O(s)$ factors, encoded length $O(s^2)$, and running time $O(s^3)$. Adjoining shuffles extends the construction to $\\mathsf V$ with polynomial bounds. We also give explicit boundary generating sets and their local flip--shuffle relations. Changes of generators in the Lochak--Schneps and Bleak--Quick presentations yield a two-flip presentation of $\\mathsf T$ and a presentation of $\\mathsf V$ with two flips, one shuffle, and nine relations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07293",
  "author_total": 1,
  "authors": [
    {
      "name": "Ayberk Zeytin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dqwm6f37mywzx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07293",
  "fulltext_url": null,
  "id": "dqwm6f37mywzx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07293",
  "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.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7220909796",
  "pdf_url": "https://arxiv.org/pdf/2610.07293",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dqwm6f37mywzx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07293",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07293"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Boundary Algorithms for Thompson Groups",
  "title_text": "Boundary Algorithms for Thompson Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/dqwm6f37mywzx",
  "venue": "arXiv",
  "versions": []
}