{
  "abstract": "We construct an infinite family of solutions to the Mondrian art problem with absolute defect bounded above by $280$, of side lengths $n_0 = 315$, $n_1 = 106785$, and $n_{j+2} = 340n_{j+1} - n_j$, where $n_j$ is congruent to $315 \\pmod{630}$. This absolute bound shows that the minimum defect does not necessarily increase with $n$, providing a counterexample to a conjecture which has been open since the problem's original proposal. Our design is derived from a well-known seven-rectangle dissection over the real quadratic field $\\mathbb{Q}(\\sqrt{19})$, with non-integer side lengths; we tailor the side lengths to be integers via an infinite Pell family. Using the same method, we devise a second family with defect $560$ that contains infinitely many side lengths which are divisible by any given positive integer, implying that for any $k$ there are infinitely many side lengths $n \\equiv 0 \\pmod{k}$ with defect bounded above by $560$. This constant bound offers a dramatic improvement on the previous quadratic bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19193",
  "author_total": 2,
  "authors": [
    {
      "name": "Cooper O'Kuhn"
    },
    {
      "name": "Freeman Slaughter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9hs7tn707s38m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19193",
  "fulltext_url": null,
  "id": "9hs7tn707s38m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19193",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2209|Optimization and Packing Problems"
    ]
  ],
  "openalex": "W7222337813",
  "pdf_url": "https://arxiv.org/pdf/2610.19193",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9hs7tn707s38m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19193",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19193"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Bounded-Defect Construction for the Mondrian Art Problem",
  "title_text": "A Bounded-Defect Construction for the Mondrian Art Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/9hs7tn707s38m",
  "venue": "arXiv",
  "versions": []
}