{
  "abstract": "Examples and counterexamples define the boundaries of mathematical propositions, test foundational conjectures, and resolve open structural problems in abstract algebra. In loop theory, an Osborn loop is a crucial generalization of a Moufang loop satisfying a specialized variable-sandwiching identity. While small finite non-associative examples are known, constructing large examples of proper Osborn loops (loops that are neither conjugacy closed nor Moufang) remains a computational bottleneck. In this paper, we establish an efficient framework for generating large proper Osborn loops by taking the direct product of non-associative conjugacy closed (CC) loops and Moufang loops. We outline the boundary constraints necessary to prevent structural collapse into sub-varieties and provide explicit examples up to order 2025 validated via the GAP package \\texttt{LOOPS}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09176",
  "author_total": 1,
  "authors": [
    {
      "name": "Muhammad Shah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2ys9500tn578.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09176",
  "fulltext_url": null,
  "id": "b2ys9500tn578",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09176",
  "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",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2608|Mathematics and Applications"
    ]
  ],
  "openalex": "W7212108771",
  "pdf_url": "https://arxiv.org/pdf/2609.09176",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2ys9500tn578.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09176",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09176"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Simple Way of Getting Large Examples of Osborn Loops",
  "title_text": "A Simple Way of Getting Large Examples of Osborn Loops",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/b2ys9500tn578",
  "venue": "arXiv",
  "versions": []
}