{
  "abstract": "We introduce SemiBase, a project that computes and formally certifies finite identity bases for small semigroups. Deciding finite basability is undecidable for finite algebras and remains open for finite semigroups. The task requires a proof that a candidate basis is complete, or a proof that none exists, rather than a single first-order validity query. LLM-guided agents search for these proofs; a referee agent rebuilds them from source, and the Lean kernel checks the resulting corpus in a final audit. Humans choose targets and approve final outcomes. We certify every semigroup of order at most 6: all 1309 semigroups of order at most 5 and all 15973 of order 6, including proofs that the four known nonfinitely based semigroups have no finite basis. The bases for order 6 define 505 distinct varieties, whose inclusion order Vampire determines except for four pairs. The resulting catalogue is a machine-checked account of results scattered across the literature and a tested foundation for order 7.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02500",
  "author_total": 5,
  "authors": [
    {
      "name": "João Araújo"
    },
    {
      "name": "Jan Hůla"
    },
    {
      "name": "Mikoláš Janota"
    },
    {
      "name": "Edmond W. H. Lee"
    },
    {
      "name": "Bartosz Naskręcki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90rd2rvzaeska.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02500",
  "fulltext_url": null,
  "id": "90rd2rvzaeska",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02500",
  "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",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7220444619",
  "pdf_url": "https://arxiv.org/pdf/2610.02500",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/90rd2rvzaeska.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.02500",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02500"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Proving at Scale for Universal Algebra",
  "title_text": "Proving at Scale for Universal Algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/90rd2rvzaeska",
  "venue": "arXiv",
  "versions": []
}