{
  "abstract": "FINDING: The search results are largely pedagogical (introductory congruence lectures) and one recent arXiv paper on Ramanujan-type congruences for 4,6-regular partitions — no direct McKay-Thompson series material surfaced. The core mathematical content is the existence of infinite families of congruences for partition functions \\( b_4(n) \\) and \\( b_6(n) \\) modulo primes \\( m \\), with explicit examples.\n\nMATH: - For \\( b_4(n) \\) (4-regular partitions): congruences exist modulo primes \\( m \\geq 2 \\), infinitely many families. - For \\( b_6(n) \\) (6-regular partitions): congruences modulo primes \\( m \\geq 5 \\), infinitely many families. - The generating functions are modular forms of half-integral weight; congruences arise from the action of Hecke operators on spaces of cusp forms. - Explicit examples (from the paper, not shown in the search snippet) would involve specific primes \\( m \\) and arithmetic progressions \\( an+b \\) such that \\( b_k(an+b) \\equiv 0 \\pmod{m} \\). - No co\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9g7ngsyaw3jn9.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23526430",
  "fulltext_url": null,
  "id": "9g7ngsyaw3jn9",
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  "landing_url": "https://zenodo.org/records/23526430",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
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  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9g7ngsyaw3jn9.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:48Z",
      "native_id": "23526430",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23526430"
    }
  ],
  "subjects": [],
  "title": "Congruence Families for 4- and 6-Regular Partitions — E8 Intelligence Research",
  "title_text": "Congruence Families for 4- and 6-Regular Partitions — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:48Z",
  "url": "https://research.draconitic.com/paper/9g7ngsyaw3jn9",
  "venue": "Zenodo",
  "versions": []
}