{
  "abstract": "This paper investigates generalized self-referential decimal power tower identities of the form \\sqrt[k]{T(n)} = n, extending the classic 262144 square-root puzzle to higher root indices k > 2. By leveraging prime valuations and algebraic reductions, we show that non-trivial solutions reduce to power base representations, avoiding intractable tower evaluations. Under strict individual digit constraints, we prove the existence of exact non-trivial solutions with colossal indices exceeding 10^{100} (such as n = 4294967296 and n = 3433683820292512484657849089281) and establish negative search bounds up to 10,000 digits. Full Python search scripts and data verification are included.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Josue Amaro Aleman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dsb3yq0r59fa8.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23463514",
  "fulltext_url": null,
  "id": "dsb3yq0r59fa8",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23463514",
  "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,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23463514/files/Power_Towers.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dsb3yq0r59fa8.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:53Z",
      "native_id": "23463514",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23463514"
    }
  ],
  "subjects": [],
  "title": "Self-Referential Decimal Power Towers and Integer Roots: Algebraic Reductions, Combinatorial Variants, and Certified Computational Search",
  "title_text": "Self-Referential Decimal Power Towers and Integer Roots: Algebraic Reductions, Combinatorial Variants, and Certified Computational Search",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:53Z",
  "url": "https://research.draconitic.com/paper/dsb3yq0r59fa8",
  "venue": "Zenodo",
  "versions": []
}