{
  "abstract": "We introduce the Ceiling Continued Fractions (FCT) framework for constructing three-term Egyptian fraction representations in the Erdős--Straus conjecture from divisors of the shifted integers \\(p+i\\). A probabilistic model for their arithmetic structure leads to an asymptotic upper-bound heuristic for cumulative failure. The resulting bound is summable, and the first Borel--Cantelli lemma assigns probability zero to the event that infinitely many primes survive the full FCT block. Computational tests on \\(10^9\\) Mordell-type primes at each of the scales \\(10^{17}\\), \\(10^{52}\\), and \\(10^{131}\\) found no counterexamples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.04551",
  "author_total": 1,
  "authors": [
    {
      "name": "Andres Ventas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ecnr0tzsqyxe8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.04551",
  "fulltext_url": null,
  "id": "ecnr0tzsqyxe8",
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  "landing_url": "https://arxiv.org/abs/2605.04551",
  "language": null,
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  "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.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7160493909",
  "pdf_url": "https://arxiv.org/pdf/2605.04551",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ecnr0tzsqyxe8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2605.04551",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.04551"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Ceiling Continued Fraction Approach to the Erdős-Straus Conjecture: Heuristic finiteness of counterexamples",
  "title_text": "A Ceiling Continued Fraction Approach to the Erdős-Straus Conjecture: Heuristic finiteness of counterexamples",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/ecnr0tzsqyxe8",
  "venue": "arXiv",
  "versions": []
}