{
  "abstract": "Recently, René Peschmann proved perfect-cuboid nonexistence on 1,072 explicit master-tuple fibers with $\\max(m,n)\\le100$, leaving 968 fibers in the same bounded parameter range. In this paper, I eliminate all 968 remaining fibers. Most fibers fall to fairly short rank-zero or covering arguments, while the final cases need the stronger local-global sieves. Together with Peschmann's theorem this excludes perfect cuboids on all 2,040 admissible fibers with $m\\le100$; the result is still a bounded-fiber theorem rather than a proof of the full perfect-cuboid conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14526",
  "author_total": 1,
  "authors": [
    {
      "name": "Ricky Cipollini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0hq1qp18t6cv9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14526",
  "fulltext_url": null,
  "id": "0hq1qp18t6cv9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14526",
  "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",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.14526",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0hq1qp18t6cv9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14526",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14526"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Elimination of René Peschmann's 968 Remaining Hard Fibers for the Perfect Cuboid Problem",
  "title_text": "Elimination of René Peschmann's 968 Remaining Hard Fibers for the Perfect Cuboid Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/0hq1qp18t6cv9",
  "venue": "arXiv",
  "versions": []
}