{
  "abstract": "We study smooth fibred two-knots whose fundamental quandle is the prism quandle of order fifty-six. The candidates arise from framed circle surgery along a section of a mapping torus, using the two possible normal-framing classes. We prove that both ambient homotopy four-spheres are diffeomorphic to the standard four-sphere. The candidates have the same knot group and diffeomorphic exteriors, but they are inequivalent even as topological pairs. Every smooth fibred realization of this quandle in a homotopy four-sphere is equivalent, up to knot orientation, to exactly one of these two knots. Standardness follows from a Whitehead-link model for the orbit orbifold together with circle-action recognition. Inequivalence is detected by the third cyclic branched covers, on which a spin-bordism secondary invariant takes different values. Thus the parameter-seven prism quandle admits smooth fibred realizations in the standard four-sphere.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29839",
  "author_total": 1,
  "authors": [
    {
      "name": "Michal Jablonowski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53wmz6nccpc8n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29839",
  "fulltext_url": null,
  "id": "53wmz6nccpc8n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29839",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214292586",
  "pdf_url": "https://arxiv.org/pdf/2609.29839",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53wmz6nccpc8n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2609.29839",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29839"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Fibred realizations of the prism quandle $P_7$ in the standard four-sphere",
  "title_text": "Fibred realizations of the prism quandle P_7 in the standard four-sphere",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/53wmz6nccpc8n",
  "venue": "arXiv",
  "versions": []
}