{
  "abstract": "A two-component Bose--Einstein condensate can host a pseudospin Hopf texture coupled to the viscous normal flow of its thermal cloud. Motivated by OpenAI's reported finite-time Navier--Stokes singular solution, we evolve such a texture in a smooth flow reproducing the geometry and similarity scaling of the collapsing axisymmetric core. The evolution creates and annihilates preimage pairs while preserving the Hopf charge. The first one-to-three transition exhibits the square-root opening characteristic of a Thom $A_2$ fold. A subsequent three-to-five transition precedes a burst-like regime of recurrent fold catastrophes and near-caustic activity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24490",
  "author_total": 1,
  "authors": [
    {
      "name": "Antti J. Niemi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/akm27mhvfb2d4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24490",
  "fulltext_url": null,
  "id": "akm27mhvfb2d4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24490",
  "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",
      "cond-mat.quant-gas"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.PS"
    ],
    [
      "openalex",
      "3107|Cold Atom Physics and Bose-Einstein Condensates"
    ]
  ],
  "openalex": "W7213997607",
  "pdf_url": "https://arxiv.org/pdf/2609.24490",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/akm27mhvfb2d4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.24490",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24490"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "amo"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Fold Catastrophes in a Hopf Texture Driven by a Navier--Stokes Blow-Up Analog",
  "title_text": "Fold Catastrophes in a Hopf Texture Driven by a Navier--Stokes Blow-Up Analog",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/akm27mhvfb2d4",
  "venue": "arXiv",
  "versions": []
}