{
  "abstract": "We introduce a new algorithm for computing persistent homology of Vietoris-Rips filtrations, which offers a considerable improvement both in terms of time and memory over the existing implementations of the persistence pairing algorithm. The key innovation, called active enumeration, is made possible by a new theoretical framework of Reduction to Zero Differentials (hence RedZeD) in which to view persistent homology.",
  "abstract_shown": true,
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  "article_type": null,
  "arxiv": "2606.06310",
  "author_total": 2,
  "authors": [
    {
      "name": "Chris Kapulkin"
    },
    {
      "name": "Nathan Kershaw"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b6q7s2pzhxngy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.06310",
  "fulltext_url": null,
  "id": "b6q7s2pzhxngy",
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  "landing_url": "https://arxiv.org/abs/2606.06310",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CG"
    ],
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      "arxiv",
      "cs.MS"
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      "arxiv",
      "math.AT"
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  "pdf_url": "https://arxiv.org/pdf/2606.06310",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b6q7s2pzhxngy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2606.06310",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.06310"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "RedZeD: Computing persistent homology by Reduction to Zero Differentials",
  "title_text": "RedZeD: Computing persistent homology by Reduction to Zero Differentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/b6q7s2pzhxngy",
  "venue": "arXiv",
  "versions": []
}