{
  "abstract": "Existing link-based combinatorial preprocessing methods speed up the computation of persistent homology by removing a vertex or edge only when its link remains a cone. We replace this condition with a quantitative homological certificate. The reduced homology of the filtered link of a generator (a vertex or edge) defines a local obstruction module whose future part describes the effect of deleting that generator. Its barcode certifies either exact deletion or an explicit bound on the bottleneck error, and a conflict colouring extends this guarantee to families of generators. Our implementation, HomTrim, removes an additional 13% to 41% of the input edges beyond domination-only preprocessing and reduces backend persistence time by factors ranging from 1.55 to 4.61 on weighted flag filtrations. The same module also yields regularity diagrams that measure how far a generator can move before becoming visible to homology, together with a multiscale stability result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28160",
  "author_total": 1,
  "authors": [
    {
      "name": "Siddharth Pritam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/02ffj6d61brqc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28160",
  "fulltext_url": null,
  "id": "02ffj6d61brqc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28160",
  "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",
      "cs.CG"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7214173175",
  "pdf_url": "https://arxiv.org/pdf/2609.28160",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/02ffj6d61brqc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28160",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28160"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Homological Trimming and Regularity of Filtrations via Local Obstruction Modules",
  "title_text": "Homological Trimming and Regularity of Filtrations via Local Obstruction Modules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/02ffj6d61brqc",
  "venue": "arXiv",
  "versions": []
}