{
  "abstract": "We develop a semisimple obstruction theory for finite-length abelian categories. To each object \\(X\\) we associate a canonical obstruction subobject \\(\\mathcal O(X)\\), consisting of the part invisible to all morphisms into semisimple objects. The quotient \\(X/\\mathcal O(X)\\) is semisimple and universal among such morphisms, yielding a canonical semisimplification reflector and characterizing semisimplicity by the vanishing of obstruction. Iterating the construction gives an obstruction filtration which, in finite-length module categories, recovers the classical radical filtration and Loewy theory. Obstruction is also heart-dependent: under Happel--Reiten--Smalø tilting, extension data can appear as new obstruction layers, leading to obstruction shadows and visible torsion. Thus classical radical theory arises as the fixed-heart module-theoretic instance of a categorical framework for semisimple reconstruction, persistence, and variation of heart.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11497",
  "author_total": 1,
  "authors": [
    {
      "name": "Joe Gildea"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3th3e1qye6q7t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11497",
  "fulltext_url": null,
  "id": "3th3e1qye6q7t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11497",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221124923",
  "pdf_url": "https://arxiv.org/pdf/2610.11497",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3th3e1qye6q7t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11497",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11497"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Universal Semisimple Reconstruction and Obstruction Theory",
  "title_text": "Universal Semisimple Reconstruction and Obstruction Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/3th3e1qye6q7t",
  "venue": "arXiv",
  "versions": []
}