{
  "abstract": "Let $\\mathrm{rep}(\\mathbb I)$ be the category of finitely generated persistence modules on the interval $\\mathbb I\\subseteq\\mathbb R$. We study the maximal rigid subcategories of $\\mathrm{rep}(\\mathbb I)$. Maximal rigid interval consistent subcategories are classified via tilting modules over the corresponding discrete type $A$ quiver. We compare several related notions, (weak) tilting and maximal rigidity, in both the context of hereditary abelian categories with enough projective objects and $\\mathrm{rep}(\\mathbb I)$ and prove that every maximal rigid interval consistent subcategory is weak tilting and every maximal rigid consistent below subcategory is tilting. We also establish a continuous analogue of Ingalls-Thomas's bijection by showing a bijection between integrally supported maximal rigid consistent below subcategories and integrally generated torsion classes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31689",
  "author_total": 3,
  "authors": [
    {
      "name": "Haowei Liu"
    },
    {
      "name": "Zonghui Liu"
    },
    {
      "name": "Shijie Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bg1m2c0arrn56.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31689",
  "fulltext_url": null,
  "id": "bg1m2c0arrn56",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31689",
  "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.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223696466",
  "pdf_url": "https://arxiv.org/pdf/2610.31689",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bg1m2c0arrn56.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31689",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31689"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Tilting theory on continuous quivers (I) maximal rigid and tilting subcategories",
  "title_text": "Tilting theory on continuous quivers (I) maximal rigid and tilting subcategories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/bg1m2c0arrn56",
  "venue": "arXiv",
  "versions": []
}