{
  "abstract": "The TF-cone conjecture of Asai and Iyama predicts that the TF equivalence class of an integral $g$-vector is the open cone generated by the canonical summands of all its positive multiples. We give a counterexample to this conjecture. For the tensor product of the three-arrow Kronecker algebra with the path algebra of $s\\to t$, a vector $w$ has a two-dimensional TF equivalence class, whereas every positive integral multiple $mw$ is generically indecomposable. The cone generated by these canonical summands is therefore a single ray. The same example disproves the relative-interior version proposed by Haerizadeh and Yassemi.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14814",
  "author_total": 2,
  "authors": [
    {
      "name": "Jindong Yan"
    },
    {
      "name": "Shenglin Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bjccbcjpzzts1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14814",
  "fulltext_url": null,
  "id": "bjccbcjpzzts1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14814",
  "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": "W7221772514",
  "pdf_url": "https://arxiv.org/pdf/2610.14814",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bjccbcjpzzts1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.14814",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14814"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Counterexample To The TF-cone Conjecture",
  "title_text": "A Counterexample To The TF-cone Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/bjccbcjpzzts1",
  "venue": "arXiv",
  "versions": []
}