{
  "abstract": "We prove that the negative $r$-spin tautological relations of Chidambaram--Garcia-Failde--Giacchetto are a consequence of Pixton's $3$-spin relations, for every $r\\ge2$, and deduce that they hold in the tautological Chow ring of $\\overline{\\mathcal{M}}_{g,n}$. In particular, our result for $r=2$ implies that Kazarian--Norbury $K$-relations hold in Chow. The proof factors through two essential parts. The first part shows that the tautological relations arising from Chiodo's class imply the negative $r$-spin relations. This requires an intricate study of limiting behavior of the Givental--Teleman graph contributions. In the second part, we show that the Chiodo relations are a consequence of Pixton's $3$-spin relations as an application of a generalization of Janda's work on tautological relations from CohFTs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36509",
  "author_total": 2,
  "authors": [
    {
      "name": "Deniz Genlik"
    },
    {
      "name": "Felix Janda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5mk71xxkp7jyq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36509",
  "fulltext_url": null,
  "id": "5mk71xxkp7jyq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36509",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214981752",
  "pdf_url": "https://arxiv.org/pdf/2609.36509",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5mk71xxkp7jyq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.36509",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36509"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "From $3$-spin to Negative $r$-spin: Limits of Cohomological Field Theories and Tautological Relations",
  "title_text": "From $3$-spin to Negative r-spin: Limits of Cohomological Field Theories and Tautological Relations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/5mk71xxkp7jyq",
  "venue": "arXiv",
  "versions": []
}