{
  "abstract": "We classify all natural, conformally covariant, symmetric (0,2)-tensors of conformal weight -2 and differential order less than or equal to 4 in dimension 4, built from the metric, the Schouten tensor, covariant derivatives, and the Kulkarni-Nomizu product. We prove that the space of such tensors is exactly 2-dimensional, spanned by the Bach tensor (order 2) and the Eastwood-Singer tensor (order 4). The algebraic core is formally verified using Lean 4 with Mathlib. The 8x11 constraint matrix and divergence-free condition are verified computationally with exact rational arithmetic. Both English and Russian versions provided; Russian version available as ancillary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07750",
  "author_total": 1,
  "authors": [
    {
      "name": "Yury N. Berdinsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/enrdwgkcfr25f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07750",
  "fulltext_url": null,
  "id": "enrdwgkcfr25f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07750",
  "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.MP"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7212058897",
  "pdf_url": "https://arxiv.org/pdf/2609.07750",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/enrdwgkcfr25f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.07750",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07750"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Classification of Conformally Covariant 2-Tensors from the Kulkarni--Nomizu Product in Dimension 4",
  "title_text": "Classification of Conformally Covariant 2-Tensors from the Kulkarni--Nomizu Product in Dimension 4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/enrdwgkcfr25f",
  "venue": "arXiv",
  "versions": []
}