{
  "abstract": "We study Clifford-weighted noncommutative residues associated with Dirac operators and connections. On closed spin manifolds a double commutator of the square of the Dirac operator, paired with a Clifford commutator, recovers the localized Riemann curvature tensor. We prove presentation independence for its extension to arbitrary classical one-forms, recompute four-Clifford functionals, and give explicit Weyl, Schouten and Einstein curvature combinations. For spectral triples with an admissible residue calculus we define a partial spectral curvature functional on two arbitrary represented one-forms and two exact represented one-forms. Its well-definedness is distinguished from module tensoriality: explicit flat noncommutative-torus computations exhibit both a failure of general presentation descent and nonzero partial pairings. A connection-based curvature pairing provides a separate construction, including noncentral pure Clifford-degree-two examples. We also derive ordered first- and second-derivative torsion residues on free torus modules and prove an obstruction to ordinary alternation for unrestricted noncentral inputs. All constants, coefficient orders and hypotheses are kept explicit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34256",
  "author_total": 1,
  "authors": [
    {
      "name": "Yong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8nxcxzkpjaqde.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34256",
  "fulltext_url": null,
  "id": "8nxcxzkpjaqde",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34256",
  "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.DG"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7223805359",
  "pdf_url": "https://arxiv.org/pdf/2610.34256",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8nxcxzkpjaqde.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34256",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34256"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Clifford-weighted residues, partial spectral curvature, and torsion",
  "title_text": "Clifford-weighted residues, partial spectral curvature, and torsion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/8nxcxzkpjaqde",
  "venue": "arXiv",
  "versions": []
}