{
  "abstract": "Let $\\mathbb{A}=\\mathbb{R}1_{\\mathbb{A}}\\oplus\\mathfrak{m}$ be a Weil algebra with $\\mathfrak{m}^{N+1}=0$. We study the exponential geometry of the proper orthogonal group $\\mathrm{SO}(3,\\mathbb{A})$ through finite Weil prolongation. An exact Rodrigues formula is obtained for every element of $\\mathfrak{so}(3,\\mathbb{A})$, and the exponential map $\\mathfrak{so}(3,\\mathbb{A})\\to\\mathrm{SO}(3,\\mathbb{A})$ is proved to be surjective. Although every proper orthogonal Weil tensor is therefore exponential and has an unnormalized Rodrigues representation, a factorization of a generator into one scalar angle and one unit axis may fail above the identity; the obstruction is established for every logarithmic branch, including scalar angles $2kπ$. The analytic mechanism is an explicit finite-regularity rigidity theorem: an $\\mathbb{A}$-holomorphic map on $U+\\mathfrak{m}$ with scalar-valued real trace is uniquely its finite Weil jet. Together with functoriality, this yields exact transfer of functional, matrix, orthogonality, and composition identities. The results provide a rigorous basis for dual, multidual, hyper-dual, and hyper-multidual calculations in theoretical and computational kinematics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28505",
  "author_total": 1,
  "authors": [
    {
      "name": "Daniel Condurache"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/162byqxtg5pxq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28505",
  "fulltext_url": null,
  "id": "162byqxtg5pxq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28505",
  "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.GM"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7214306834",
  "pdf_url": "https://arxiv.org/pdf/2609.28505",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/162byqxtg5pxq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28505",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28505"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "Finite Weil Jets, Identity Transfer, and the Exponential Geometry of Proper Orthogonal Tensors",
  "title_text": "Finite Weil Jets, Identity Transfer, and the Exponential Geometry of Proper Orthogonal Tensors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/162byqxtg5pxq",
  "venue": "arXiv",
  "versions": []
}