{
  "abstract": "This paper organizes the complete operator set and the integral theorems of classical vector analysis into a single unified system. The starting point: every differential operator is an invariant slice of one object — the derivative tensor of the field — and every integral theorem is one rung of a single dimensional ladder. On the first floor stands the operator quadruple div–rot–dev–jad (the irreducible decomposition of the derivative tensor, 9=1+3+5 in components), held together by jet, the full second-order tensor invariant; each carries an exact, first-order integral reduction theorem, valid in identical form in R^3, R^4 and R^5. The second floor is built from compositions: the Hessian as jet∘grad, the Laplacian as div∘jet, the Green identities and the Monge-Ampere theorems. Converse theorems (Poincare lemmas, Helmholtz decomposition) sharpen the system into equivalence criteria. As a highlighted application, under the w=ict embedding the jad operator applied to the four-potential yields the electromagnetic field tensor: the homogeneous Maxwell equations and the flux theorem arise as identities, the wave equation and Poynting's theorem as compositions — within this system the sourcelessness of the magnetic field is not a postulate but a theorem. The paper includes the complete R^5 invariant table, jump (boundary-condition) and transport extensions, worked verification examples, the Kaluza-Klein tower of the five-potential, and six research directions. The theorems of the system were also verified symbolically for arbitrary (general polynomial) fields: the published R^4/R^5 invariant tables term by term, the ladder theorems from R^3 to R^5, the Piola family and the null identities — 23 checks, all passed.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "László Márk",
      "orcid": "0009-0006-5033-633X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90ebsg1yap2tb.bib",
  "cited_by": 17,
  "doi": "10.5281/zenodo.21532473",
  "fulltext_url": null,
  "id": "90ebsg1yap2tb",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.21532473",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Advanced Differential Geometry Research"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
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  "openalex": "W7171133033",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-24",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/90ebsg1yap2tb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:18Z",
      "native_id": "W7171133033",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.21532473"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "openalex:3103|Advanced Differential Geometry Research",
      "subfield": "general"
    },
    {
      "field": "mathematics",
      "origin": "openalex:2608|Advanced Differential Geometry Research",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Unified System of Tensor Invariants and Their Integral Reduction Theorems",
  "title_text": "A Unified System of Tensor Invariants and Their Integral Reduction Theorems",
  "type": "preprint",
  "updated_at": "2026-11-07T13:20:41Z",
  "url": "https://research.draconitic.com/paper/90ebsg1yap2tb",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}