{
  "annotation_id": "4259e642-045a-49c1-9373-c3dc1a1b84d1",
  "date_created": "2026-03-02T18:00:39.420000Z",
  "date_modified": "2026-03-02T18:00:39.420000Z",
  "file_hash": "8c192518a930abad79e5e1ab55a3820db05da6ff581f30e39754170a4bd496f4",
  "private": false,
  "record": {
    "abstract": "An expression for a third-order link integral of three magnetic fields is\npresented. It is a topological invariant and therefore an invariant of ideal\nmagnetohydrodynamics. The integral generalizes existing expressions for\nthird-order invariants which are obtained from the Massey triple product, where\nthe three fields are restricted to isolated flux tubes. The derivation and\ninterpretation of the invariant shows a close relationship with the well-known\nmagnetic helicity, which is a second-order topological invariant. Using gauge\nfields with an SU(2) symmetry, helicity and the new third-order invariant\noriginate from the same identity, an identity which relates the second Chern\nclass and the Chern-Simons three-form. We present an explicit example of three\nmagnetic fields with non-disjunct support. These fields, derived from a vacuum\nYang-Mills field with a non-vanishing winding number, possess a third-order\nlinkage detected by our invariant.",
    "arxiv_id": "physics/0203048",
    "authors": [
      "Gunnar Hornig",
      "Christoph Mayer"
    ],
    "categories": [
      "physics.plasm-ph"
    ],
    "doi": "10.1088/0305-4470/35/17/309",
    "journal_ref": "J. Phys. A: Math. Gen., Vol. 35, No. 17 (2002) 3945-3959",
    "title": "Towards a third-order topological invariant for magnetic fields",
    "url": "https://arxiv.org/abs/physics/0203048"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "04d862ed-99c3-48de-a8e3-d56c639788b0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}