{
  "annotation_id": "a0a7b1c8-71c5-4439-9e60-78270827adbd",
  "date_created": "2026-02-17T05:53:12.490000Z",
  "date_modified": "2026-02-17T05:53:12.490000Z",
  "file_hash": "31bdd8d8a11fc80039b9541cd6060203351f137c641fb1f4c10518794f03bea6",
  "private": false,
  "record": {
    "abstract": "We construct an explicit algebraic realisation of three fermion generations within a single Clifford algebra, transforming under the full Standard Model $SU(3)_C\\times SU(2)_L\\times U(1)_Y$ gauge group, in which an intrinsic $S_3$ family symmetry permutes three algebraically distinguished but gauge-equivalent fermion sectors without replicating the gauge bosons. Fermionic states are represented by minimal left ideals of the complex Clifford algebra $\\mathbb{C}\\ell(10)$, while the three-generation structure arises from an embedded discrete $S_3$ symmetry acting on the space of algebraic spinors. The Standard Model gauge generators are identified as elements commuting with this $S_3$ action and act on physical states via the adjoint (commutator) action. The resulting spectrum reproduces the correct Standard Model quantum numbers for three linearly independent generations of fermions.",
    "arxiv_id": "2601.07857",
    "authors": [
      "Niels Gresnigt"
    ],
    "categories": [
      "physics.gen-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Electroweak Structure and Three Fermion Generations in Clifford Algebra with S3 Family Symmetry",
    "url": "https://arxiv.org/abs/2601.07857",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "15a59af8-9755-4e61-a54d-089cbc4c9dff",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}