Pith Number

pith:QYOIQGYT

pith:2026:QYOIQGYT427MOZJCRW5UZJZMB6

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Higgs and Yukawa Structure in a Clifford Algebra Model with Three Generations and $S_3$ Family Symmetry

Niels Gresnigt

Algebraic Cl(10) model adds Higgs sector via S3 symmetry, producing six doublets with Type-II Yukawa structure and no tree-level FCNCs

arxiv:2604.24795 v2 · 2026-04-26 · physics.gen-ph

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Claims

C1strongest claim

Using the S3 family symmetry that permutes three algebraically distinguished fermion sectors, we construct Higgs components as right-action operators and extract the corresponding Yukawa coefficients by means of a trace pairing. This yields two first-generation Higgs doublets with the correct electroweak quantum numbers and a natural Type-II-like separation between down-type and up-type Yukawa channels. ... If electroweak symmetry breaking is implemented in the usual way, tree-level flavour-changing neutral currents are not expected in this limit.

C2weakest assumption

The prior algebraic construction of three fermion generations in Cl(10) is taken as given and valid; the S3 action is assumed to extend cleanly to the newly defined Higgs right-action operators without introducing inconsistencies or extra terms that would spoil the Type-II structure or quantum number assignments.

C3one line summary

An algebraic extension in Cl(10) with S3 symmetry incorporates the Higgs sector to produce six doublets and Type-II Yukawa couplings without tree-level FCNCs in the symmetric limit.

Cited by

1 paper in Pith

Fermion Mass Hierarchies and the Exceptional Jordan Algebra

Receipt and verification

First computed	2026-06-19T16:12:20.354130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

861c881b13e6bec765228dbb4ca72c0fae5885ab5adc5c83e11b6f5a19087e42

Aliases

arxiv: 2604.24795 · arxiv_version: 2604.24795v2 · doi: 10.48550/arxiv.2604.24795 · pith_short_12: QYOIQGYT427M · pith_short_16: QYOIQGYT427MOZJC · pith_short_8: QYOIQGYT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QYOIQGYT427MOZJCRW5UZJZMB6 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 861c881b13e6bec765228dbb4ca72c0fae5885ab5adc5c83e11b6f5a19087e42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3767227e44fda94c6868e74dbb4a1bb406060f6ef211e74824e4e1588ea0aa6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.gen-ph",
    "submitted_at": "2026-04-26T04:26:46Z",
    "title_canon_sha256": "2f9f3c431f1da26d3d1a4d140ec4326f94cfc264ab4e06dd3635558295b006b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.24795",
    "kind": "arxiv",
    "version": 2
  }
}