{
  "abstract": "We investigate a semi-empirical flavour framework based on two linked hypotheses: a golden/pentagonal organisation of fermion mixing and the recurrence of its hierarchy maps in the quark-mass spectrum. The two large lepton angles are specified by the fifth-order Chebyshev conditions $T_5(θ_{12}^{\\ell})=0$ and $T_5(θ_{23}^{\\ell})=-1$, with angular arguments in radian measure, while the smaller reactor angle follows the approximate bilinear relation $θ_{13}^{\\ell}\\simeqθ_{12}^{\\ell}θ_{23}^{\\ell}/π$. An alternative golden-partition construction yields nearly identical large-angle predictions and an exact circular--hyperbolic duality. The golden ratio $φ$ also enters two distinct geometrical prescriptions for the Cabibbo angle, while the heptadecagonal seed $α_C=π/17$ governs the suppressed mixing hierarchy. The near-equality $\\tanα_C\\simeq\\cos54^\\circ/π$ further connects the two geometries. The resulting quark hierarchy obeys the quadratic map $θ_{13}^q=\\sqrt{θ_C^2+(θ_{23}^q)^2}-θ_C\\simeq(θ_{23}^q)^2/(2θ_C)$. Transferring the quadratic and bilinear maps to quark masses yields the crossed relations $m_d\\simeq m_c^2/(2m_t)$ and $m_u\\simeq m_b m_s/(m_F/φ)$, where $m_F=G_F^{-1/2}$. The complementary triples $(t,c,d)$ and $(b,s,u)$ reproduce both mass targets within $1\\%$ for the adopted reference values. Gatto--Sartori--Tonin-type correspondences and Froggatt--Nielsen scaling provide compatible phenomenological interpretations. These results suggest a common golden/geometrical organising structure for flavour mixing and mass hierarchies, whose underlying dynamical origin remains to be established.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03704",
  "author_total": 1,
  "authors": [
    {
      "name": "Jacek Ciborowski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9sptkmcghz8z3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03704",
  "fulltext_url": null,
  "id": "9sptkmcghz8z3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03704",
  "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",
      "physics.gen-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03704",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9sptkmcghz8z3.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.03704",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03704"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.gen-ph",
      "subfield": "general"
    }
  ],
  "title": "Fine structure of fermion mixing and quark-mass hierarchies",
  "title_text": "Fine structure of fermion mixing and quark-mass hierarchies",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/9sptkmcghz8z3",
  "venue": "arXiv",
  "versions": []
}