{
  "abstract": "This work presents an analytical, parameter-free derivation of the lepton mixing matrix and active neutrino mass spectrum from an icosahedral $A_5$ flavor manifold coupled to the three-generation Iwahori-Hecke algebra $H_3(q)$. Partitioning the icosahedral vertex curvature across the six fundamental Weyl chambers of $H_3(q)$ fixes an elementary angular defect $Δ_{AD} = π/18$, unifying ultra-high-energy mass generation and low-energy flavor mixing as dual realizations of a single geometric invariant. At the topological braiding threshold $μ\\sim M_0$, the right-handed Majorana scale $M_0$ breaks scale invariance and drives the five-dimensional Temperley-Lieb quotient into its hyperbolic regime with loop modulus $d'_{AD} = 2\\coshΔ_{AD}$, where Quantum Yang-Baxter Baxterization projects the algebraic roots onto a hierarchical heavy spectrum $M_1 > M_2 > M_3 > 0$. Integrating out and inverting these states via a flavor-isotropic Seesaw mechanism Type-I locks in the normal mass hierarchy with $m_1 \\approx 3.64$ meV, $\\sum_i m_i \\approx 63.5$ meV, and $m_β\\approx 9.45$ meV. Simultaneously, probability conservation requires analytic continuation onto the compact unitary circle, factorizing the mixing matrix into the $A_5$ Golden Ratio baseline, a unitary boundary twist generated by the longest Coxeter involution, and a discrete Majorana parity matrix. This geometry yields $θ_{13} = 8.49^\\circ$, $θ_{12} = 32.11^\\circ$, $θ_{23} = 45^\\circ$, and maximal Dirac CP violation, $δ_{CP} = \\pm π/2$, while discrete $SO(3)$ parities quantize the relative Majorana phases, $α_{13} = -π, α_{23} = 0$, preventing $0νββ$ decay cancellation, $m_{ββ} \\approx 1.14$ meV, and suppressing renormalization group drift to $\\dotθ_{ij} \\sim 10^{-7}$ rad.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31406",
  "author_total": 1,
  "authors": [
    {
      "name": "Enrique Arrieta-Diaz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fhw7bw5fcx0vj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31406",
  "fulltext_url": null,
  "id": "fhw7bw5fcx0vj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31406",
  "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",
      "hep-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3106|Neutrino Physics Research"
    ]
  ],
  "openalex": "W7214675088",
  "pdf_url": "https://arxiv.org/pdf/2609.31406",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fhw7bw5fcx0vj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.31406",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31406"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Topological Geometry of Neutrino Mass and Mixing",
  "title_text": "Topological Geometry of Neutrino Mass and Mixing",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/fhw7bw5fcx0vj",
  "venue": "arXiv",
  "versions": []
}