Topological Geometry of Neutrino Mass and Mixing
Abstract
This work presents an analytical, parameter-free derivation of the lepton mixing matrix and active neutrino mass spectrum from an icosahedral A5 flavor manifold coupled to the three-generation Iwahori-Hecke algebra H3(q). Partitioning the icosahedral vertex curvature across the six fundamental Weyl chambers of H3(q) fixes an elementary angular defect ΔAD = 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∼ M0, the right-handed Majorana scale M0 breaks scale invariance and drives the five-dimensional Temperley-Lieb quotient into its hyperbolic regime with loop modulus d'AD = 2coshΔAD, where Quantum Yang-Baxter Baxterization projects the algebraic roots onto a hierarchical heavy spectrum M1 > M2 > M3 > 0. Integrating out and inverting these states via a flavor-isotropic Seesaw mechanism Type-I locks in the normal mass hierarchy with m1 ≈ 3.64 meV, ∑i mi ≈ 63.5 meV, and mβ≈ 9.45 meV. Simultaneously, probability conservation requires analytic continuation onto the compact unitary circle, factorizing the mixing matrix into the A5 Golden Ratio baseline, a unitary boundary twist generated by the longest Coxeter involution, and a discrete Majorana parity matrix. This geometry yields θ13 = 8.49∘, θ12 = 32.11∘, θ23 = 45∘, and maximal Dirac CP violation, δCP = ± π/2, while discrete SO(3) parities quantize the relative Majorana phases, α13 = −π, α23 = 0, preventing 0νββ decay cancellation, mββ ≈ 1.14 meV, and suppressing renormalization group drift to θ̇ij ∼ 10−7 rad.
Related
- Étale Fundamental Groups: a geometric and topological approach to fundamental groups in algebraic geometry
- Topological Classification of Univariate Sparse Polynomials via Tropical Geometry
- Topological Quantum Gates on FCIs with Bounded Quantum Geometry
- Topological invariant responsible for the integer QHE and non-commutative geometry
- Spectral Reconstruction of Hyperbolic Geometry as a Topological Invariant of a Self‑Adjoint Operator
BibTeX
@misc{arrietadiaz2026topological,
title = {{Topological Geometry of Neutrino Mass and Mixing}},
author = {Enrique Arrieta-Diaz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31406},
eprint = {2609.31406},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31406},
}
RIS
TY - UNPB
TI - Topological Geometry of Neutrino Mass and Mixing
AU - Enrique Arrieta-Diaz
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.31406
UR - https://arxiv.org/abs/2609.31406
AB - 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∼ 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 = 2coshΔ_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 ≈ 3.64 meV, ∑_i m_i ≈ 63.5 meV, and m_β≈ 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^∘, θ_12 = 32.11^∘, θ_23 = 45^∘, and maximal Dirac CP violation, δ_CP = ± π/2, while discrete SO(3) parities quantize the relative Majorana phases, α_13 = −π, α_23 = 0, preventing 0νββ decay cancellation, m_ββ ≈ 1.14 meV, and suppressing renormalization group drift to θ̇_ij ∼ 10^−7 rad.
ER -