The Geometry of Flavor: Deriving Mixing Matrices from FTL Tetrahedral Rotations

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1. Verfasser: Ebanks, Andrew
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Veröffentlicht: Zenodo 2026
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author Ebanks, Andrew
author_facet Ebanks, Andrew
contents <p>The mixing angles of the CKM and PMNS matrices have historically remained among the most<br>elusive parameters of the Standard Model, lacking a first-principles derivation. We demonstrate<br>that these angles emerge naturally from the geometric overlap between the internal orientation<br>of a tetrahedral disclination and the fixed symmetry axes of the vacuum lattice. We derive the<br>Physical Cabibbo angle as an Aristotle-corrected Fibonacci rotation, θC ≈ 12.74◦, and the second<br>quark mixing angle as a clamped sixth-order harmonic, θ23 ≈ 2.4◦. In the neutrino sector, we show<br>that mixing angles correspond to circuital winding modes, identifying the reactor angle θ13 as a<br>manifestation of the Aristotle Gap (δAr = 7.356◦). Finally, we provide a geometric origin for CP<br>violation as the structural ”torque” required to twist a chiral disclination against the lattice pre-<br>stress (δCP ≈ 69.2◦). These results establish a zero-parameter map of the flavor sector, reducing the<br>arbitrary interaction logic of the Standard Model to the ”geometric friction” of a discrete vacuum.</p>
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publishDate 2026
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spellingShingle The Geometry of Flavor: Deriving Mixing Matrices from FTL Tetrahedral Rotations
Ebanks, Andrew
Flavor Mixing Hierarchy
CKM Matrix
PMNS Matrix
Aristotle Clamping Factor
Cabibbo Angle
CP Violation
Color-Geometry Duality
Neutrino Oscillations
etrahedral Rotation Groups
<p>The mixing angles of the CKM and PMNS matrices have historically remained among the most<br>elusive parameters of the Standard Model, lacking a first-principles derivation. We demonstrate<br>that these angles emerge naturally from the geometric overlap between the internal orientation<br>of a tetrahedral disclination and the fixed symmetry axes of the vacuum lattice. We derive the<br>Physical Cabibbo angle as an Aristotle-corrected Fibonacci rotation, θC ≈ 12.74◦, and the second<br>quark mixing angle as a clamped sixth-order harmonic, θ23 ≈ 2.4◦. In the neutrino sector, we show<br>that mixing angles correspond to circuital winding modes, identifying the reactor angle θ13 as a<br>manifestation of the Aristotle Gap (δAr = 7.356◦). Finally, we provide a geometric origin for CP<br>violation as the structural ”torque” required to twist a chiral disclination against the lattice pre-<br>stress (δCP ≈ 69.2◦). These results establish a zero-parameter map of the flavor sector, reducing the<br>arbitrary interaction logic of the Standard Model to the ”geometric friction” of a discrete vacuum.</p>
title The Geometry of Flavor: Deriving Mixing Matrices from FTL Tetrahedral Rotations
topic Flavor Mixing Hierarchy
CKM Matrix
PMNS Matrix
Aristotle Clamping Factor
Cabibbo Angle
CP Violation
Color-Geometry Duality
Neutrino Oscillations
etrahedral Rotation Groups
url https://doi.org/10.5281/zenodo.19998975