The Geometry of Flavor: Deriving Mixing Matrices from FTL Tetrahedral Rotations
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2026
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| _version_ | 1866901572826431488 |
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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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19998975 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| 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 |