A single Cl(10) Clifford algebra with embedded S3 symmetry realizes three fermion generations matching Standard Model quantum numbers without gauge boson replication.
An Exceptionally Simple Theory of Everything
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abstract
All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold.
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Electroweak Structure and Three Fermion Generations in Clifford Algebra with S3 Family Symmetry
A single Cl(10) Clifford algebra with embedded S3 symmetry realizes three fermion generations matching Standard Model quantum numbers without gauge boson replication.