A single Cl(10) Clifford algebra with embedded S3 symmetry realizes three fermion generations matching Standard Model quantum numbers without gauge boson replication.
Spin(7)-subgroups of SO(8) and Spin(8).Expositiones Mathemati- cae, 19(2):163–177
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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.