Abstract
Connections are found between elements of a "fermionic" space and space-time employing symplectic and orthogonal geometric algebras. These connections are used to justify the introduction of a modified parity-violating Dirac-type operator into the algebraic-unification spinor Lagrangian. The first of two fermion hyperfields is considered and shown to consist of one lepton-quark family and one antifamily which can now be identified consistently with those of the electron and antimuon. The observed weak mixings are produced via an SU (2) nonsymmetry of the modified Lagrangian.

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