Part 11: Symmetry Breaking, Fermion Mass Hierarchies, and Flavor Mixing in the Unified Gravitational Dirac Operator

Building directly upon the symmetric gravitational Dirac operator established in Part 10, this paper formulates the explicit electroweak and flavor symmetry-breaking transition . By introducing directional edge anisotropy governed by powers of the truncated-cube geometric parameter , the cubic degeneracy of the unbroken phase is lifted across the three fermion generations. Unitary flavor rotations in the generation-ordered eigenbasis preserve the exact Hermiticity of the internal mass operator while simultaneously generating realistic mass hierarchies across quarks, charged leptons, and seesaw-suppressed neutrinos, alongside the physical Cabibbo–Kobayashi–Maskawa () and Pontecorvo–Maki–Nakagawa–Sakata () mixing matrices. Finally, both flavor-mixing operators are embedded into the charged weak currents of the gauge block within the complete curved-spacetime operator .