A Minimal Complex-Fiber Geometric Algebra Model of the Standard Model and Dark Matter

We present a unified geometric model of Standard Model fields within a compact three–complex-dimensional Clifford/Geometric Algebra fiber over 4D spacetime. Taking the ladder generators αj , α†j (j = 1, 2, 3) as the primary basis, spacetime γμ matrices and the Dirac current arise as derived objects, and the requirement that this current transform as a proper Lorentz vector restricts left versus right actions on the super-spinor ψ. This single covariance rule yields an unbroken U(2)L ≃ SU(2)L × U(1)L on the left and U(3)R ≃ SU(3)R × U(1)R on the right, reproducing the Standard Model gauge structure without additional symmetry postulates. A Hermitian fiber metric gj¯k (x), induced by a spacetime pullback field fjμ(x), generates the full fiber spin connection; its curvature decomposes into gravitational, electroweak, hypercharge, and color sectors with the correct quadratic field terms. Fermions are organized by idempotent left ideals into one SM generation plus a decoupled dark copy, with no cross-sector Feynman diagrams. The Higgs interaction is tied to the non-Kahler part of the induced fiber geometry and yields iso-spin–split Dirac masses; the dark sector inherits mirror-flipped charges and iso-spin partner masses. The model predicts electrically neutral dark matter dominated by heavy dark neutrinos and stable dark neutrons, and accommodates gauge coupling unification near 1016GeV. Remaining open problems include a first-principles derivation of the Yukawa hierarchy and mixing matrices, which we outline as targets for future work.