Z-Geometric Dynamics: The Geometric Origin of Parity Violation

Within the framework of Z-Geometric Dynamics (Papers I, II) and its topological description of particle structure (Paper III), this paper reveals the geometric origin of parity violation in weak interactions. In the five-dimensional parameter space S^5, the electron is captured on the brane at y=0 by a black hole horizon, the proton resides on the brane at y=L, and the weak gauge field arises from the mixed component of the five-dimensional spin connection ω_μ^i5. This asymmetric "two-sided thickness" structure naturally leads to left-handed electrons participating in weak interactions while right-handed electrons remain completely decoupled, thereby yielding maximal parity violation. We explicitly compute the angular distribution of muon decay, obtaining dΓ/dΩ ∝ 1-(1/3)cosθ, in excellent agreement with the experimental value -0.333 ± 0.005. Finally, we present falsifiable predictions: possible small right-handed currents at high energies, the connection between W' boson mass and the recent CDF W mass anomaly, and precision corrections to the neutron β-decay asymmetry parameter. All "extra dimensions" in this paper refer to a mathematical parameter space describing the internal topological structure of particles, not physical spacetime dimensions.