The Geometric Origin of the Weak Interaction: Derivation of the Fermi Constant and Parity Violation in the ODD Framework

The Standard Model describes the Weak interaction via massive boson exchange, with its strength given by the empirical Fermi Constant, GF . The Operator-Derived Dimension (ODD) framework provides a fundamental, geometric origin. In this model, particles are vibrational eigenstates of a transverse 4D slice embedded in a rotating 5D bulk. Weak decays correspond to quantum tunneling between the n = 1 (muon-like) and n = 0 (electron-like) states. Parity violation arises naturally from the chiral structure of the transverse projection operator. By explicitly accounting for the ODD vacuum, defined as the intersection of three 4-dimensional hyperspheres, we derive GF from first principles. The calculation, GODD F ≈ 1.185 × 10−5/GeV2, matches the experimental value, 1.166 × 10−5/GeV2, to within 1.6%, strongly supporting the geometric origin of the Weak force.