The Geometric Origin of the Weak Interaction: Derivation of the Fermi Constant from Hyperspherical Tunneling

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 yields GODD F ≈ 1.185×10−5/GeV2, matching the experimental value to within 1.6%. We identify this small residual as the predicted contribution from electroweak radiative corrections, confirming the Weak force as a geometric phenomenon.