Geometric Weak Force Theory (GWFT): First-Principles Derivation of the Fermi Constant from Hyperspherical Topology

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.