The Geometric Origin of the Weak Interaction: First-Principles Derivation of the Fermi Constant from the ODD Mass Ladder

The Standard Model parametrizes the Weak interaction using the empirical Fermi constant GF . Within the Operator-Derived Dimension (ODD) framework, this interaction emerges from geometric tunneling between hyperspherical fermion eigenstates embedded in a 5D bulk with a fundamental curvature scale kUV ≈ 173 GeV. We derive the geometric overlap factor for this  interaction from the phase separation between the electron (ne) and muon (nμ) on the universal ODD mass ladder. This allows for a first-principles calculation of GF . We demonstrate that the framework correctly predicts the order of magnitude of the interaction and allows for the precise calculation of a required geometric normalization constant, Nweak ≈ 9.37. This result establishes the Weak force as an emergent geometric phenomenon whose strength is locked to the structure of the fermion mass hierarchy.