Geometric Weak Force Theory (GWFT): 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 . We present the Geometric Weak Force Theory (GWFT), derived from the Operator-Derived Dimension (ODD) framework, where this interaction emerges from geometric tunneling between hyperspherical fermion eigenstates. The interaction strength is determined by the phase separation between the electron (ne) and muon (nμ) on the universal ODD mass ladder, anchored to the UV bulk curvature scale (kUV ≈ 173.000 GeV). We demonstrate that the framework allows for the precise calculation of a required geometric normalization constant, Nweak ≈ 9.37, which is formally defined as the matrix element of the transverse projection operator between the initial and final states. This establishes the Weak interaction as an emergent, geometric phenomenon whose strength is locked to the structure of the fermion mass hierarchy.