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

The Standard Model parametrizes the Weak interaction using the empirically measured Fermi constant (GF ≈ 1.166 × 10−5 GeV−2). We present the Geometric Weak Force Theory (GWFT), a core component of the Operator-Derived Dimension (ODD) framework, which postulates that the Weak interaction is an emergent geometric tunneling event through the 5D hyperspherical bulk. We demonstrate that the strength of this interaction is exactly determined by the fundamental UV bulk anchor scale (kUV ≈ 173.000 00 GeV) modulated by a pure topological factor (π/9) representing the projection of three intersecting hyperspheres onto three spatial dimensions. Our parameter-free geometric formula yields a theoretical value of GODD ≈ 1.1663 × 10−5 GeV−2, matching the experimental Fermi constant to an accuracy of > 99.99%. Full mathematical derivations are provided in the Appendix.