The Geometric Electron Theory: Deriving the Ground State Fermion in the ODD Framework

In the Standard Model, the electron’s mass, spin, and internal kinematics are axiomatic inputs. In the Operator-Derived Dimension (ODD) framework, we prove they are necessary geometric consequences of a 5D hyperspherical vacuum. We demonstrate that vacuum stability uniquely fixes the topological index μ = 2 of the Transverse Slicing Operator ˆQ. We provide a deductive proof that this stability forces the existence of a threshold resonance state with the exact quantum numbers of the electron (spin-1/2, Fermi statistics). Furthermore, we prove that the electron’s mass is not an arbitrary parameter, but the absolute topological boundary of the observable universe.By dividing the required 4π spinor rotation by the π/2 geometric phase step of the domain wall, we derive the exact phase boundary Φmax = 8. From the independently derived bulk UV anchor (174.67 GeV), this exact integer boundary predicts a baregeometric mass of 0.609 MeV, perfectly bounding the observed physical electron. Finally, we derive the electron’s Zitterbewegung (trembling motion) frequency directly from this μ = domain wall topology.