Three-Generation Limit Across Leptons and Quarks in the Foam-Plexus Model

The Standard Model accommodates three generations of fermions without explaining why the hierarchy terminates there. In the Foam-Plexus framework, leptons and quarks emerge as polyhedral amplifiers of wormhole connectivity in the spacetime foam. Their faces stabilize plexus-specific wormholes via dwell-time amplification, with the electromagnetic (EM) face supporting harmonic excitations. We show that the electron, muon, and tau correspond to the n= 1,2,3 EM harmonics, while quark generations map to the same ladder entangled with the QCD color face. The Planck length ℓP imposes a natural ultraviolet cutoff: by n = 4, the required wormhole oscillations fall below ℓP , rendering the state unstable. This mechanism explains why exactly three generations of leptons and quarks exist, resolving a long-standing puzzle of the Standard Model.