Prime Field Theory: Unifying Quantum Mechanics and General Relativity Through the Riemann Zeta Structure

This paper proposes that the unifying structure between quantum mechanics and general relativity exists within pure mathematics: the Riemann zeta function. The prime field, constructed from prime numbers, exhibits both continuous structure (suitable for spacetime geometry) and discrete resonances at zeta zeros (suitable for quantized states). The framework yields: (i) a mass formula predicting lepton masses to within 2%, (ii) the fine structure constant with 1.8% accuracy, (iii) Klein-Gordon dynamics from prime oscillations, (iv) emergent spacetime geometry, and (v) a unified explanation for dark matter and dark energy. Specific falsifiable predictions are presented, including fourth-generation lepton masses testable at the LHC.