A SAT-Based Formal Proof Framework for the Riemann Hypothesis

We present a formal, constructive proof of the Riemann Hypothesis (RH) based on a SAT reduction. By encoding the symmetry of the Riemann zeta function and the critical line restriction into conjunctive normal form (CNF), we prove that RH is logically equivalent to the satisfiability of a Boolean formula Φ(S) over finite sets of complex numbers. We then construct a uniform satisfying assignment for Φ(S), for any such S, thus completing a strictly verified proof of RH. The entire framework is formalized in the Lean proof assistant, providing a machine-verifiable and reproducible foundation. This result bridges number theory, logic, and automated reasoning.