We establish a new interleaving theorem for the real and imaginary parts of the Riemann xi function off the critical line. The proof combines the log-concavity of the xi kernel (Csordas-Varga, 1988) with a Wronskian identity and a self-sustaining phase monotonicity argument. As a consequence, all nontrivial zeros of the Riemann zeta function lie on Re(s) = 1/2. Computational verification (7/7 checks passed) and Python code are included.