Proof of the Riemann Hypothesis Via the CRT Product Structure Sieve Framework

We present a complete proof of the Riemann Hypothesis, specifically the von Koch equivalent form π (X) −Li (X) =O (√X logA X). The proof builds on the CRT product structure sieve framework developed in the companion paper, which provides a linear sieve that circumvents the classical parity problem. The key new ingredient is a rigorous exponential sum cancellation estimate that controls the total sieve error over the parameter space. This estimate, combined with a hierarchical covering of 2, X by intervals of the form (p, p²), yields the required global error bound. The proof is self-contained modulo the foundational results from the sieve framework, which are summarized in Section 2 with complete references.