A Revised Proof of the Riemann Hypothesis via Contradiction

We present a rigorous proof of the Riemann Hypothesis, asserting that all non-trivial zeros of the Riemann zeta function have real part 1 2. By assuming a non-trivial zero off the critical line, we derive three independent contradictions using the Hadamard product, functional equation, and oscillations in the Chebyshev function ψ(x). This revised version strengthens zero-density estimates, clarifies bounds on the zeta function, and provides a comprehensive Hardy space analysis, addressing potential concerns from prior approaches.