Proof of the Riemann Hypothesis via Distributional and Laplace Methods

This preprint presents a complete proof of the Riemann Hypothesis based on a distributional framework and a reductio ad absurdum argument. The analysis relies on the Laplace transform of a distribution constructed from the non-trivial zeros of the zeta function. A contradiction with the Beurling–Nyman criterion is obtained under the assumption of a zero off the critical line. The proof is detailed, formally structured, and supported by distribution theory, Nevanlinna value distribution, and analytic estimates.