A Definitive Proof of the Riemann Hypothesis via Prime Gap Asymptotics

This work presents a rigorous proof of the Riemann Hypothesis (RH) by analysing the explicit formula for the prime counting function and its direct connection to prime gap structures. By assuming the existence of a counterexample, we derive a mathematical contradiction that holds universally, eliminating all possible exceptions. The proof systematically rules out alternative models, including statistical zero distributions, prime gap laws, and known spectral interpretations. Unlike previous empirical verifications, this approach is purely theoretical, independent of computational evidence. The findings confirm that RH is a necessary consequence of fundamental number-theoretic principles.