An Unconditional Proof of the Uniform Non-Cancellation Hypothesis - Removing the Spectral Obstruction to the Riemann Hypothesis

This work studies spectral rigidity phenomena arising in explicit trace formulas of Selberg–Kuznetsov type. We analyze the interaction between discrete spectral contributions and geometric terms, establishing a uniform non-cancellation mechanism that rules out exceptional Laplace eigenvalues below the continuous spectrum threshold. The results are formulated unconditionally within the explicit-formula framework and are motivated by applications to analytic approaches related to the Riemann Hypothesis.