The Signal Sieve: A Prime Model - On the Dimensional Mismatch and the Negligible Theorem of Divergent Sequences

This article presents a paradigm shift in the interpretation of the Riemann Hypothesis (RH). We move from the view of RH as a static analytic mystery to a dynamic ``Signal Sieve.'' By distinguishing between the convergent properties of series tricks and the divergent properties of prime sequences, we expose a dimensional mismatch in modern number theory. We propose the Negligible Theorem to resolve the Hilbert-Riemann paradox, grounding the truth of prime distribution in the consistent application of the ``1-unit engine'' at a given magnitude.