A Signed Large–Sieve Inequality for the Prime–Power Log Lattice: Cancellation as the Only Surviving Mechanism in Strip–RKHS

Recent work has shown that absolute sampling bounds for the prime–power lattice \Lambda=\{\log p^k\} fail in the strip-associated reproducing kernel Hilbert space governed by the Poisson kernel. This eliminates all approaches based on positive Carleson or absolute frame inequalities. In this paper we isolate the remaining analytic mechanism: signed cancellation. We reduce the Riemann Hypothesis, in this substrate, to a single explicit signed large–sieve inequality for a logarithmic bilinear form over prime powers. The reduction identifies one precise analytic hinge: uniform control of an off–diagonal log–Hilbert kernel. No density, absolute, or positivity arguments remain available.