A Rigidity-Based Reduction of the Riemann Hypothesis to a Linear Injectivity Problem

This note reformulates the Riemann Hypothesis as a rigidity and uniqueness problem rather than a zero-enumeration problem. Within an admissibility framework governed by the classical analytic invariants of the Riemann zeta function, we show that RH is equivalent to the injectivity of explicit-formula test functionals on admissible zero configurations supported on the critical line. The reduction isolates a single functional-analytic bottleneck: whether admissible linear probes (interpretable as expected-value keys or spectral observables) separate discrete tempered measures on the critical spine. The work is structural and conditional in nature and does not claim a proof of RH, but clarifies the precise analytic obstruction remaining. This work is a structural reduction. It does not assert the truth of the Riemann Hypothesis, but shows that under standard admissibility and rigidity assumptions, RH is equivalent to a linear injectivity (determinacy) problem on the critical line.