The Riemann Hypothesis as a Saturation Law

We exhibit an explicit family of finite Hermitian operators built from Farey fractions for which the Riemann Hypothesis is equivalent to a lower bound on a quadratic form, and we prove unconditionally that the critical exponent in that bound is optimal. The critical exponent 3 therefore cannot be improved: RH asserts that the deficit sits exactly at its proven floor. We interpret the identity as a conservation law - a unit of spectral mass split between a flat-mode channel and a commutator (fluctuation) channel - under which RH becomes a saturation principle: maximal transfer of mass from the flat mode into the fluctuation spectrum. The equivalence mechanism is the classical Mertens criterion; the contribution is the operator formulation, the exact identity, and the sharpness theorem. We close with a comparison to the Nyman-Beurling, Báez-Duarte, Li, and Connes reformulations, including Burnol's unconditional lower bound for the Báez-Duarte distance, the closest prior sharpness phenomenon. Its conclusions are limited to the assumptions, evidence, and testing conditions stated in the manuscript. It belongs to the arithmetic operator and Branch C research program. This is a corrected preprint edition released under the Creative Commons Attribution 4.0 license.