When a topological quantity satisfies a local conservation law, its apparent non-conservation inside a finite region need not signal dissipation. It may instead reflect a geometric leakage of information through the boundary. We make this idea precise in the Chern-Simons formulation of compressible fluid dynamics recently proposed by Bustamante, Andrianopoli, Trigiante, and Zanelli, in which the proto-helicity is a helicity-type invariant of topological origin that satisfies a local conservation law. On an open domain, this local law leads not to exact conservation but to a balance equation in which the time variation of proto-helicity is entirely determined by the flux of a geometric current through the boundary. The bulk equations remain unchanged; only the boundary conditions are modified. A structural graviton-fluid correspondence emerges from comparison with the AdS3 Chern-Simons framework. In this correspondence, the radiative component of the boundary flux serves as boundary gravitons that carry topological information toward the conformal boundary. The spectral properties of the boundary flux give rise to three distinct decay regimes for the proto-helicity: a stable regime associated with bound states, a transiently localized regime associated with caviton-like structures, and a dispersive regime corresponding to pure radiation. These regimes provide a spectroscopic diagnostic of the interior geometry based solely on boundary observations.