We derive two model-independent results for spacetimes with globally bounded tidal fields. These are operational resolution scales of the local-inertial approximation and tidal dynamics; no spacetime discreteness is implied. Given an invariant bound \(\lambda _{\max }\le \lambda _\textrm{bound}\) on the electric Riemann eigenvalues \(E_{ij}\equiv R_{\hat{0}i\hat{0}j}\) along freely falling worldlines, we prove (i) a rigorous upper bound on accumulated geodesic deviation through any bounded curvature interior, controlled by \(\tau _*\equiv \lambda _{\max }^{-1/2}\) , and (ii) the existence of a critical wavenumber \(k_*\sim \tau _*^{-1}\) separating adiabatic from non-adiabatic perturbation transfer through high-curvature epochs, with Bogoliubov coefficients exponentially suppressed for \(k\,\tau _*\gg 1\) . Both results depend only on the tidal bound (and, for mode transfer, on a mild timescale assumption for the curvature-driven effective potential) and are otherwise insensitive to metric details. For preparation, we collect the standard operational consequences of bounded curvature, including the accuracy-dependent local-inertial domain \(L_\textrm{LI}(\varepsilon )\sim \sqrt{\varepsilon }\, \lambda _{\max }^{-1/2}\) and, for conformally flat cores in four dimensions, the benchmark ratio \(\tau _*/L_*=24^{1/4}\) with \(L_*\equiv K_{\max }^{-1/4}\) . We quantify the robustness of this coefficient under departures from maximal symmetry via the Weyl-to-Kretschmann ratio \(\epsilon _C\) . The general framework is validated numerically in the extremal Hayward geometry.
