Tidal deformation bounds and perturbation transfer in bounded curvature spacetimes

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 λ ₘₐₓ≤ λ bound λ max ≤ λ bound on the electric Riemann eigenvalues Eᵢⱼ≡ R0̂i0̂j E ij ≡ R 0 ^ i 0 ^ j along freely falling worldlines, we prove (i) a rigorous upper bound on accumulated geodesic deviation through any bounded curvature interior, controlled by τ _*≡ λ ₘₐₓ-1/2 τ ∗ ≡ λ max - 1 / 2 , and (ii) the existence of a critical wavenumber k_*~ τ _*⁻¹ k ∗ ∼ τ ∗ - 1 separating adiabatic from non-adiabatic perturbation transfer through high-curvature epochs, with Bogoliubov coefficients exponentially suppressed for k\,τ _* 1 k τ ∗ ≫ 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 LLI(ε )~ √ε \, λ ₘₐₓ-1/2 L LI ( ε ) ∼ ε λ max - 1 / 2 and, for conformally flat cores in four dimensions, the benchmark ratio τ _*/L_*=241/4 τ ∗ / L ∗</mml:mo