Horizon as a Non-Markovian Memory Bath: Dynamical Scrambling and Testable Gravitational-Wave Correlations

We introduce a Dynamical Effective Model in which the Black-Hole Horizon Behaves as a Distributed Memory Bath, modeled by an ensemble of localized degrees of freedom with causal delayed coupling to external perturbations. This minimal framework yields robust, falsifiable predictions: (i) the emergence of a universal saturation timescale t_sat ≈ 23.5 (simulation units), independent of the number of horizon degrees of freedom, analogous to structural features of information scrambling; (ii) its translation to a physical scrambling time t_scr ≈ 120 s for a 10e6M⊙ black hole; and (iii) the consequent production of structured, temporally correlated residuals in the gravitational wave signal after t_scr, distinct from both a Kerr ringdown and Gaussian noise. Using realistic LISA injections, we demonstrate these residuals exhibit coherent oscillations, a non-flat power spectrum, and significant temporal autocorrelation. Crucially, the coherent component can be amplified via stacking of multiple events, providing a concrete detection strategy. This work establishes a new phenomenological link between horizon memory dynamics and observable late-time gravitational wave signatures. ([email protected])