Continuous, State-Dependent Temporal Response Scales in GNSS Satellite Clock Residuals

We investigate whether GNSS satellite clock residuals are better described by a purely instantaneous response or by a finite temporal response with a characteristic time scale τ . Using event-centered stacks built around apoapsis and periapsis passages, we compare an immediate model with exponential and Gaussian kernel-response models. Across the strongest candidate satellites, the finite-response models consistently outperform the immediate model, with continuous best-fit response scales spanning approximately 15.66 min and improvements of up to ΔAIC . 78. A continuous-τ optimization shows that the preferred scales are not evidence for strict quantized time modes; rather, they form a continuous, state-dependent response spectrum whose local maxima cluster around a few tens of minutes. Resolution tests using coarsened sampling indicate that the strongest candidates remain finite-response dominated, although the inferred τ can shift when temporal resolution is degraded. The results therefore support a conservative interpretation: GNSS clock residuals contain reproducible signatures consistent with finite, state-dependent temporal response scales, while stronger claims such as discrete eigenmodes are not required by the present data. These findings motivate a continuous temporal-response extension of Time- Field General Relativity (TFGR), in which scale dependence and finite memory coexist without contradiction.