Scale-Dependent Conformal Coupling: Suppression of Proper-Time Accumulation in Divergent Curvature Regimes

We present an effective phenomenological framework in which the operational flow of proper time is dynamically suppressed in regions of extreme spacetime curvature through a scale-dependent conformal coupling. Rather than removing curvature singularities from the background geometry, the model modifies the physical metric experienced by observers using a curvature-invariant-dependent conformal factor. In the strong-field limit, accumulated proper time asymptotically vanishes, leading to a form of temporal freezing. This mechanism preserves causal structure while reducing the physical observability of singular behavior.