Apparent Completion vs Asymptotic Freeze-Out: A Quantitative Index for Observer-Dependent Horizon Physics

This work introduces the Apparent Completion Index (ACI), a new general-relativistic measure that quantifies how different observers perceive the progression of infalling motion near a black hole horizon. While a distant observer sees asymptotic freeze-out, the infalling observer experiences full completion of the fall. ACI unifies these perspectives by mapping observable contraction, time dilation, and causal limits directly from the Schwarzschild metric. The framework provides a testable, quantitative structure for observer-dependent horizon physics and contributes to the broader discussion of black hole information and causality.