Local Temporal Degree of Freedom:Theory of Time Emergence Based on System Intrinsic Recursion and Environmental Coupling

General relativity explains time dilation via geometric curvature of spacetime, but it fails to distinguish differences in material system structures and cannot derive mathematically self-consistent extreme time dilation in extreme physical scenarios. Breaking away from the traditional framework of spacetime geometry, this paper starts from the essence of system information interaction, and proposes a theoretical model that determines the objective time flow rate jointly by the environmental coupling coefficient α and the effective intrinsic recursion intensity β, with the core formula ξ= 1 − (1 − α)β, and strictly limits 0≤α≤1 and 0≤β≤1. The model clarifies that time flow rate is essentially the result of the emergence of internal information recursion efficiency and inter-system information exchange smoothness of systems. Gravity and velocity regulate α and β simultaneously by interfering with the internal and external information transmission of systems, which can self-consistently explain the timing offset of GPS satellite atomic clocks, time dilation effects in high-speed and strong gravitational fields, and distinguish the temporal response differences between complex living systems, quantum timing systems and macroscopic structureless matter. It solves the logical defects of single-variable theories in extreme scenarios and provides a brand-new information theory perspective for the study of spacetime physics.