The Dynamic Equilibrium of Vacuum: Deriving the Hubble Constant via the Causal Influx Differential Equation

This paper provides a deterministic derivation of the Hubble constant based on the dynamic equilibrium of vacuum energy within a discrete elastic lattice. By introducing the Causal Influx Hypothesis, the work demonstrates that cosmic expansion is not a passive divergence of coordinates, but an active, self-compensating mechanism of energy replenishment that maintains the invariance of vacuum energy density. A fundamental geometric identity is established between the causal horizon and the Hubble radius, providing a theoretical resolution to the "Hubble tension". The derived value of 68.18 km/s/Mpc, calculated directly from fundamental constants, aligns with high precision with current observational data. This research addresses the paradox of vacuum energy dilution during expansion and offers a consistent dynamic framework for the spatial fabric.