Numerical Validation of the Discrete Extramental Clock Law: Hierarchical Emergence of Objective Time from Ordinal Conjunctions in Chaotic Systems

The Discrete Extramental Clock Law proposes that objective time in chaotic systems emerges discretely from statistically significant ordinal conjunctions across multiple trajectories, modulated by a universal gating function g(τs)g(τs​) rooted in Kendall's rank correlation and Feigenbaum universality. This study provides numerical evidence for the ontological hierarchy: high local chaotic activity (e.g., positive Lyapunov exponents) does not advance objective time; only global ordinal coherence (high ∣τs∣∣τs​∣) generates effective temporal ticks. Using coupled logistic maps, the Lorenz attractor, fractional-order extensions, and empirical \textit{Aedes aegypti} population data, we demonstrate negative correlation between local variance/Lyapunov activity and the rate of emergent time advance, fractal inheritance in tntn​ (Dtn≈1.98Dtn​​≈1.98), and robust noise tolerance. These results challenge the universality of Newtonian time in chaotic regimes, supporting emergent discreteness even in classical chaos.