Causal Density Dynamics and Markov Entropy in Artificial Cognition

Causality is hard. But prediction is measurable. If one signal helps predict another, we can at least say that information is flowing in a directed way. This paper measures that directed predictability, and it measures how “sticky” the system’s coarse states are, inside a non-trained cognitive runtime. Technically, we analyze a 15,040-tick unified log table and three empirically-defined epochs: E1 (lowentropy baseline), E2 (high-entropy plateau), and E3 (low-entropy baseline). Directed predictability is quantified via a fast Granger pipeline [1, 2, 3] over six scalar observables (entropy, complexity, firing variability, reward mean, TD error, and novelty/uniqueness). We report causal density [4, 5] as the fraction of significant directed edges at α = 0.01 (lag p = 5). Macrostate dynamics are separately summarized as a Markov chain over coarse labels (high/low entropy × output band), and we report stationary entropy H(π) and entropy rate Hrate in bits [6, 7, 8]. Results show a pronounced regime dependence: causal density drops from 0.80 in E1 to 0.30 in E2 and partially recovers to 0.47 in E3, while the macrostate stationary entropy collapses from 1.56 bits (≈ 2.95 effective states) in E1 to 0.10 bits (≈ 1.07 effective states) in E2. The included bundle provides deterministic scripts and hashes for all tables and figures referenced here.