5.1 - Framework
We turn our attention from the mechanism of the individual tick to the aggregate behavior of the system over deep time. The engine constructed in the previous chapter ticks reliably, adding and subtracting relations based on local cues, yet we must ask what global state emerges when these microscopic fluctuations balance out. We confront the core question of statistical mechanics applied to causality: in a system where every change is constrained by the strict axioms of acyclicity and unique paths, does the sheer multiplicity of compliant graphs impose a thermodynamic order on the evolution? We seek the graph-theoretic equivalent of an equilibrium state, where the fundamental degrees of freedom are causal links and the generative drive is the tendency of the network to explore its combinatorial state space.
5.2 - Equation
5.2 Master Equation {#5.2}
5.3 - Simulation
5.3 Computational Verification (The Simulation) {#5.3}
5.4 - Analysis
5.4 Equilibrium Analysis {#5.4}
5.5 - Stability
5.5 Geometric Stabilization (Topological Stability) {#5.5}
5.6 - Synthesis
5.6 Formal Synthesis {#5.6}