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Chapter 13 — Yang–Mills Flow
Discrete Yang–Mills gradient flow on the space of connections. How curvature-energy minimisation automatically stabilises the world's essential structure over time.
Chapter 14 — Time Evolution
How the instantaneous world W_t evolves with t. Hybrid dynamics on the state space, event-driven transitions, and the emergence of coarse trajectories.
T14 — Gradient Flow Convergence (Łojasiewicz)
The projected gradient flow on Σ_m converges to a critical point. With analytic energy (b_D = 0), convergence is exponential via the Łojasiewicz inequality. The dynamical existence theorem — variational minimizers are reachable by descent.