#gradient-flow

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.

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.