Series: The Learn Arc — 50 posts through the Active Inference workbench. Previous: Part 46 — Session §9.3: Case study Hero line. Perception, action, and learning are not three algorithms. They are three gradients of the same free energy, acting on different variables. Session 10.1 is the synthesis — every piece of the series in one sentence. The single equation, three handles Chapter 10 is the closing chapter. Session 10.1 earns the word synthesis by showing that everything the series introduced collapses to one equation with three levers: ∂F/∂μ → perception (update the belief) ∂F/∂a → action (change the world) ∂F/∂θ → learning (update the parameters) Different timescales, different variables, same F . Five beats Perception is fastest. Beliefs update every step. This is Eq 4.13 in discrete time, Eq 4.19's first gradient in continuous time. The gradient flows until the belief balances prior and likelihood. Action is simultaneous but acts through the world .…