Series: The Learn Arc — 50 posts through the Active Inference workbench. Previous: Part 39 — Session §7.5: Worked example Hero line. Generalized coordinates replace the single state s_t with a tower: s , s' , s'' , s''' , … The belief is over the state and all of its derivatives at an instant . That is what makes continuous-time inference tractable. Why a tower Discrete-time active inference gets a free lunch: every t gives you a fresh observation, and Eq 4.13 is a single softmax. In continuous time there is no clean tick. You need a representation that captures both where the state is and where it is heading at the same moment. Generalized coordinates solve this. Instead of s_t , the agent carries (s, s', s'', s''', …) — position, velocity, acceleration, jerk, and so on — as its instantaneous estimate. The gaussian prior binds them together with a characteristic smoothness. Five beats Generalized state = position + derivatives. The belief is a multivariate gaussian over (s, s', s'', …) .…