Oscillatory Dynamics as a Necessary Condition for Learning in a Closed-Loop Feedback Architecture

This document presents a hypothesis concerning the relationship between oscillatory dynamics and learning in a closed-loop feedback architecture. It asks whether rotational or oscillatory dynamics around a learning equilibrium are a necessary condition for successful learning within the specified architecture. The proposition is preliminary and unproven. It is published to invite independent mathematical examination, experimental replication and potential falsification. The author does not claim to have established or discovered a general learning principle. The central objective is to obtain a rigorous answer to the question posed.