When we speak of recursive self-improvement (RSI), are we speaking of a phenomenon, a mechanism, or a prospect? Towards autonomous and evolving intelligence, RSI is being claimed at many scales, while no single framework that formally describes these emerging instances exists. Its counterpart in the classical realm, iterative policy improvement, is characterized by generalized policy iteration (GPI), a framework of broad applicability with well-understood theoretical properties, but only where the update principle and the evaluation base lie outside the agent. In this paper, we propose General