I just want to add that the "recursive" part of recursive self improvement is by no means a given, even if an AI can improve itself.

Recursive self improvement is by its nature a step wise behavior not a continuous one, I would argue. Why? Because you can imagine an AI improve itself by simply fixing random bugs and fixing things using techniques that are in its training, and doing refactoring and so on, all without any real change in capability.

These are not recursive improvements. Recursive improvements usually need conceptual breakthroughs. It is possible to get conceptual breakthroughs with LLMs I believe, maybe it can improve something by tying together ideas from disparate disciplines for example, but I have at least for time being, limited success getting that to work in a way that is creatively new and surprising. Not sure how to get it to feel as creative as the best humans can be.