Well for starters the use of the term "Recursive" is very dubious.

This is as far as the eye can see all very iterative, there is no tail-call or anything fancy, it is loops. Also "Recursive" I feel kind of tries to imply the LLM's weights are being pushed around in some feedback, because to recurse you have to invoke the thing you're recursing into at its very start right? That would be reinforcement probably, and there is none of that in any such RSI so far, at least not public. Please someone contradict me with examples.

So please: "ISI" for iterative self improvement is fine. Also "ISI" does not fit the (outdated!) Vernon Vinge "singularity" trope, and that is a good thing!