Do you have empirical proof any LLM can generate another program that can be trained to simulate it?
Otherwise it is science fiction.
I didn't ask for it, one of the Phi models got confused part way though and started giving me a python script for machine learning instead of what I actually asked for.
I'm saying I have no evidence that humans have ever demonstrated this capability either, and if we were to invent such an algorithm and model (even more generally than LLM) the AI that is this would by definition necessarily have to pass this test.