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The combination of the most probable tokens doesn't necessarily have to be in the training set, thus creating something completely novel.

If you shuffle a deck of cards, you likely have a novel sequence of cards. I'm not sure how that is relevant?

I was responding to this "merely produces syntactically likely combinations of the training data".

That is called a hallucination.

Yes, like the Jacobian counterexample.

That LLM was attached to a Python and MATLAB evaluator. It generated plausible things to feed into a real computer.

Weird take as a lot of things humans invent and test are done in similar ways.

Only if it's incorrect.