Yes, some recursion can be implemented in a loop. Op-amp feedback, and analog audio delays, just for two examples certainly are a valid subset of real recursion

Yes, some recursion can be implemented in a loop. Op-amp feedback, and analog audio delays, just for two examples certainly are a valid subset of real recursion, the kind that only recurse once, as opposed to two or more times. It is a form of recursion, so I still disagree with your argument. Note the actual question explicitly stated that tail-recursion is in-bounds. The Ackermann function recurses twice, so yes it would need some kind of memory, which could theoretically be implemented with an analog stack of some kind. And I agree that loop-based (single recuse) op-amp feedback can’t compute Ackermann, but the question was whether recursion is possible in analog circuits, and the answer is that single-recurse already exists widely, and double recurse or more could be done by someone determined, there’s no theoretical constraint.