Translation AI though has provable behavior cases though: round tripping.

An ideal translation is one which round-trips to the same content, which at least implies a consistency of representation.

No such example or even test as far as I know exists for any of the summary or search AIs since they expressly lose data in processing (I suppose you could construct multiple texts with the same meanings and see if they summarize equivalently - but it's certainly far harder to prove anything).