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).
Getting byte exact text isn't the point though: even if it's different, I as the original writer can still look at roundtripped text and evaluate that it has the same meaning.
It's not a lossy process, and N round-trips should not lose any net meaning either.
This isn't a possible test with many other applications.
English to Japanese loses plurals, Japanese to English loses most honoriffics and might need to invent a subject (adding information that shouldn't be there and might be wrong). Different languages also just plain have more words than others with their own nuances, and a round trip translation wouldn't be able to tell which word to choose for the original without a additional context.
Translation is lossy. Good translation minimizes it without sounding awkward, but that doesn't mean some detail wasn't lost.
How about a different edge case. It's easier to round trip successfully if your translation uses loan words. It can guarantee that it translates back to the same word. This metric would prefer using loan words even if they are not common in practice and would be awkward to use.
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).