While "perfect third" may not exist as a name for an interval, it does make sense to apply the adjective "perfect" to the interval "third" in order to distinguish a just intonation third (4/5) from a well-tempered intonation third (1/2)^(4/12).
You can construct a system under which the phrase makes sense but musicians and musicologists will look at you weird if you say it. The LLM just forges bravely on, however.
