How do Cortana and the Chief know that the Forerunner they meet is in fact the Didact?
Maybe I missed it but Cortana seems to just pluck the name out of the air, and then everyone (even the Librarian, with whom they've had no contact) refers to him as such for the rest of the game. It seems as though there's no canonical way for them to know that this guy is the Didact until the meet the Librarian and she lays it out for them
Their in-game logic seems to be "I read about a Forerunner called the Didact once, I just met a Forerunner, therefore that Forerunner is the Didact" - no dice, this doesn't work