1/4/2013 8:47:23 PM PermalinkThere are two Didacts: the one in Halo 4 is the Ur-Didact, the original, the one the Librarian talks to is the Bornstellar-Didact, another forerunner who was imprinted with Didact's memories and personality.
1/4/2013 8:45:55 PM PermalinkThe Librarian strands herself on Earth some time after imprisoning the Ur-Didact - she says in the Terminal that "in the days to come, the Halo rings will fire," so the events of Halo 3's Terminals where she converses with the Bornstellar-Didact play out normally.
For best results in downloading the Destiny Beta to your Xbox One, don't launch the game until the download is complete. The Destiny Beta FAQ has been updated with info on how to troubleshoot your Xbox One download (scroll down). http://www.bungie.net/en/View/Bungie/DestinyBetaFAQ
If encountering Party Stabilization errors on Xbox One: try turning off your console, fully unplugging, then plugging in and trying again.