Is the Didact in Halo 4 the Bornstellar Didact or the Ur-Didact?
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The Ur-Didact. As the guy above me said, he was shown fighting the humans. Also, Bornstellar had much more empathy towards humanity so his character doesn't fit.
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Considering the terminals showed him looking over the body of the Lord of Admirals I would say that it's the Ur Didact.
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Not sure if this is right, but it might help. http://www.halopedia.org/Didact