I thought his voice at the end was him reflecting on the humans kicking his butt during their war 100,000 years prior. I don't recall the exact wording, but I assumed this was that or perhaps the weird "second form" thing the Forerunners take on when they die (Bornstellar talks about this in the beginning of Cryptum).
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I seriously doubt that the Didact is dead. He fell through a giant slip-space portal underneath the composer. Meaning he ended up somewhere in space, and seeing as what happened to John twice in a row, the Didact was probably retrieved or revived somehow, as to specifics we don't know yet. But you never know, he could actually be finished. I just have trouble thinking 343 would throw away such a great villain in one game. I personally think the Didact was the best villain the Halo series has had. "Humanity's imprisonment, is a kindness." There was so much hate and contempt within that statement it actually sent a chill through me.