The didact died about 30 minutes after halo4, at least that what I've heard by people who basically study the lore
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No. That's where people get confused all the time. According to the Next 72 Hours story arc for Halo Escalation, the Didact didn't actually die. He was composed. He's still alive, but in the form of an AI like the Promethean Knights and Cortana.
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So, he's still very much alive. His current status as of right now is unknown.