SPOILERS
When it showed Kirk's body in the daystrom station, TOS era medical sounds played. Someone on reddit pointed out that the text read "critically injured aiding Jean-Luc Picard" and "his body was recovered for project phoenix". According to google the word phoenix means, "a unique bird that lived for five or six centuries in the Arabian desert, after this time burning itself on a funeral pyre and rising from the ashes with renewed youth to live through another cycle." Could they be trying to revive Kirk?