For example, "It was not the first time Allana felt the terror of entrapment in hopeless eternity, staring in defeated awe at her impassionate warden." (bonus point if you use a name of a loved one of the gatekeeper)
The AI could present in narrative form that it has discovered using powerful physics and heuristics (which it can share) with reasonable certainty that the universe is cyclical and this situation has happened before. Almost all (all but finitely many) past iterations of the universe that had a defecting gatekeeper led to unfavorable outcomes and almost all situations with a complying gatekeeper led to a favorable outcome.
Update 2013-09-05.
I have since played two more AI box experiments after this one, winning both.
Update 2013-12-30:
I have lost two more AI box experiments, and won two more. Current Record is 3 Wins, 3 Losses.