I volunteer to be the gatekeeper or the AI, provided there are no stakes. My email address is firstname.lastname@example.org.
I do not believe that humans are immune to manipulation or persuasive argument, and since I am a human, it's possible I could be persuaded to let the AI out of the box.
Using the jester's reasoning, it's possible to make him believe that the earth is flat by writing down "either this inscription is true and the earth is flat, or this inscription is false and the earth is not flat, but not both" this makes an unflat earth logically impossible!
I wonder what this says about the law of the excluded middle, I guess that it slides if self reference is involved.