Hmmmm, given such conditions, couldn't the Gatekeeper even create an "AI in a box" inside another, invisible box, to actually simulate what would happen if it let the original AI out? I don't find it a very intellectually satisfying solution, but it does seem to technically fit the spirit of the game.

I'd have to keep you in the box, however: (a) it's not an intellectually engaging solution and I don't want to lose $10, but also (b) I can think of ways for the AI to have reasonably faked those results. The AI can dictate the results, but not the actual Truth.

If I was playing "just for fun", with no wager and no real internal commitment to treat you as a truly dangerous threat, I'm not sure whether I'd let you out or not, but I probably wouldn't have put in as much effort to reinforcing point (b), and I'd feel like it was cheating to keep you in solely on point (a).