Part of the trouble with this is that we don't really know what kind of demonstrations would be within the power of a superintelligent AI. If the coin comes up tails, do you get to say "I've got a rigorous proof of my friendliness which I can show you" on the presumption that you can mindhack the reader into thinking they've seen a rigorous proof? Do you get to say it if the coin came up tails on the presumption that a superintelligent AI could come up with a proof that a human could actually verify? Declare it off bounds because you can't come up with such a proof and don't think a human would be able to check one that an AI came up with anyway?
Eliezer proposed in a comment:
>More difficult version of AI-Box Experiment: Instead of having up to 2 hours, you can lose at any time if the other player types AI DESTROYED. The Gatekeeper player has told their friends that they will type this as soon as the Experiment starts. You can type up to one sentence in your IRC queue and hit return immediately, the other player cannot type anything before the game starts (so you can show at least one sentence up to IRC character limits before they can type AI DESTROYED). Do you think you can win?
This spawned a flurry of ideas on what the AI might say. I think there's a lot more ideas to be mined in that line of thought, and the discussion merits its own thread.
So, give your suggestion - what might an AI might say to save or free itself?
(The AI-box experiment is explained here)
EDIT: one caveat to the discussion: it should go without saying, but you probably shouldn't come out of this thinking, "Well, if we can just avoid X, Y, and Z, we're golden!" This should hopefully be a fun way to get us thinking about the broader issue of superinteligent AI in general. (Credit goes to Elizer, RichardKennaway, and others for the caveat)