I agree if the utility function was unknown and arbitrary. But an AI that has already done 3^^^3 simulations and believes it then derives further utility from doing 3^^^3+1 simulations while sending (for the 3^^^3+1th time) an avatar to influence the entities it is simulating through intimidation and fear while offering no rationale for those fears and to a website inhabited by individuals attempting to be ever more rational does not have an unknown and arbitrary utility function.
I don't think there is any reasonable utility function that is consistent with the actions the AI is claiming to have done. There may be utility functions that are consistent with those actions, but an AI exhibiting one of those utility functions could not be an AI that I would consider effectively omnipotent.
An omnipotent AI would know that, so this AI cannot be omnipotent and so is lying.
I don't think there is any reasonable utility function that is consistent with the actions the AI is claiming to have done.
What is your definition of 'reasonable' utility functions, which doesn't reference any other utility functions (such as our own)?
This is our monthly thread for collecting arbitrarily contrived scenarios in which somebody gets tortured for 3^^^^^3 years, or an infinite number of people experience an infinite amount of sorrow, or a baby gets eaten by a shark, etc. and which might be handy to link to in one of our discussions. As everyone knows, this is the most rational and non-obnoxious way to think about incentives and disincentives.