In the latest William Gibson novel Agency, a bunch of human characters are constantly told exactly what to do by a superhuman AI in order to have everything turn out for the best. They accept the notion that this character, who they only talk to over their phones, is an AI, when it seems like it could just as easily be a fictional construct created by a person or organization. There's one part of the book where a character is convinced off-page that the AI is a superhuman AI by talking to it for a bit, although we're not privy to the conversation.
What I'm wondering is, how could a superhuman AI best prove that it was a superhuman AI through chat? Is there a more or less definitive way to do it? Is there a fast way to do it?