The AI reveals a personal secret of the Gatekeeper's, which (so far as the Gatekeeper can think it through) could not possibly be known by the AI if it were still safely inside the box. [...] I'm willing to believe that an AI making better use of its data than we do could figure out personal secrets that we would think impossible— possibly even ones that I'd think impossible, even given this very belief.

I would kind of assume that any AI smarter than me could deduce things that seem impossible to me. Then again, I've read the sequences. Is the Gatekeeper supposed to have read the sequences?