A new variation on the Gatekeeper idea, thanks to Zvi Schreiber.

We block all but one IO channel for our AGI.

We create a formally verified proof-verification system as a gatekeeper. We pass the Gatekeeper a decision problem with a  formal proof that it is in the complexity class UP ("Unambiguous Non-deterministic Polynomial-time").  The Gatekeeper verifies the proof, and passes the decision problem to the AGI. If the AGI provides an answer, the Gatekeeper validates that this is the unique valid answer (which it can do in polynomial time) and if so it passes  the answer to us. 

The advantage of this approach over one-bit and other Oracles is that the AI can do some useful problem solving with zero discretion as to the data it communicates. It can either give the unique answer or no answer at all. Such a gatekeeper is feasible with today's technology. 

To keep the AGI from communicating by choosing the timing of its answer, the Gatekeeper  always communicates the answer (or the fact that there it is not yet one from the AGI) after exactly 1 hour.  

(The idea of restricting an Oracle AI to choosing from predetermined list of verifiable answers has been mentioned, but I don't remember anyone adding this formalism.) 

The usual caveats on Oracles apply. Like other Oracles, this is a stopgap rather than a solution to the FAI problem.

1. The laws of physics still give the AGI a  causal link to its environment, even if it is in a Faraday cage. 
2. Even a one-bit Oracle AI can exert optimization power when asked multiple questions. 
3. Answers aren't enough to ensure safety: We may be asking the wrong questions or not understanding the implications of the answers.