It is not listed as of yet, but it does work if you punch in gpt-4o. I will stick with gpt-4-0125-preview for now because gpt-4o is majorly prone to hallucinations whereas gpt-4-0125-preview isn't.
Yes, I actually do, and I ran multiple tests. Unfortunately I don't want to give them away, as I then absolutely risk OpenAI gaming the tests by overfitting to them.
At a high level, ask it to produce a ToC of information about something that you know will exist in the future, but does not yet exist, but also tell it to decline the request if it doesn't verifiably know the answer.
Update: gpt-4o-2024-05-13 is listed now.