OpenAI's o1 in September, o3 demoed 3 mo later. Where are they really at?

o1 was released in September 2024, and just three months later, OpenAI demoed o3 (skipping o2 due to a naming conflict with a telecom company).

This makes me wonder:

• How long had OpenAI already been working with or refining o1 before its public release? Were they sitting on it for months, maybe even 1 year beforehand?
• Could o1 (or o3) have influenced Ilya's decision to leave and found his own AI lab, given its potential implications?
• And more interestingly, where are they now? Given the leap from o1 to o3, are they quietly testing o4 or even o5 in their labs? Is this the reason for their recent vagueposting about singularity and AI automated R&D?

What caught my attention during the o3 demo was one of the researchers mentioning that we might see "jumps like o1 --> o3 every three months from now on."

If that's true, we might be accelerating into a future where the pace of AI iteration far outstrips what we’ve seen before.

Curious to hear your thoughts on this.