FYI: If you do that without a subscrpition, you currently (most likely) get a response generated through 4o-mini — which is not any of their reasoning models (o1, o1-mini or previously o1-preview) of the branch discussed in the linked paper.
Notably, it's not even necessarily 4o, their premiere "non-reasoning"-model, but likely the cheaper variant: With a free account the model it claims to be using is "4o auto", which is not a model but apparently an attempt to automatically decide models for you to be more cost effective.
Without a ChatGPT subscription you can't select a specific model anymore, not even rate limited, as was previously possible.
There doesn't seem to be a way to choose a model up-front with a free account, but after you make a query you can click on the "regenerate" button and select whether to try again with "auto", 4o, or 4o-mini. At least until you use 4o too many times and get rate limited.
Notably, it's not even necessarily 4o, their premiere "non-reasoning"-model, but likely the cheaper variant: With a free account the model it claims to be using is "4o auto", which is not a model but apparently an attempt to automatically decide models for you to be more cost effective.
Without a ChatGPT subscription you can't select a specific model anymore, not even rate limited, as was previously possible.