I think it can make a summary of any text; I’m not sure that’s proof that it’s explicitly using written summaries to track the conversation.

And humans also typically can’t recite the first message in a conversation from memory. That doesn’t mean they have no memory at all, or that their memory takes the form of continually reciting and updating a written summary of the conversation.

I’d be curious to hear OpenAI’s response to OP’s question.