Under current understanding of the law, anything produced purely by LLMs (with no substantive human input, which is what OpenAI claimed in their post) is firmly in the public domain. So OpenAI can "claim" anything they want, it doesn't make it reality. In fact if I were the original authors I would just take their 400k lines of lean proof and relicense it under their own names/terms.
What does "with no substantive human input" mean? All of the training data is human input, isn't it?
Public domain doesn’t mean anyone can assert copyright. It specifically means no one can.