It is just a copyright violation. My guess is that it would be fine if you use already scraped data as you haven't accepted TOS, but they have every right to block you or access to your business if you violate this.

I thought the copyright office said that ai generated material isn’t copyrighted?

You’re correct. US law states that intellectual property can be copyrighted only if it was the product of human creativity, and the USCO only acknowledges work authored by humans at present. Machines and generative AI algorithms, therefore, cannot be authors, and their outputs are not copyrightable.

Sorry for asking a stupid question.

How much Theseus do I need to ship before I can copyright it as my own? Is there some threshold for how much of an AI generated work needs to be modified by "human creativity" prior to it being copyrightable?

As far as I can tell, you can claim credit for the output of a tool which produces something at your direction. If you write an algorithm to generate patents, and you execute that algorithm and submit its output to USPTO under your own name, no problem. If you gave credit to the algorithm, their policy is to deny the claim.

Can OpenAI claim copyright on GPT’s outputs?

I am not a lawyer, mind, but if they're trying to claim sole copyright the output of the machine's collaboration with its users, that sounds awfully dubious. Knowing lawyers, and having some familiarity with copyright law, the only thing i can confidently say is that your question will take several very expensive years to answer.

Sorry, can't edit my comment now. I meant it is "not a copyright violation, but just a TOS violation."

And even if they do, if someone uses the api and makes a publicly available website with no clickwrap, it would be legal to scrape that right?