I don't even understand the conflict tbh. Probably I'm just dense. Tristan is not claiming NS, just a huge advance which may solve NS soon. OAI is claiming NS and willing to credit Tristan for the ideas and publish after.
Oai offers two options, the second Tristan views as dishonest. But Tristan rejects the first, why? Because he thinks it's theft? But then why would OAI threaten him?
He claims to have found a counterexample for NS (see the second paragraph of the article), but the paper is not ready yet.
OpenAI claims to already have a full proof (which they produced in the past 5 days after the rumors leaked). Hence the dispute.
What I find interesting is the timeline of when he found counterexample for NS is very unclear. Did Tristan find a counterexample weeks ago or was it very recently? Was it after OpenAI solved it? The wording is intentionally vague.
Either way, there was a massive rush to publish these results.