What's going on with OpenAI and the Navier-Stokes controversy?

Tristan Buckmaster, a mathematician at New York University, and Levent Alpöge, a researcher employed at Anthropic but working in a personal capacity, had been developing their own solution and made use of multiple different LLMs in their efforts, including Anthropic Claude, OpenAI's Codex tool and its Astra frontier model. According to a statement by Buckmaster, OpenAI may have doubled down on its efforts regarding Navier-Stokes after learning that a team including rival Anthropic was close to a solution. He questioned whether OpenAI had leveraged the work he and his colleague had done with Codex to obtain its own breakthrough. "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer," the statement reads.