1) OpenAI and Buckmaster did not solve the same problem. Per https://x.com/IlinVasily29521/status/2097554700321329393 , here is a breakdown of who solved what.

  Tristan + Levent: 3D incompressible Euler with forcing
  OpenAI: 3D incompressible Euler without forcing
  OpenAI: Navier-Stokes with forcing
  No one: Navier-Stokes without forcing

Euler equations = Navier-Stokes without viscosity. Forcing means external force. Absence of viscosity and presence of external force make blowup easier to construct.

Tristan+Levent ticked the weakest case, OpenAI ticked the two next weakest, then the final case is unsolved. Only the last two are eligible for the Millennium Prize. The Navier-Stokes general case remains unsolved.

Navier-Stokes has an extra viscosity term compared to Euler, which makes the problem noticeably harder to find a blowup. They are not the same problem.

2) The approach both chose to use (by Luis and Diego) was published in 2023 and is included in every frontier model's training dataset. An AI model could independently choose the same route as Luis and Diego, without access to Buckmaster's work.

3) You mischaracterized OpenAI's statement. They issued a blanket denial on using Buckmaster's Codex data from after July 3.

"We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training. After investigating, we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way.”

July 3 was the training cutoff date for the model that solved Navier-Stokes. No user data after that date influenced the model.

4) Buckmaster and Alpöge found their blow-up for 3D incompressible Euler with forcing on August 15 https://cims.nyu.edu/~tristanb/statement.pdf , over a month after the model training cutoff point. They stated they did not have real progress prior to this point.