Alpöge and Buckmaster resolve the forced Euler problem with an Anthropic internal model

Levent Alpöge (Anthropic) and Tristan Buckmaster (NYU) independently produced a resolution of the forced Euler regularity problem using an internal Anthropic model, announced the same day as OpenAI's Navier–Stokes post. Per Buckmaster's statement, the pair had worked on related problems for nearly a year with Claude and Codex (primarily GPT-5.6 Sol), reaching a breakthrough on 2026-08-15; he alleges OpenAI's first prompt on the problem was sent only after information about their work had reached OpenAI, and that OpenAI would not answer whether its model was trained on their Codex drafts. OpenAI acknowledges their priority on forced Euler, says it offered a joint announcement, that no user data was accessed, but cannot rule out that de-identified product-usage data informed model improvements; the two proofs cover different Euler variants (forced vs. unforced). Buckmaster also reports Alpöge was told he could not co-author an OpenAI paper given the OpenAI–Anthropic competitive relationship. The statement's HN thread (2,035 pts) outdrew the announcement itself.

Two readings matter. Technically, a second lab has now driven Millennium-scale mathematics with an internal model, and the collaboration pattern — a year of guided Codex/Claude work preceding the breakthrough — is itself a replicable research workflow. Institutionally, the dispute exposes the questions every agent-platform vendor must eventually answer: whether user sessions can inform competing internal efforts, and how rival-lab contributors are credited. Willison's framing is the sharpest: could your own partial solution, produced in someone's product, help a later model finish it first?