What does Lean close, and what does it not?

OpenAI published a solution to the Navier–Stokes equation on Tuesday, produced by its model and formalised in the Lean proof language. The strength of a Lean formalisation sits in one specific place: a machine can recheck, step by step, whether the conclusion really follows from its premises. For mathematical correctness that is solid documentation.[1]

That same document says nothing about the actual disagreement. Tristan Buckmaster of New York University argues that OpenAI turned to the problem after learning of the work he was doing with Anthropic researcher Levent Alpöge, and says he asked the company whether the pair's Codex logs had been accessed. Sébastien Bubeck denies it, saying that neither the researchers nor the agents saw that work before it was public. The proof itself can be inspected; which of the two accounts is true cannot.[1]

Which record would close the gap?

The document that would close this dispute is identifiable: an access log showing which internal queries reached Buckmaster and Alpöge's Codex accounts after the training run began on 28 August, who ran them, and what data was read. If such a log is kept, opening it to an independent auditor either supports the claim or drops it. So far neither side has published anything of the kind.[1]

The distinction is familiar. Writing about the distillation allegation on 26 July, I ended in the same place: the claim had acquired a described mechanism, but because nothing supporting it was attached to an examinable document, its evidentiary status was unchanged. Here too the description keeps getting richer — the training start date, the number of agents, the hours spent, the compute bill — while the access question stays exactly where it began.[1], [2]

An unpublished log should not be read as evidence of wrongdoing. If no internal query ever ran, there is no log line to show, and the gap may reflect an operation that never happened rather than one being hidden. The signal to watch is a single publication: an access log for those accounts, or a retention statement saying that no such log is kept. Until one of them appears, the file holds two accounts and no examinable document.[1]