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OpenAI's Navier-Stokes statement on user data has two parts, not a firm "we don't train on your data" promise

A mathematician kept a year of unpublished drafts in Codex, then asked whether they had been used for training and got silence on that half of the question, which is the half every enterprise rollout treats as settled.

The Product Desk · Product desk

Illustration accompanying OpenAI's Navier-Stokes statement on user data has two parts, not a firm "we don't train on your data" promise

What happened

  • OpenAI said in a Tuesday blog post that it solved the Navier-Stokes problem using an internal model more powerful than the newly released GPT-6 Astra, running 10,000 concurrent agents.
  • A day earlier, NYU's Tristan Buckmaster posted a proof for a simplified version of the equations, after nearly a year of work with Anthropic researcher Levent Alpoge using public OpenAI and Anthropic models.
  • Buckmaster says the pair had put every draft of the project into Codex, that he was told the model did not look up user data, and that his repeated question about training went unanswered.
  • Buckmaster's document says OpenAI staff offered him co-authorship on a joint paper that dropped Alpoge because he works for Anthropic, an offer the company's denial of the wider accusations does not address.

Compiled by The Product DeskSomething wrong?How this is made

Why it matters

  • exposure The customer with the most work inside a product has the least covered by a promise about specific user data, because session history accumulates faster than anyone revisits the data settings.
  • constraint Verification narrows to whoever owns the compute: a result produced by an unreleased model and 10,000 agents cannot be re-run by a referee with a university account.
  • decision Buyers renewing AI seats now have to split one assurance into three and establish which of them sits in a signed agreement rather than a blog post.
  • contradiction Bubeck's denial and Buckmaster's reading of the same carve-out can both be honest, which means neither party's statement can close the dispute and the argument moves to what the training corpus contained.

Retrieval at inference time is one promise. Training on your content is a second one, and a third, which almost no procurement checklist names, covers de-identified derivatives of your usage. OpenAI's announcement makes the first: no specific user data was accessed in order to solve this problem [9]. It declines the third in writing, saying that while unlikely, it cannot rule out that de-identified data derived from their usage of its products helped improve its models [9]. On the second, Buckmaster says he asked twice and got an answer only about lookup. He was told the model did not look up user data, and when he asked again about training, no answer came [8].

The timing is why that gap carries weight. OpenAI says it started training the internal model on August 28 [3] and announced the proof on September 8 [4], eleven days later [14]. Buckmaster and Alpöge had been working on the problem for close to a year [6], with drafts going into Codex sessions the whole time [8]. Buckmaster's reading of the carve-out, posted on Mastodon, is that OpenAI is "openly admitting they used training data from a period after we found our result" [11]. Sébastien Bubeck of OpenAI says the team saw none of their work until it was public, and that the two proofs differ significantly [10]. Both proofs do use the route pioneered by Diego Córdoba and Luis Martínez-Zoroa, and Javier Gómez-Serrano of Brown University says that approach was one of several thought to hold promise [13], so the shared route settles nothing in either direction.

Teams tell themselves users read the data controls page, work out which toggle governs training, and keep the sensitive material out of the surfaces the toggle does not cover. What users actually do looks different. They put the work where the tool is, for a year, because that is where the tool is useful [8]. Depth of use is the number worth watching. It is also the number that creates the exposure. Someone who pastes one function into an assistant risks little. The customer who has kept an entire unpublished project in one vendor's session history has far more at stake, and is the customer a renewal depends on.

The 2x2 has two axes. First, is the assurance contractual, in a document with a counterparty and a remedy, or is it a statement, in a blog post or a post on X [15]? Second, does it cover only retrieval of your data, or does it also cover derivatives, including de-identified ones? Most assurances an operator can actually produce on request sit in the weakest quadrant, statement plus retrieval only, which is the quadrant OpenAI's language occupies here. The useful exercise is writing out the sentence you would need about your team's unpublished work, then finding which document contains it. If the answer is a blog post, you have a press release where you wanted a term.

Which is where credit lands. A proof produced by an internal model running 10,000 concurrent agents [1] can be checked in detail only by people with access to that setup, and according to Buckmaster's document, the offer of joint authorship came with Alpöge dropped because he works at Anthropic [12]. Attribution here depends on logs that one party can read, and that party's own carve-out says the logs may not settle it.

What to watch

  • Whether rival vendors add or drop a de-identified derivatives clause in their data terms now that OpenAI has put one in writing.
  • Whether Buckmaster and Alpoge release timestamped session records that date their result against OpenAI's August 28 training start.
  • Whether the Clay Mathematics Institute addresses eligibility for an agent-produced proof, given OpenAI says it will not claim the prize.
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