OpenAI ships a Lean build that checks its Navier-Stokes proof against its own definitions

A Lean build settles exactly one question. It machine-checks the result under the definitions encoded in the formalization ^[10]. Compile the repository and you know the argument follows from those definitions. You do not know that those definitions are the Clay problem. That judgement stays with mathematicians, who have to decide whether the definitions and theorem statements faithfully capture the problem and whether the analytical paper supports the formalized result; by runtimewire's account that review has barely started ^[11].

So the burden does move, and it moves one hop. The disputable object stops being the argument and becomes the statement, which is a far smaller thing to read. The repository helps there: it carries separate Navier-Stokes and Euler formalizations plus instructions for independent proof checking ^[9]. Their premises differ. The Euler singularity is for the unforced equations ^[16], while the Navier-Stokes construction starts the fluid at rest and applies a smooth force with compact support in space and time ^[6], and OpenAI says that construction establishes alternatives C and D of Clay's official formulation, in three-dimensional space and on the periodic torus ^[8].

The run is the part no outside party can check. OpenAI's accounting puts the Navier-Stokes search at 2.7 million messages and roughly 130 billion output tokens ^[19], against 4.9 million messages and about 300 billion output tokens for the whole multi-problem attempt ^[20]. That puts 43 percent of the output tokens on the one problem that landed ^[3]. Spread 130 billion tokens across 88 hours and the sustained rate is near 410,000 output tokens per second ^[1]. Spread them across the roughly 10,000 concurrent agents and each wrote about 13 million tokens ^[2].

The money is looser. OpenAI executives placed the computing expense in the millions of dollars on a press call, according to Axios ^[21]. If that figure covers the Navier-Stokes run alone, a $2m bill works out near $15 per million output tokens and a $10m bill near $77 ^[4]. That band is a whole bill divided by output tokens, so it also absorbs input processing, the cached internet material and the code execution the agent groups were given ^[15].

The timeline is tight enough to be worth checking against itself. Training began on August 28th ^[14] and was four days in when researchers dispatched agent groups on September 1st after hearing rumours that two Millennium Problems had fallen ^[15][6]. The Navier-Stokes group reached its result on September 5th ^[18], so 88 hours fills all but eight hours of that window ^[5]. GPT-6 Astra then spent another 17 hours on formalization and verification ^[18]. OpenAI used Codex to consolidate intermediate results and pass them between groups ^[17], and has released neither that orchestration system, nor the model, nor its benchmark results, nor a cost breakdown ^[22]. The model itself is described only as significantly more capable than GPT-6 Astra, with training still underway ^[3].

Clay still lists the problem as unsolved, and OpenAI says it does not intend to claim the $1 million prize ^[13], which under Clay's rules it could not collect for at least two years in any case ^[7]. Until the statement audit is done, the fast verdict available to anyone is the one a build returns, and that verdict is about the definitions in the repository.