OpenAI puts a machine-checkable Lean proof of finite-time blowup in a public repo

At the announcement there was nothing outside the company to look at, which is the position TNW reported it from ^[15]. What changed is that there is now something to run. A Lean formalisation can be machine-checked by anyone with the toolchain, and per TNW that is the one part of this package that does not require trusting the vendor ^[2].

OpenAI says the formalisation and verification took a further 17 hours on GPT-6 Astra ^[3], the model that shipped last week. The search itself was run by an internal system the company describes as significantly more capable, with Astra demoted to checking the answer ^[11]. Set 17 hours against the roughly 88 hours the agents spent and checking came in near a fifth of finding: 17 divided by 88 is about 19 percent ^[21].

The finding side reads like a purchase order. Around 10,000 concurrent agents worked from 1 to 5 September, about 88 hours, consuming 2.7 million messages and roughly 130 billion output tokens ^[10]. Divided through, that is about 13 million output tokens per agent ^[19] and about 270 messages each ^[20]. OpenAI has previously put the compute bill in the millions ^[12]. This was not one model reasoning hard for a long time, the way teams often picture a mathematical result coming together; it was a swarm run on a three-and-a-half-day meter.

A Lean check certifies the theorem that was written down, force term included ^[2][8]. It does not certify that the theorem written down is the one the Clay Institute asked for, and TNW's read is that the forced-blowup question belongs to mathematicians rather than to a technology desk ^[16]. Turning down a $1M prize after 26 years of failed attempts signals something more than modesty ^[7], and that is what makes the declining sentence the most informative line on the page.

The credit position moved too. OpenAI denied Buckmaster's suggestion that it had pursued directions derived from his unpublished work with Alpöge ^[13]. The offer that has since appeared reads like an acknowledgement rather than a dismissal, and it costs nothing that a formalisation could ever verify.

Any result that arrives with a claim attached should be checked against two tests, kept in separate columns. One: is there an artifact you can check without the vendor's cooperation. Two: does that artifact cover the sentence in the headline. Both yes, and the headline is yours to repeat. If there is an artifact but coverage remains unresolved, which is where this sits, you take the theorem while holding the headline. Coverage asserted with no artifact is where this story stood in September. If neither holds, you are reading a press call. The discipline is refusing to let a passing score in column one settle column two.