THE SHORT VERSION
The mathematicians checking OpenAI's proofs warn: our role isn't certification

The three researchers OpenAI asked to shepherd verification of its proofs — Russell Impagliazzo and Ramamohan Paturi, who proposed the Exponential Time Hypothesis, and MIT's Ryan Williams — wrote in an open letter that “our involvement should not be taken as certification of the claim,” adding that a result of this significance “requires careful, independent scrutiny.”
The group signed no nondisclosure agreements and will not be paid, and the physics claim is being handled differently still: a group led by Nobel laureate David Gross chose not to release the AI-produced material and will write the Yang-Mills result up itself, so outsiders cannot yet examine it.
OpenAI's own post calls the manuscripts “raw research data” and notes the Yang-Mills result covers existence only, not the mass gap the Clay Millennium Prize requires — none of the three claims has passed peer review.