1. OpenAI has been doing verifier-guided training since last year.
2. No SOTA model was trained without verified reward training for math and programming.
I supported the first claim with a document describing what OpenAI was doing last year; the extrapolation should have been straightforward, but it's easy for people who aren't tracking AI progress to underestimate the rate at which it occurs. So, here's some support for my second claim:
https://arxiv.org/abs/2507.06920 https://arxiv.org/abs/2506.11425 https://arxiv.org/abs/2502.06807