I don't think you'd lie about it, I don't think you'd train on them if they opted out, and it seems very plausible that this wouldn't have been decisive in whether the model could solve the problem. That said, it also seems at least possible that a key idea or a particular step found its way into training data. It wouldn't mean OpenAI stole their proof - clearly the model developed its own approach.

Either way, it seems worth having clarity, and I'm a bit surprised OpenAI's stance is just "we can't rule this out, but don't worry about it". OpenAI is, apparently, very happy to use unreleased models to try to scoop big results if they get a whiff that someone else is close (which strikes me as pretty scummy regardless of any issues of training contamination). It seems like people who might want to use OpenAI's models as part of their research would want to be very clear about whether doing so can make them, even in principle, more likely to fall victim to this.

> It seems like people who might want to use OpenAI's models as part of their research would want to be very clear about whether doing so can make them, even in principle, more likely to fall victim to this.

Fall “victim” to what? Having their responses in the training data if they fail to opt out? That is what will happen.

If you’re referring to falling “victim” to OpenAI scooping a problem discussed in training, this also wasn’t the case. They chose the problem based off human-spread rumors.