It's unknowable and not possible to prove if any one specific conversation contained the insights for solving Navier–Stokes.
We also don't know if the authors unintentionally provided data to OpenAI through alternate means, such as via alternate accounts or model feedback queries.
Further, given that this is all in the open now, they can search the training data. No way somebody is using some specific unique cutting edge mathematical approach to solve a fluid dynamic problem 99.9% of people have never heard of and it's not locatable. Considering they spent $15,000,000 already on this, they could afford to grep around to be able to state that their hands are clean.
Knowability and likelihood are almost orthogonal here. If I commit a crime and perfectly destroy the evidence, my deed may be unknowable. That doesn’t make it more or less likely.
> not possible to prove if any one specific conversation contained the insights for solving Navier–Stokes
It may be. We haven’t seen the researchers’ transcripts. We don’t know what Buckmaster or his co-author uploaded to OpenAI or with what permissions (or if OpenAI actually respects those toggles).
The fact they can't make a blanket denial triggers everyone's bullshit detectors, and they're getting eviscerated over it.
Again, see the Apple lawsuit. OpenAI has never been constrained by facts in what it can and can’t say.
To the extent anything is setting off my bullshit detector, it’s in the idea that this time is different (Moreover, the idea that we should assume this divergence without evidence.)
OpenAI doesn’t have the benefit of doubt. They shouldn’t for anyone who’s honest and reasonable. That doesn’t mean they’re automatically at fault. But when the twentieth person comes forward and says a pattern is continuing, I’m giving them the preliminary benefit of doubt. It’s a bit extreme to conclude based on that. But it’s far more baseless to swing to the other side and claim we need to clear the table for a serial offender.
That they don't is telling.