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Even if that were true, they've already admitting to throwing vast quantities of resources to scoop a researcher who was about to publish (because they'd learned, somehow, of his breakthrough). If that doesn't bother you I think you need to take a step back and have a good think about this.
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*to scoop a team working with Anthropic, their chief competitor.

Also, they didn't have the solution. They had a lesser problem no one cared about.

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My understanding is that the Euler solution was in fact a significant achievement, but it's well short of Navier-Stokes (Euler doesn't include viscosity). It's not clear whether Buckmaster and Alpöge's approach would have eventually led to a full Navier-Stokes solution or how long it would have taken.
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First to publish -- it's always been this way.
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I can say categorically that OpenAI is not a credible or trustworthy company.
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Where did OpenAI say this?

And it still leaves open the question of the prompt itself, which can just as easily encode information about the same knowledge.

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Regardless, they started working on this problem after hearing that one of their customers was already working on it. It almost doesn't matter about the training data. This is the provider you are paying undermining your career.
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Why should we trust them?
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Well all we have are vague accusations without evidence and a very specific denial also without evidence, so I guess just believe whatever you want.
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The threats weren't denied, and they did offer an authorship to Buckmaster, which would be very strange if he had nothing to do with it.
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The offer was for him to do for their proof what he had done to Anthropic's, he would clean up the proof and extract human-understandable concepts from it. If he did that work he would deserve author credit IMO.
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Because like all state-sponsored thieves actions it is never what you know happened that matters, but rather whether you can prove it... Even then... ymmv =3
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