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If I came up with this counterexample, I sure as hell wouldn't give credit to Claude.

Indeed, the incentive is the opposite: hiding the fact that they used an AI would boost their own personal brand.

He worked for Anthropic, so such a claim would be very unconvincing

Because only people who work for Anthropic use AI tools? What is the reasoning here? The guy is a mathematician, after all.

You have it backwards. Only people not working for Anthropic do not use AI tools.

Yes.

Though not everyone who works in the sausage factory still wants to eat sausages.