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Watermarking only applies where the AI has a free choice (https://www.anthropic.com/news/claude-text-watermark).

i think practical question is whether the detector survives ordinary transformations of the text. if for say i paraphrase a watermarked answer with another model, do we expect the original signal to disappear and the second model's signal to replace it?

There are multiple ways to paraphrase and the paraphrasing model is going to use its own random number generator whenever it thinks there's more than one possible choice. (Not really binary; the RNG will have more or less effect.)

So it will definitely be watermarked by the paraphrasing model. But the question is whether the original signal survives at all. There might be a weak signal that's detectable with enough text?

If its paraphrased to any significant degree I'd expect the original to not survive. The second model's watermark would of course be there regardless.

Does it still apply with zero entropy?

No. Anthropic's example is completing the sentence "Isaac Newton's most famous work was called Principia ..." has only one correct answer, so nothing to watermark.

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