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What happens if someone handwrites a Claude output, then someone uses that handwritten text as a reference. Now you've got a watermarked idea which may have no direct linkage to the usage of Claude.
If the algos work as advertised, watermarked token sequences have an extremely low probability. Copying the words by hand doesn't change that.

The mechanism seems to survive editing. The extreme probabilities get a little less extreme, but are still extreme enough to be distinctive.

But it wouldn't survive paraphrasing, because the output would be entirely human and the token correlations would disappear.

It might not survive referencing if only a sentence or two is used.

The practical issue is how true the claims are. It's one thing to create a proof of concept, another to see how it works in use.

And this is potentially catastrophic for code, because the grammar and word choices of code are completely different and more fragile than standard English.

How is that different from referencing digital text that someone copied and pasted from Claude?
Because there's an expectation of authenticity from the written word. If you've referenced something handwritten, you don't expect it to be the output of an LLM.

Similarly, if you quote someone word-for-word, you wouldn't anticipate their words to be flagged as Claude content, but if someone memorized Claude output word-for-word. That would still be classified as a Claude output.

Going forward you could categorize the influence of Claude on a population based off a percentage match between their spoken words with the LLM prose.

Are you worried about being accused of using LLMs to generate your work? As long as you don't plagiarize you have nothing to worry about.
I'm not too sure about that, people making stuff have already gotten penalized by overzealous AI detectors, most recently Kurtzgesagt.
You can't make a blanket statement like this without knowing how the watermark is implemented.
What if I unknowingly read content written by Claude in various articles and it influences my own writing style?