Thanks. Regarding plagiarism, I agree that it is possible to check; I don't know how easy it is. But I do note that the mathematicians who complained that their work was plagiarised by AI did not seem to realise that they, themselves, were using a plagiarism machine and were instead quite comfortable admitting that, yeah, we worked our Euler result out together with Sol, Claude and the gang.
To clarify, they do attribute the original ideas to Cordoba and Martinez-Zoroa, but they don't seem to acknowledge that their result which they say was achieved "with a great deal of help from LLMs" is also derivative of others' work.
Independence is about avoiding making errors because of the influence of error-prone models. I guess I didn't explain it well.