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Typically I'd cite to whatever it was I copied. I've never seen any kind of writing that sourced to the copy function. Have you?

And you can cite the LLM you've used, no different to citing a quote by a person.

And to answer your other question of how,

There's plenty of documentation on that directly from the source (openai, etc.) and elsewhere.

Precisely the point, you cite the model and that’s it. Even when these models are known in some cases to reproduce training text directly.

Humans are known to do that too?