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Please explain how this would work. The SHA sum would be different 100% of the time. In other words, you would never get the same SHA sum twice.

Fair enough. It might work as follows:

I generate some text using ChatGPT.

ChatGPT sends HaveIBeenGenerated a checksum.

I publish a press release using the text verbatim.

Someone pastes my press release into HaveIBeenGenerated.

Is there something like perceptual fingerprinting but for text?

It is called an embedding, OpenAI does these ;)

Eventually we would have to call ChatGPT to the witness stand, and ask it whether it remembers telling these specific words to that man over there.

Tweaking 1 char would change the checksum

Which IMV is fine, since you were arguably using ChatGPT as an assistant versus a tool for brazen plagiarism.

But you can automate that too, with a different tool.