My entire point is that compression is irrelevant. A lossily compressed image can absolutely still be in breach of the original's copyright. Showing that some kind of compressed artifact may not be doesn't change that.
"I can use a lossy compression algorithm such that the original could never be recovered from the image I've produced, but that derived image would surely be under copyright."
I've tried my best to show where I think you're wrong. I think all that's left is arguing over the exact definitions of "recoverable" and "irretrievable". As I said, the courts will have to decide that.
I have no clue what you're talking about tbh. I can use a lossy compression algorithm that is definitionally holding less information than the original while still be subject to the copyright of the original. This is just obviously true, converting a PNG to a JPEG does not invalidate the copyright on the PNG. You can also produce an imagine using a lossy compression algorithm that is not subject to the copyright of the original, I haven't said that that's not true.
Regardless, the argument that LLM output is or is not subject to copyright based on information theory is entirely defeated by what I've said.
I've tried my best to show where I think you're wrong. I think all that's left is arguing over the exact definitions of "recoverable" and "irretrievable". As I said, the courts will have to decide that.