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I think as long as the human puts in substantial and transformational effort, they can claim to be the copyright holder of the entire work, yes.

Compare taking snapshots with a camera.

Because some photographer somewhere can claim to have put in a lot of effort, we all get IP protection for photographs by default.

Yes, I didn't include the monkey in my 'we'.

In the US it isn't the sweat of the brow, but rather a minimal threshold of human creativity.

Oh, good point. It's not related at all to effort then. Either way it still has to be a human.

Software is considered a complete piece of work. Therefore as long as you modify a single character - that whole product is under your copyright.