Copyright isn't about mathematical derivatives its about protecting the licensed distributor as the sole source of the work. A single screen of a movie or a single page at least is part of the work. Even the first letter of the first word of a book represents a larger portion of the work. It's one nothingth of the work because you can't even derive that first letter from it. Judges are probably substantially interested in the purpose of the law. In math not so much.
I have nothing against arguing that hosting hashes is illegal. It is not that far from facilitating piracy. What I am quite sure is that the hash itself is not covered by copyright.
If you can prove that I am hosting a file whose hash is equal to the hash of a mp4 file that encodes your movie then you can (probabilistically) prove that I am hosting that same file. This is also exactly how bittorrent authentication work if I remember correctly. (my only defense would be to exhibit a non-your-movie- file that still has the same hash)
But this would be no different (or at least comparable) than offering an easy to use list of download links. It would still have nothing to do with whether those links/hashes are derivative or not.
The only possibility I see is to argue the hash as a simple fact without copyright protection, But, the contents of a book is also a piece of factual information yet copyright is not irrelevant.
PS: As much as you want to use burning as an analogy, a burned book can’t be used to verify a download of the original work where popcorn time’s hashes can.