I guess I should have expanded: a watermark is useful to reduce the number of possibilities of who could have released it. Over time, the more information is gained, the closer you are to a singleton (the result of the intersection of sets). Whether that takes 1 or 10 watermarks does not make a real difference over time, especially when specialized websites release thousands of such PDFs.

So if you have a watermark that associate files with the time they have been downloaded, and download it from multiple networks etc. at the same time, and remove the diff from these versions, you'll still have the time-based watermark in the resulting file, so you'll leak when you downloaded it.

Well sure. Try not to download them at the same time.

Problem is you only have to fail once to leak information, and there are only a finite number of bits of information you can leak before your identity is known.

Of course it does. If two files are identical then by definition there is nothing in them that can be used to tell them apart.

There is still the metadata the operating system stores with the file, even when the file is 1:1 identical. When you use Apple AirDrop to send a file to a friend the OS remembers who sent the file to your friend. Now if the police ever looks at your friend‘s computer they can see who this file came from. Or your friend saves it onto a usb formatted with an Apple File System the metadata is still preserved.

Sounds like you have an operating system problem not a watermark problem.

Nit: This is a function of the file system, not the operating system.

I don't see why.