I understood somewhat more. I guess that the system is more related to making sure only the correct people (owner) puts changes/annotations to a document, not necessarily about pdf (and actually there are more suitable document types for this).
Who are gonna to store and mine the blockchain will be the person interested in see and download those files. There are no incentives while mining
If you go by this model you'll be an easy target for anyone wants to do a 51% attack and put into the blockchain any bad files / changes / checksums he wants.
You need something better (safer) than this.