Re: Had an idea - looking for a math buff to tell me if it's possible

no no no.. it's simply, since the OP posited a math solution, md5. ship the size of file + hash, compute file on the other side. All files can be moved anywhere regardless of the size of the file in a single packet.

MD5 compression is lossy in this context. Given big enough files you're going to start seeing hash collisions.