What Silent Aviator is stating, is there isn't a "federal law, regulation, or rule".
When you apply for the certificate, you are agreeing to fly below 400 feet.
Otherwise there's not any real law that states you must fly below 400 feet. There's only safety guidance. Of which the FAA is trying damn hard to make it seem like law. Once you apply for your registration certificate, you are then agreeing to fly below 400 feet. Now you are obligated to fly below 400 feet after you've registered.