The lower receiver on ALL AR's are registered either pistol or rifle by the maker. No exceptions. The lower receiver is the gun. The gun could be examined, and determined whether the lower is a pistol or rifle lower.
Example: I had an open bolt Mac 10 carbine. If you are not familiar with this type of gun it has a lower and upper receiver - the lower receiver is the gun. My Mac 10 lower was specifically stamped with a "c" to designate it as a carbine receiver (most made were pistols, very few carbines were made).