Polly,
Welcome to the forum.
That's a nice project you've acquired.
Based on CA10 RR 3052, I would take it that the cases are from a '56 Road Rocket. Looking at the various engine and frame number lists, including from BSAOCUK, there is no reference to "RR". I am making a leap and assuming that "R" and "RR" are interchangeable. There has been some discussion of this here on the forum, with one explanation being that BSA used "RR" for export models (maybe thinking, it's more "Road Rockety" for the the unwashed masses, like me). Someone here might have the definitive answer. I suspect and hope they will chime in to correct me if needed.
That bike has some nice and, I assume, original parts on it, like the Altette horn, the brass tach drive, etc. It also seems to have a bowl extender on the monobloc carb. That and the cafe tank lead me think that one of the previous owners liked to ride her real fast. Not saying that's a bad thing. I am interested in knowing if that tank was an option offered by BSA or an aftermarket part of the period. Someone?
I am making a wild assumption you are somewhere on Earth. Would you mind sharing a slightly more specific locale?
Looking forward to your story of getting her started and fun with the restoration.
Richard L.