Well, factory records put the engine serial number and frame number together. However, those records have long since been archived by Honda as I understand, so the purist part of it is sort of unnecessary. It is possible to register yourself as an owner of a used Honda.
This one would be for show. There were three major versions of the HR214. The PX, which was push with recoil start, the SX that had a 2 speed transmission with recoil start, and the SM that had the 2 speed transmission with electric start. I've become sort of an HR214 nut, I guess, as I have an SX that I use, an SX for show, and I'm in the process of restoring an SM. Just like a PX to complete the set.