BNCR is a lens mount developed by Mitchell for use with its reflex 35 mm movie cameras (long back-focus; Bausch & Lomb Super Baltars and equivalents).
It was an update of the BNC mount (short back-focus; Bausch & Lomb Baltars and equivalents) done to accommodate the reflex viewer in the later cameras.
This radial indexing is of particular importance when shooting an anamorphic format (CinemaScope or Panavision, or equivalent).
The quality of this design has been a key influence in the design of the Arri PL and Panavision PV mounts, both of which are the main film camera mounts in use today, and both of which have four-pronged flanges oriented based on locating pin-notch combinations.
With the slow obsolescence of the Mitchell cameras, which likely took so long because they were so well regarded in mechanical design aspects, such as their steady intermittent movement registration ("Compensating Link" movement) and strong mounts, the mounts have gradually become less common in the past two decades, but remained an option for third party cameras produced as recently as the 1980s.