If you well read the published Mauser books you well read reference to the three ring sizes. You can call them anything you want. I just wrote what I read in published books
Well I understand that but by your own admission, there were only two measured sizes, which (2+2) also means there are only 2 ring types. Now of course, you could have various actions, such as an "intermediate action" as described in this thread, but to call it "intermediate ring" when the ring size is the same as the large, is pretty misleading/confusing/contrary. If you have 3 ring types (which are all differentiated by their measurement) then you should also have 3 different ring sizes.