To elaborate, does it necessarily mean that spending life at a Citadel of the Wyverns from Year One to Year Twelve makes you more of a Wyvern than one who was only there for Years Eleven and Twelve? And if you were there for the first ten years and then became a Gryphon or some other creature, could you still claim Wyvernhood as an alumnus?
To me, there are practical as well as metapractical answers to these questions. Here are a couple.
First, the fact is that for many years, there weren't enough spaces for all the Wyverns — and many of those who wanted to, and possibly deserved to, continue being Wyverns were excluded.
Second, some non-Wyverns (and some who came from beyond and entered Year Eleven) turned out to have more Wyvernhood in them than some fellow-travellers who were there all along and showed no loyalty thereafter.
There are many other answers to many other related questions. But the crux is this: the idea of Wyvernhood is an imaginary, and there are almost infinitely many conceptualisations of that imaginary. By the nature of such things, any conceptualisation will exclude some people, excepting all-inclusive ones which don't add anything useful to the conversation.
So who is a Wyvern? He who was Sir Wolff laughed when I told him about it all. Nonchalantly, he pointed at the Sword of Oldham — he keeps it in a corner behind the door — and said, "Do you think that blade makes me more of a Wyvern than the many others who have never seen it and yet swear by it?"