I call these definitives in talking about how certain features of a soul remain the same throughout lifetimes. More generally, linchpins are what hold a story together -- aspects of character, setting, plot, etc. for which removing them will cause it to come apart at the seams. Case in point, Superman is always Good, and if you bork that as in *Man of Steel, people will boo it as "not Superman."
Regarding numbers, most characters have a handful of defining traits. For European-descended cultures, three is a good number. If you're writing Native American, though, it's going to be four; and it will never be four in Japan. Know the magic and unlucky numbers for your culture of context. So if you're writing AU and you want the characters to be recognizable, set up those points and it's likely to work. However, there's an exception: if you only want to change one thing, it can be one of those core points, and the AU will probably still work. Racebending and genderbending are classic examples. One of my favorite Robin Hood stories had Robin unable to shoot worth a damn, and Marian as the crack archer.
The same aspects apply when you're writing someone else's character, setting, etc. and you want to maintain continuity, rather than going AU. This is a vital skill for shared worlds. You have to be able to identify what makes a person or place both distinctive and appealing. This can be a big challenge if you live somewhere very different. No matter how much research on northerly climates I do for writing Northern Torn World stories, I still keep screwing up, and ellenmillion (who lives in Alaska, the inspiration for Torn World) keeps finding errors. Conversely, I have been pleasantly surprised by how often my readers and cowriters pick up details from Terramagne that I have written down but not posted.