From what I've read on this forum, the idea that a core or an original might or should exist causes some people stress, though it may not for you Catsgalore. The word core is so powerful, one definition is "the central, innermost, or most essential part of something." If you discover you're multiple, you're going to be looking for clues, answers, explanations. And this meaning of core can sound really important, as in, it would be a relief to figure out at least this part of your system, and it feels like it could be necessary.
The word original is similarly powerful. It may satisfy the question we all face, who am I, underneath all this? Who would I have become if I'd had a healthy childhood? A problem is that there has not been a set meaning for either core or original in DID. So my definition of the words is different from others and from some literature.
My system actually does identify one alter, Adam, as "the core" and "the original." But in a way, using the words distorts how we know him. The words add a layers of connotation that come from many posts here but mostly from the older literature on DID. He is our youngest and we think the earliest traumas happened to him. We've even had memories and flashbacks that seem to support that. But they really happened to us, to me.
The following is cautionary. I think for many, a core or an original is a mirage. Some people feel like they should or probably have one. However, it just doesn't seem to make any sense for a lot of systems. As MakersDozen pointed out, infants don't start out with a unified sense of self. So from one angle, how can there even be an original? Plus, original has connotations of being genuine, unadulterated. What would that make everyone else? The thought for a few people posting here that they are not the original person, or that they are an alter, or both, is terrifying and/or unacceptible. But DID literature considers everyone to be an alter, a part of a DID system, none more authentic than any other.