@JESinstr, as we have discussed in the past, I find your way of conceptualizing skiing unduly complicated. This is the internet and communication here relies heavily on words. I have no doubt that on snow your use of straight line travel and circular travel, your definition of "carving," and your choice of not using the word "turn," works well in person. I remember you also work with gravity and inertia to describe how a turn works.
Those descriptors are just not working for me, here, online. I get that you find what I think to be fundamentally flawed. However, I do not think that about your way of thinking. I don't find the content your conceptualization describes to be different from what I know, or at least I can't remember if something you know differs from something I know. I believe it's how we cut up the pie that's different.
I simply find other ways of describing skiing to be more direct and more easily communicated to non-instructors and instructors alike.
That said, I do find it amazing that you said "I can't seem to find anything about what carving is."