Perhaps this is the distinction I am trying to convey. when the axis of rotation is within the skier's CoM then an actual moment of inertia will be formed within the skier itself, which equates to the skier spinning. When the axis of rotation is outside the skier, then the skier no longer has their own moment of inertia that can perpetuate spinning, the skier becomes like a ball on the end of a string which is only rotating and turning by virtue of continuous external forces making it happen. By this analysis makes the skier just a lump of mass in a larger rotational system, that is rotating around some theoretical center point by virtue of the ski to snow external forces.
I don't know what language will explain this distinction, but there is a distinction and it matters a lot in skiing. Maintaining yourself as a ball on the end of a string rather then becoming yourself the center of the circle is the difference between turning and spinning. And since there is no string, it's manipulated in real time by our edges. Turn off the edges and a non spinning skier will continue straight. if the axis is within the skier and they are spinning then turn off the edges and the skier keeps spinning. That is the distinction. I am not sure what is the correct physics terminology at this point according to you PhDs to note this distinction.
Yep.... that's why I didn't want to touch the "pure carving" scenario..... the longer the turn radius, the more the skier becomes a lump of mass.
In addition, that's why I put on those disclaimers about edge bite and edge engagement, otherwise the skier will spin out. Along with the "handle bar", spinning out in a short turn is another hazard with the forward pressure.