I can't think of a single thing where the HOWTO is described with those 4 "skills". They are far too broad. Sure we can recognize that our body executes those skills while skiing, but the mystery of how to combine those broad skills to ski well has not been defined that way.
By the way, they are considered "skills", not "movements". They are not nearly specific enough to be considered actual movements.
"Balance" is a skill, not a movement. There are a variety of "movements" that can help you acheive the dynamic balance you want in skiing. But those are not defined by PSIA.
"Pressure control", also not a movement. There are a variety of different movements that can be used to manipulate pressure. Again, no HOWTO provided.
Rotary is a skill in general, but could be called a movement, however there are so many ways to interpret it as to render it largely useless as a teaching concept. Are we talking about rotation of the ski or rotation of the femur? Depends on who you talk to, I've heard it both ways. Rotation of the femur happens in a number of different dimensions and aside from pointing out that our femur is pretty much constantly rotating in the hip socket in this dimension or that during all skiing activities, its useless information for HOWTO ski. Its simply a recognition that the femur moves about in the hip socket in imprecisely defined ways.
Edging...well.... you could interpret that a number of different ways. Are you referring to the actual verb action of tipping the skis? If so, ok I like it so long as more specific information is provided for how and when to tip. If you are talking about finese over the edge feel as they are on the snow, again its a broad skill...its not a specific movement. again a variety of different movements can result in the skis being tipped more or less, resulting in more or less edging. Those movements are not defined by PSIA. This broad category merely says, "hey, you have edges, so use them".
Those really are not specific movements, they are broad categories, which while interesting to take note of, simply do not tell people how to construct good ski turns.
What is missing is the HOWTO.
Your other comments comparing this system or that system were not even accurate, much less relevant to the discussion about the need for more detail. You said a couple of totally inaccurate things about PMTS, which demonstrates ignorance on the finer points of their system. That's fine, its immaterial. What is material is that detail is missing from PSIA and others as well when they have used similar fuzzy skill concept pedagogy.
Interestingly, this absence of detail is actually a ploy to avoid criticism in my view. Its hard to find any specific faults with a system that doesn't give any specifics. hehe.
Great strawman there! If you notice, I asked about 'describing', not 'instructing' or 'how to', thanks for your thoughts on it anyway though. I am much more familiar with the NZ system, so saw the PSIA 'skills' as pretty much the same as our 4 movements, with balance equal to fore-aft, pressure control equal to vertical movements, and edging equal to lateral. If you think it's all that different, that's fine.
You yourself said that PMTS lacks a rotational element, so I can't really see how that part could be that inaccurate, my main exposure to PMTS is through the forums there, and I am pretty sure that counteracting isn't really compatible with full body inclination, but if it is, perhaps you'd care to civilly explain it to me.