Both my math and slalom abilities, relative to @Than_Bogan's are pretty similar...way lacking! On a more positive note, as a 32off skier and a post-grad engineering degree (too many years ago) I am able to understand and enjoy the general concepts in these academic discussions.
So, from own experience it is pretty easy to "see" that, at least through 32off, can be accomplished with various ski paths. From observation, I suspect that 35/38 also can allow some variability in ski path (although less than the longer line lengths). When seeing 39/41 skiers, it is less obvious to my naked eyes, whether the ski paths are truly different despite different skier styles. This reminds me of a long ago conversation with Jamie B. where he explained that running 41 required him to stay within a 2 inch wide path (think of a 2" hose, he said).
If these observations are correct, it implies that the modelling efforts described here could potentially help those of us less accomplished skiers, but less so, real short line skiers. On the other hand, we (the less accomplished) do not really need sophisticated modelling (or any modelling) to "optimize" our ski paths because it is pretty obvious when we do it "right" (or at least better).
My curiosity then is whether those of you who have looked in some detail at modelling ski paths, and/or actually run 39/41, are able to confirm (or suggest) that 39/41 can only be run as per Jamie B. "2in. hose". Because if the answer is yes, these modelling efforts, however interesting, have only academic value, since both ends of the line length spectrum cannot "learn" much from it.
But as a "mini-geek" (compared to @Than_Bogan - ha) I enjoy this stuff, so keep it up!