Here is my definition of a stored cut:
For something to be considered a stored cut, it must satisfy 2 conditions:
1: The move must not be available when the puzzle is in its "solved state", save partial turns (i.e. ghost cube)
2: Some combination of moves must exist where the move can be reached.
I think my Coumpound Crystal
puzzle sum the idea up quite nicely. For a further explination about "reaching" the cuts, I made a Youtube Video
For some other examples, look at Oskar's crazy Comet
, Uncanny cube
, and Asteroid Attack
As far as the relationship with jumbling goes, All I can say is that I cannot think of any (not-unbandaged) jumbling puzzle that has stored cuts. I may be wrong here, but every time a jumbling puzzle has had unbandaging applied to it, the resulting added cuts end up being stored cuts; I cannot think of a counterexample. Earlier in my post I link to Oskar's Asteroid attack, which may seem like a counterexample to what I said, but it is actually an unbandaged jumbling puzzle.
Like every other discussion that relates to jumbling, it seems that asking a single questions plants a seed that eventually grows and branches out into a tree full of questions.
I plan on coming back later and fleshing out this post (I'm in the middle of class now
) Hopefully someone will add on to what I've said, because I have only brushed on the topic.