I'm not sure Carl or others agree with my definition or not...
I don't. But I do find this a VERY interesting discussion. It also makes me wonder how many times I've been mentioned here and I missed it entirely.
but since there isn't a consensus around what "deep cut" means in all cases I don't think there is a "correct" answer.
I agree. There probably isn't a "correct" answer as with many terms here people have their own definitions and they don't all agree with each other. My definition of a deep cut is any cut which divides the puzzle up into two isomorphic groups of pieces. Now using my definition the Slice-turn Kilominx is a deep cut puzzle. However in this particular case, the Slice-turn Kilominx, my definition agrees with Brandon's. It doesn't agree with many other's. Here is another common one which states the Slice-Turn Kilominx ISN'T deep cut.
Deep cut puzzle: "All planes and axes of rotation pass through the same point"?
Note I don't like this definition as it assumes all cuts are planar.
Here is a good thread to read through on the topic.http://twistypuzzles.com/forum/viewtopic.php?f=1&t=11001
Per my definition the Gear Cube is deep-cut.
My definition, in short, is that if every turnable portion of the puzzle is equivalent to some other turnable portion + reorientation then the puzzle is deep cut.
Basically if the result of every turn is ambiguous as to what was turned, then the puzzle is deep cut.
Hmmm... you know what you've just defined? This is basically exactly my idea of what and Order=1 puzzle is. The gears in a gear cube apply a type of "restriction" (I've called it bandaging... but again we could argue about the definition of that term) to a 3x3x3. The 3x3x3 I consider an Order=2 puzzle as each axis only has 2 independant layers of rotation. The gears in the gear cube reduce this to just 1 independant layer per axis of rotation. Which at its heart is just another way of saying "every turn is ambiguous as to what was turned". You can view any of the 3 layers as the independant one but if you turn that layer the behavior of the other 2 is determined... i.e. NOT independant.
So Brandon's definition of deep cut is equivalent to my definition of Order=1.
P.S. I agree that a fixed set of definitions that everyone accepted would be nice but I don't see it ever happening for sereveral reasons.
(1) People have already accepted their own definitions and they all have valid reasons and getting everyone into the same mind set will be next to impossible.
(2) The definitions NEED to have some flexability. If you set them in stone today. Someone like Oskar would go out of his way to make a puzzle which broke one of them and we'd have to start over. And if Oskar didn't I'd sure try myself. Its fun breaking things.
P.S.S. This reminds me I still don't know where I stand of the topic of "deeper then deep cut" which has been a hot topic of late. I agree there is something very interesting going on there but I'm not yet sure cut depth is the best way to think about it. I was very glad to see David's RotoPrism 2 was an awarded puzzle at IPP
and I'm pretty sure that is due to the interesting properties associated with this "deeper then deep cut" concept.