why parity?

[Sean Lev]

I know this is a bit of a bump, but I made this video a few weeks ago(it's terrible but it still discusses parity). I'm no expert, but mathematically parity is if a number is odd or even. In cubing, parity is whether there have been an even number of turns or an odd number. A parity error is then an odd number of turns have been made which does not permit the cube to be solved.

[Forte]

I haven't watched the video, but the parity refers to the number of 2-swaps, not the number of turns lol

The 3x3 always has an even permutation parity. You can tell because every face turn does a 4-cycle of corners and a 4-cycle of edges (six 2-swaps in total). That's why when you just switch just two pieces (and make it have odd permutation parity), it becomes unsolvable.

When you have PLL parity on the 3x3 stage of a 4x4, what you're actually saying is that your 3x3 stage thing has an odd permutation parity.