How to fix 7x7 PLL parity!

I've always done it like that, I guess I'm smart, too :cool:
But I will usually just assemble it with the 3x3 pieces solved, which is only a little bit of sorting.
 
Backing this up with a bit of theory:
Offsetting 4 centre caps by 90 degrees will make you solve 4 edges offset by 90 degrees, in a 4-cycle manner, and a 4 cycle is an odd number of piece swaps, which cannot happen in an odd cube, so 1 more extra swap will show up as the PLL parity.
Void cube parity exists because we may unknowing create a 4-cycle in the E slice, causing the 1 more extra piece swap to happen.
 
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