Yes, I agree it is a bit cheating. They recover the S and K by applying U to itself in interesting ways, but that's like saying 'this tool is so universal, you

Yes, I agree it is a bit cheating. They recover the S and K by applying U to itself in interesting ways, but that's like saying 'this tool is so universal, you can use it as a hammer and a chisel by banging one instance of the tool with another tool just like it'. That's not a very mathematical way of putting it I guess but I believe that is more or less the spirit of it.