S/Kademlia dynamic crypto puzzle In S/Kademlia two crypto puzzles is used, one static and dynamic. The static is used to generate a key pair that makes an eclipse attack difficult to achieve, the dynamic to make Sybil attacks harder. 



In the dynamic, I am very confused about the x which is found, since I can’t find any evidence for this ever being used again in the system, is it send along in a signature or what is it used to?

I do not think the paper mentions any use of it, I at least have not been able to find it, why I ask here for the use of x.
It's part of the solution to the cryptopuzzle.  The goal is to find $x$ that makes $P$ satisfy the criterion; once you've found such an $x$, you can verify that it is a valid solution (and so can anyone else).