A quick problem that came up yesterday...
Proof of unique validator
Motivation: we want a sybil-resistant P2P network. This is about to become more important due to data availability sampling.
We particarly want to ensure that validators get assured access to DAS to prevent attackers from compromising liveness.
So, one family of solutions involves validator nodes giving each other priority at the P2P. Many specific solutions--S/Kademlia, maybe special GossipSub groups for validators, or just reserving at least m out of n slots in the routing table for validators.
In each case, we get the following problem: