Problem 3: Nonce Watermarks
Mining pool admins and members of the pool can agree to have their own block watermarked.
This is not the case. Suppose a pool member finds a nonce, and publishes a ZK block solution. Even if the pool also finds this nonce by rescanning, it cannot associate the ZK block solution with it. This is because the ZK NIZK proofs (the GGPR scheme) are information-theoretically hiding.
Yes, it was my mistake. Thank you Andrew for clarifying this to me.
For weakly Nonoutsourceable Puzzles was true but for strongly Nonoutsourceable Puzzles the pool admin can only get a clue of who might be a cheater but no real evidence.
Nevertheless the clue may be strong (for example, if the supposedly cheating miner that is member of the pool has 0.1% of the total hashing power, the probability that this miner has not cheated is 1/600000) .