You are lying, you already know that clients are able to detect if the coordinator tries to partition its inputs:
Okay why can't you prove it then? You keep repeating this claim, but you haven't come up with any methods that would allow you to simultaneously exploit the trustless protocol in 3 different ways:
Why wouldn't my solutions protect me? Explain how I can still be Sybil attacked if I use the methods I described to you. Start with method 1, explain how the malicious coordinator could defeat it, then go on to method 2, explain how the malicious coordinator could defeat it, then go on to method 3 and explain how a malicious coordinator could defeat it.
Thanks to its design, the WabiSabi protocol is completely invulnerable to a Sybil attack and you've provided absolutely no evidence or argument otherwise.
Remember that it was proven that there is not just one, not just 2, but 3 different ways you can verify that the coordinator is not performing a Sybil attack!
- First, register your private coin to the coordinator. If it's accepted, then there's no Sybil attack.
- Second, ask your friend to register a coin to the same round. If it's accepted, then you've confirmed for a second time that there's no Sybil attack.
- Third, just to be absolutely sure, back out of the round during signing to check to see if the transaction was built to target you. If the transaction is created, you've confirmed for a third time that there's no Sybil attack.