Yes, the mixing masternode sees the whole picture of one specific session and no single client can figure out who 2 others are. But if not so many users are mixing then few colluding clients can try to look for txes they have in common and try to follow the 3rd participant. If they are lucky enough they can even catch few rounds but, again, only if number of users is low. For interactive mixing protocols it's really crucial how many non-colluding users are mixing at some point of a time.Client wallets cannot log mixing. Only the specific masternode performing that specific mixing session can log it. I believe @UdjinM6 can confirm this?
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