and the monero user might churn their output at some point.

the ONLY difference is your point about cryptographic verifiablity.

which is a legit advantage to transacting on a L2.

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> the monero user might churn their output at some point

And the tracer might be able to detect that

In the attached chainalsysis video, between 34:51 and 36:44, they observe that the user sent some of his xmr and they identify the "main" recipient as either a self custodial wallet (Exodus) or a mining pool. After logging that, they follow the change output and watch to see where *that* goes next. Churning (i.e. sending to yourself) clearly helps but since there's a public record of the tx and what happens next, it is not foolproof. LN is better on this front: there's no public record of the transactions and not even the sender knows where his money goes.

https://v.nostr.build/D4Nzp22vRF35IRnz.mp4