> on LN the sender sees the node pubkey

...which might be a decoy

> just like a stealth address on XMR

...except that does not support decoys due to the lack of transaction chaining on monero. If Jimmy sends money to a monero "public address" he can cryptographically prove that the pubkey therein controls the money. (Btw, that is the first step of every trace, unless the tracer can find someone who already sent money to whoever they're looking for, which has the same result.)

Not so with LN: if Jummy sends money to a lightning invoice he does not know if the pubkey therein ever controls the money even for a second. It might be a trampoline node serving as a decoy recipient, because every lightning has built in support for this. It's part of the protocol design to allow this: thanks to how HTLC forwarding works, the recipient can always put a decoy recipient in the bolt11 invoice without the sender being able to detect it, and if the recipient does that, the decoy recipient looks like the recipient but never controls the money.

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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.

> 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