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I'm just thinking how devious exchanges tend to be, always finding ways to create fake paper bitcoin (by re-hypothication). Is it possible for am exchange or a group of exchanges to open lightning channels without the bitcoin to back the sats created?
Just asking toale aire we aren't shooting ourselves in the foot by relying more and more on lightning.
The only way to open a channel is with an on chain transaction. I don't see how that can be faked.
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You can even verify that all channels have funds locked onchain:

Gossip Protocol Messages

... channel_announcement: A blockchain anchored proof of the existence of a channel between two individual nodes. Any third party can verify this proof to ensure that a real channel is actually being advertised. Similar to the node_announcement, this message also contains information describing the capabilities of the channel, which is useful when attempting to route a payment. ... It's important to note that each component of the channel graph is authenticated, allowing a third party to ensure that the owner of the channel/update/node is actually the one sending out an update.
-- Mastering the Lightning Network, Chapter 11: Gossip and the Channel Graph (p.276-277)
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Right answer.
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No, assuming adversarial channel partners. It's possible for two partners to have a channel which is not backed by anything. For instance, they may have a database that keeps track of credit between them, which they will settle later. As long as they obey the protocol, they route payments and such.
However, no one can trick you into receiving fake sats. If you're using Lightning to pay for goods and services, your channel will be real, and the merchant's channel will be real. The only "fake" sats that could exists will be in the middle. It's not inflationary, just extra liquidity for the network. The only people that could get rug pulled are the ones actually opening credit-based channels.
That assumes you're using a non-custodial solution, though. It's possible that your custodial Lightning wallet is fractional reserving. However, there is no lender of last resort so any custodial service is on EXTREMELY thin ice. This isn't really inflationary either, since the actual supply of sats isn't increased.
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Yes.
Custodial wallets can have fractional reserves and paper account balances.
What you can verify are the channels to the node. What you also know is your balance with the custodial wallet.
What balance other see in their UI and what the cumulated balances are ... could theoretically be solved cryptographically but there is no incentive for custodial lightning nodes to implement such a thing
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A custodial LN wallet dealing in fake sats would have a problem pretty fast when users bankrun it. How would you even fake it?
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Simple answer, No
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