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Is there a provable way to "burn" a single satoshi for example?

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The Lightning Network is just a collection of two-party agreements on the latest channel state, and these agreements are represented by pre-signed force-close transactions which pay each party their own respective channel balance.

One way of "burning" coins then would be to negotiate a new channel state that includes an extra OP_RETURN output with the burned amount (I'm not sure if the current LN specification allows that, but there's nothing technically preventing it). However, until a channel state with this OP_RETURN output gets settled on the blockchain when the channel is closed, the two channel parties can undo the "burn" if they agree on a new channel state without it (and there's probably no reason for them not to), so this proof of burn cannot be relied on by any third parties.

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There is no way, because to provably burn coins you use scripts such as OP_RETURN, which are quite like saying "I announce that these coins are unspendable".

You don't announce anything when making a lightning transaction, other than the new state to your fellow partner exclusively. It's the same reason why you can't have things such as NFTs off-chain.

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  • Coins can be provably burned without any OP_RETURN or anouncment -- just by sending them to a provably unspendable address like the 1BitcoinEaterAddressDontSendf59kuE.
    – Jonathan Cross
    Nov 26, 2022 at 18:15
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    @JonathanCross, that isn't provably unspendable. It's part of the UTXO, and in fact, there are about 2^96 valid private keys that can unlock these outputs. But, indeed, there are ways to provably burn coins without the OP_RETURN script, just by sending coins to nowhere as it happened with transaction "5bd88ab32b50e4a691dcfd1fff9396f512e003d7275bb5c1b816ab071beca5ba".
    – Angelo
    Nov 26, 2022 at 18:40
  • Thanks, you are correct, 1BitcoinEaterAddressDontSendf59kuE is "highly unlikely to be spendable". I suppose we could do even better with a Taproot (SegWit v1) address?
    – Jonathan Cross
    Dec 10, 2022 at 19:39

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