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I was looking for ideas on how to use Submarine Swaps with Taproot/Scriptless Scripts. But I couldn't find anything.

I can imagine that it would trivially be possible to incorporate a Submarine Swaps contract in a script-path spending branch of Taproot, and have a mutual 2-of-2 MuSig key-path spending that allows spending when the Lightning invoice was paid, but this doesn't mandate it and would require the payer of the invoice to use the script-path spending of the receiver doesn't cooperate.

Is it possible to use e.g. adaptor signatures in the key-path spending of Taproot when the Lightning invoice was paid? Or is there another construction that would allow the payer of the Lightning invoice to solely spend via the key-path after receiving the preimage from the invoice?

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