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This is great!
A just a thought experiment on the ability to credibly threaten to burn a deposit
Attacker: Unless we split your future UTXO, I will burn it
How to perform attack? You could threaten the user, and request pre-signs a split of the future utxo with progressive amounts of fees until the whole thing is burned, if the user tries to send in another tx with a higher fee (front run the attack), the attacker sends in another presigned tx with more fees until the result is a burned UTXO.
The best option for the user is to accept the terms of the split
Is this theoretically possible?
The problem for BitVM is any colluding prover&challenger can disprove any valid statement which covers the truth
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A brainstorm based on your idea: