"As outlined in the BitVM whitepaper, Bitcoin can verify the correct execution of any boolean circuit and penalize its incorrect execution. This makes it functionally equivalent to a turing complete programming environment."
"This document outlines a protocol by which a prover, Paul, and a verifier, Vicky, agree on an arbitrary boolean circuit and then encode it inside tapleaves in a taproot address. Thereupon, they may fund the address in such a way that Paul is paid if he executes the script correctly but Vicky is paid if he does not."
"This method brings any computable function to bitcoin. It can be expanded upon to do SPV proofs of the existence of a utxo at a given blockheight, allowing for covenants."
"It can also allow a central party to do computations for a group, where any lies or incorrect computations result in the loss of a bond. This should allow for sidechains and rollups to be built out directly on bitcoin."
"I look forward to a future of additional experimentation on these lines. Bitcoin has scripting super powers now. Let's use them to their fullest potential."