A non-custodial threshold instrument for Bitcoin would allow value to transfer between parties without network connectivity, fees, or custodial dependency. Digital signatures and multisignature scripts provide part of the solution, but the core benefit is lost if the issuer retains a key capable of unilateral redemption. All prior multisignature schemes have positioned the issuer at or above the spending threshold. We propose a system that inverts this: the holder receives the two keys constituting the spending threshold of a 2-of-3 multisignature script, and the issuer holds one key arithmetically below it.
Asensio Arias (2026) studied this question.