The HORIZONs Co., Ltd. MUSUBI settlement is a deterministic function that takes a contract signed by two parties, a set of signed records of what an agent did under that contract, and a view of Bitcoin block headers, and computes whether the recorded acts stayed within the grant the contract gives. Anyone holding the same bytes can recompute the result without trusting the party that produced it. This document specifies one well defined part of that function, settle core v0, precisely enough that a second implementation can be written from the text and the published test vectors alone. Settlement is not runtime enforcement and is not a judgement of liability.