The power of linear and affine logic lies in their ability to model state change. However, in a trustless, peer-to-peer setting, it is difficult to force principals to commit to state changes. We show how to solve the peer-to-peer affine commitment problem using a generalization of Bitcoin in which transactions deal in types rather than numbers. This has applications to proof-carrying authorization and mechanically executable contracts. Importantly, our system can be—and is— implemented on top of the existing Bitcoin network, so there is no need to recruit computing power to a new protocol.