As the first proof-of-work (PoW) permissionless blockchain, Bitcoin aims at maintaining a decentralized yet consistent transaction ledger as protocol participants (“miners”) join and leave as they please. This is achieved by means of a subtle PoW difficulty adjustment mechanism that adapts to the perceived block generation rate, and important steps have been taken in previous work to provide a rigorous analysis of the conditions (such as bounds on dynamic participation) that are sufficient for Bitcoin’s security properties to be ascertained. Such existing analysis, however, is property-based, and as such only guarantees security when the protocol is run in isolation. In this paper we present the first (to our knowledge) simulation-based analysis of the Bitcoin ledger in the dynamic setting where it operates, and show that the protocol abstraction known as the Bitcoin backbone protocol emulates, under certain participation restrictions, Bitcoin’s intended specification. Our formulation and analysis extend the existing Universally Composable treatment for the fixed-difficulty setting, and develop techniques that might be of broader applicability, in particular to other composable formulations of blockchain protocols that rely on difficulty adjustment.