Advances in mobile computing have paved the way for new types of distributed applications that can be executed solely by mobile devices on Device-to-Device (D2D) ecosystems (e.g., crowdsensing). Sophisticated applications, like cryptocurrencies, need distributed ledgers (DLs) to function. DLs, such as blockchains and directed acyclic graphs (DAGs), employ consensus protocols to add data in the form of blocks. However, such protocols are designed for resourceful devices that are interconnected via the Internet. Moreover, existing DLs are not deployable to D2D ecosystems since their storage needs are continuously increasing. In this work, we introduce and analyze Mneme, a DAG-based DL that can be maintained solely by mobile devices. Mneme utilizes two novel consensus protocols: 1) Proof of Context (PoC) and 2) Proof of Equivalence (PoE). PoC employs users' context to add data on Mneme. PoE is executed periodically to summarize data and produce equivalent blocks that require less storage. We analyze Mneme's security and justify the ability of PoC and PoE to guarantee the characteristics of DLs: persistence and liveness. Furthermore, we analyze potential attacks from malicious users and prove that the probability of a successful attack is inversely proportional to the square of the number of mobile users who maintain Mneme.