Informally, a distributed system is grassroots if it can have autonomous, independently-deployed instances -- geographically and over time -- that can interoperate once interconnected. An example would be a serverless smartphone-based social network supporting multiple independently-budding communities that merge when a member of one community becomes also a member of another. Grassroots applications are potentially important as they may provide a foundation for digital sovereignty, which we interpret as the ability of people to conduct their social, economic, civic, and political lives in the digital realm solely using the networked computing devices they own and operate (e.g., smartphones), free of third-party control, surveillance, manipulation, coercion, or value-extraction (e.g., by global digital platforms such as Facebook or Bitcoin). Here, we formalize the notion of grassroots distributed systems and grassroots implementations; specify an abstract grassroots dissemination protocol; describe and prove an implementation of grassroots dissemination for the model of asynchrony; extend the implementation to mobile (address-changing) devices that communicate via an unreliable network (e.g. smartphones using UDP); and illustrate how grassroots dissemination can realize applications that support digital sovereignty -- grassroots social networking and sovereign cryptocurrencies. The mathematical construction employs distributed multiagent transition systems to define the notions of grassroots protocols and grassroots implementations, to specify grassroots dissemination protocols and their implementation, and to prove their correctness. The implementation uses the blocklace -- a partially-ordered DAG-like generalization of the blockchain.

翻译：非正式而言，若一个分布式系统能够在时间和空间维度上部署自主、独立的实例，并在互联后实现互操作，则称其为草根分布式系统。例如，基于无服务器智能手机的社交网络支持多个独立萌生的社区，当某社区成员同时加入另一社区时，这些社区便可合并。草根应用至关重要，因其可为数字主权奠定基础——我们将数字主权理解为：人们在数字领域仅凭自身拥有和操作的联网计算设备（如智能手机），即可开展社会、经济、公民及政治活动，不受第三方控制、监控、操控、胁迫或价值攫取（例如，不受Facebook或比特币等全球数字平台的束缚）。本文形式化定义了草根分布式系统与草根实现的概念；提出了一种抽象草根扩散协议；描述并验证了异步模型下草根扩散的实现方法；将该实现扩展至通过不可靠网络通信的移动设备（如使用UDP的智能手机）；并阐释了草根扩散如何支撑数字主权的典型应用——即草根社交网络与主权加密货币。数学构造部分采用分布式多智能体迁移系统，定义了草根协议与草根实现的概念，规范了草根扩散协议及其实现，并证明了其正确性。实现基础为块花环——区块链的一种偏序有向无环图化泛化结构。