Global digital platforms are software systems designed to serve entire populations, with some already serving billions of people. We propose atomic transactions-based multiagent transition systems and protocols as a formal framework to study them; introduce essential agents -- minimal sets of agents the removal of which makes communication impossible; and show that the cardinality of essential agents partitions all global platforms into four classes: 1. Centralised -- one (the server) 2. Decentralised -- finite $>1$ (bootstrap nodes) 3. Federated -- infinite but not universal (all servers) 4. Grassroots -- universal (all agents but one) Our illustrative formal example is a global social network, for which we provide centralised, decentralised, federated, and grassroots specifications via multiagent atomic transactions, and prove they all satisfy the same basic correctness properties, yet have different sets of essential agents as expected. We discuss informally additional global platforms -- currencies, ``sharing economy'' apps, AI, and more. While this may be the first formal characterisation of centralised, decentralised, and federated global platforms, grassroots platforms have been defined previously, using two incomparable notions. Here, we prove that both definitions imply that all agents are essential, placing grassroots platforms within the broader formal context of all global platforms. This work provides the first mathematical framework for classifying any global platform -- existing or imagined -- by providing a multiagent atomic-transactions specification of it and determining the cardinality of the minimal set of essential agents in the ensuing multiagent protocol. It thus provides a unifying mathematical approach for the study of global digital platforms, perhaps the most important class of computer systems today.

翻译：全球数字平台是旨在服务全体人口的软件系统，其中部分平台已为数十亿用户提供服务。我们提出基于原子事务的多智能体迁移系统与协议作为研究这些平台的形式化框架；引入"必要智能体"概念——即缺失后将导致通信不可行的一组最小智能体集合；并证明必要智能体集合的基数可将所有全球平台划分为四类：1. 中心化——单个（服务器） 2. 去中心化——有限且大于1（引导节点） 3. 联邦化——无限但非普适（所有服务器） 4. 草根化——普适（除一个外所有智能体）。我们以一个全球社交网络作为示例性形式化案例，通过多智能体原子事务提供了中心化、去中心化、联邦化与草根化的规范定义，并证明其均满足相同的基本正确性属性，但如预期般具有不同的必要智能体集合。我们非正式讨论了其他全球平台（如货币、"共享经济"应用、人工智能等）。尽管这可能是对中心化、去中心化及联邦化全球平台的首个形式化分类，但草根化平台此前已通过两种不可比较的概念被定义。本文证明这两种定义均隐含所有智能体皆为必要，从而将草根化平台置于所有全球平台的更广泛形式化语境中。本研究通过提供多智能体原子事务规范并确定由此产生的多智能体协议中最小必要智能体集合的基数，首次建立了对任何现有或假设的全球平台进行分类的数学框架，从而为全球数字平台（或许是当今计算机系统中最重要的类别）的研究提供了统一的数学方法。