Global digital platforms are distributed systems designed to serve entire populations, with some already serving billions of people. Here 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 (Facebook) -- one (the server) 2. Decentralised (Bitcoin) -- finite >1 (bootstrap nodes) 3. Federated (Mastodon) -- infinite but not universal (all servers) 4. Grassroots (Scuttlebutt) -- 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. 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 distributed systems today.

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