Exploring the Universality of Finality Time in Proof-Of-Stake Blockchains: Empirical Analysis and Mathematical Formulation of Size-Synchrony Antagonism

Size-Synchrony Antagonism (SSA) is a fundamental principle in Web3 systems proposed by JAM Gray Paper stating that as the size of an information system expands, the consistency of the system deteriorates due to physical constraints on the propagation speed of information, such as network bandwidth and the speed of light. However, the paper does not provide precise definitions of "size" and "synchrony," nor does it present empirical validation based on actual Web3 system data. In this paper, we define "size" as the number of geographically distributed BlockChain (BC) validator nodes on a global scale and "synchrony" as BC convergence time or finality time. We measured these parameters across various Proof-Of-Stake BC systems, including Ethereum 2.0, Polygon, Cosmos Hub, Polkadot, and Kusama. We also formulated a theoretical model to describe SSA. Analysis of the measured data revealed properties consistent with SSA, and these findings aligned well with the theoretical model.