Budish (2025) shows that the flow cost of Nakamoto-style trust scales linearly with the value secured, relying on a one-shot, free-entry formulation in which interaction is memoryless. The Nakamoto protocol violates the memoryless property through two hardcoded temporal structures: a 100-block coinbase maturity rule and a 2016-block difficulty adjustment. Both make future payoffs history-dependent. Jointly with sunk capital and pseudonymity, these features introduce continuation values, asymmetric attack costs, and Beckerian deterrence—forces the model eliminates by construction. The three assumptions analysed here are central to the model’s application to proof-of-work systems as they exist. • Nakamoto protocol violates the memoryless property by its formal definition. • 100-block coinbase maturity makes payoffs history-dependent. • 2016-block difficulty adjustment creates asymmetric attack costs. • Sunk capital and pseudonymity introduce continuation-value deterrence. • Fourteen modelling assumptions in Budish (2025) are documented.
Craig S. Wright (Sun,) studied this question.