Bitcoin: A Non-Continuous Time System

TL;DR

This paper models Bitcoin's internal time as a non-continuous, probabilistic system driven by stochastic proof-of-work processes, difficulty adjustments, and entropy dynamics, forming a self-regulating temporal architecture.

Contribution

It introduces a unified framework explaining Bitcoin's time as emerging from interconnected mechanisms of entropy, difficulty, and hash pointers, advancing understanding of decentralized timekeeping.

Findings

Bitcoin time is non-continuous and probabilistic.

Difficulty adjustment maintains entropy-maximizing regime.

System forms a self-regulating temporal architecture.

Abstract

Bitcoin constructs temporal order internally rather than synchronizing to any external clock. Empirical evidence shows that its time evolution is non-continuous, probabilistic, and self-regulated. Block discovery follows a stochastic process in which uncertainty accumulates during the search phase and collapses abruptly when a valid proof-of-work solution appears. Difficulty adjustment maintains the system near the entropy-maximizing regime and allows the network to infer the underlying global hash rate. Building on these observations, we present a unified framework in which Bitcoin time emerges from four interacting mechanisms: proof of work as a distributed entropy source, difficulty adjustment as temporal feedback, entropy collapse as discrete temporal updates, and recursive sealing through hash pointers. Together these mechanisms form a self-regulating temporal architecture that transforms distributed randomness into a coherent and irreversible global timeline, offering a generalizable foundation for autonomous timekeeping in permissionless systems.