Bitcoin derives a verifiable temporal order from probabilistic block discovery and cumulative proof-of-work rather than from a trusted global clock. We show that block arrivals exhibit stable exponential behavior across difficulty epochs, and that the proof-of-work process maintains a high-entropy search state that collapses discretely upon the discovery of a valid block. This entropy-based interpretation provides a mechanistic account of Bitcoin's non-continuous temporal structure. In a distributed network, however, entropy collapse is not completed instantaneously across all participants. Using empirical observations of temporary forks, we show that collapse completion unfolds over a finite propagation-bounded interval, while remaining rapid in practice.
@article{arxiv.2602.09027,
title = {Entropy-Based Evidence for Bitcoin's Discrete Time Mechanism},
author = {Bin Chen and Pan Feng},
journal= {arXiv preprint arXiv:2602.09027},
year = {2026}
}