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Bibliographic Details
Main Authors: Chen, Bin, Huang, Dechuang
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.26758
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author Chen, Bin
Huang, Dechuang
author_facet Chen, Bin
Huang, Dechuang
contents Distributed systems in which concurrent proposals are mutually exclusive face a fundamental stability constraint under network delay. In open systems where global state progression is event-driven rather than round-driven, propagation delay creates a conflict window within which overlapping proposals may generate competing branches. This paper derives a density-delay law for such exclusive state progression processes. Under independent proposal arrivals and bounded propagation delay, overlap is approximated by a Poisson model and fork depth is represented by a birth-death process. The analysis shows that maintaining bounded fork depth as the number of participants grows requires the density-delay product $λΔ$ to remain $O(1)$, implying that aggregate proposal intensity must stay bounded and yielding an inverse-scaling law $g(N)=O(1/N)$ at the unit level. Simulation experiments across varying network sizes and propagation delays align with a common density-delay curve, supporting the predicted scaling behavior. The result provides a compact law for stable event-driven state progression in open distributed systems and offers a scaling-based interpretation of Bitcoin-style difficulty adjustment as a decentralized way to regulate effective event density.
format Preprint
id arxiv_https___arxiv_org_abs_2603_26758
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Density-Delay Law for Stable Event-Driven State Progression in Open Distributed Systems
Chen, Bin
Huang, Dechuang
Distributed, Parallel, and Cluster Computing
Networking and Internet Architecture
Distributed systems in which concurrent proposals are mutually exclusive face a fundamental stability constraint under network delay. In open systems where global state progression is event-driven rather than round-driven, propagation delay creates a conflict window within which overlapping proposals may generate competing branches. This paper derives a density-delay law for such exclusive state progression processes. Under independent proposal arrivals and bounded propagation delay, overlap is approximated by a Poisson model and fork depth is represented by a birth-death process. The analysis shows that maintaining bounded fork depth as the number of participants grows requires the density-delay product $λΔ$ to remain $O(1)$, implying that aggregate proposal intensity must stay bounded and yielding an inverse-scaling law $g(N)=O(1/N)$ at the unit level. Simulation experiments across varying network sizes and propagation delays align with a common density-delay curve, supporting the predicted scaling behavior. The result provides a compact law for stable event-driven state progression in open distributed systems and offers a scaling-based interpretation of Bitcoin-style difficulty adjustment as a decentralized way to regulate effective event density.
title A Density-Delay Law for Stable Event-Driven State Progression in Open Distributed Systems
topic Distributed, Parallel, and Cluster Computing
Networking and Internet Architecture
url https://arxiv.org/abs/2603.26758