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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.26758 |
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| _version_ | 1866908917495234560 |
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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 |