Structural Propagation Bounds under Local Updates: Reachability, Schedule, History, Capacity, and State-Continuation

Ume Xelphia

doi:10.5281/zenodo.21937951

August 15, 2026Open Access

Structural Propagation Bounds under Local Updates: Reachability, Schedule, History, Capacity, and State-Continuation

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Key Points

To establish a theoretical propagation-bound framework for local-update systems that separates intrinsic structural reachability from operational and dynamic constraints.
Developed a mathematical framework formalizing structural propagation bounds across discrete local-update systems.
Performed a formal comparison between the proposed bounds and standard finite-rate, cone-like propagation representations without mapping update steps to physical spacetime.
Differentiated intrinsic structural reachability from constraints governed by execution schedules, operational history, network capacity, and state-continuation rules.
Formally mapped the relationship between discrete local-update boundaries and geometric cone-like propagation models while maintaining a distinction between computational stages and physical time.

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Implication

Theoretical analysis reveals distinct propagation bounds in local-update systems, clarifying reachability limits across dynamic constraints.

Abstract

This preprint presents a structural propagation-bound framework for local-update systems, distinguishing structural reachability from schedule-, history-, capacity-, and continuation-dependent constraints. It also gives a limited formal comparison with finite-rate and cone-like representations without identifying update stages with physical time or deriving relativistic spacetime. AI assistance Developed with assistance from OpenAI ChatGPT, including GPT-5.5 Thinking and GPT-5.6 Sol, for conceptual discussion, formalization, review, and manuscript revision.

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Ume Xelphia (2026) studied this question.

synapsesocial.com/papers/6a8179eff2fb91fc834ad68d https://doi.org/10.5281/zenodo.21937951

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Structural Propagation Bounds under Local Updates: Reachability, Schedule, History, Capacity, and State-Continuation

Key Points

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Implication

Abstract

Discussion

Cite This Study

Structural Propagation Bounds under Local Updates: Reachability, Schedule, History, Capacity, and State-Continuation

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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