Editing Openai/692596ae-427c-800c-903a-fe6f67c1d76a (section)

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Abstract

This paper introduces a unified framework for evaluating the coherence of complex systems by integrating three fundamental components: internal probabilistic structure, intrinsic trait variability, and externally mediated relational constraints. We argue that coherence is not solely an internal property of a system but emerges from the interplay between its internal organization and its compatibility with the surrounding environment. We formalize internal coherence, external coherence, and global coherence as measurable quantities, and we develop computational modules capable of calculating these metrics for arbitrary objects represented as state vectors and relational networks. An evolutionary engine is implemented to simulate adaptive processes that drive systems toward configurations of higher global coherence. Through a series of experimental scenarios—from an obsolete craftsman adapting to market changes, to a quantum-state collapse under measurement, to dynamics of human social relationships—we demonstrate how the framework captures both stability and adaptation across domains. This work provides a generalizable and computationally tractable foundation for studying coherent behavior in physical, social, informational, and artificial systems.

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