The Coherence Constraint: Structural Persistence Law for Distributed Artificial Intelligence

This work introduces the Coherence Constraint, a structural law governing the persistence and suppression of computational elements in distributed artificial intelligence systems. The framework proposes that elements within a distributed computational environment—such as agents, model components, hypotheses, or knowledge structures—should persist or decay according to their structural coherence with the surrounding system state. The core dynamic is expressed through a structural persistence law: dw_i / dτ = γ (C_i − C_crit) w_i where structural coherence determines whether elements are reinforced or suppressed over an internal structural time parameter τ. This formulation enables distributed AI systems to self-organize through coherence-driven persistence dynamics rather than relying solely on centralized optimization or consensus voting mechanisms. The approach provides a general coordination principle for: • multi-agent AI systems • collaborative large language model ecosystems • distributed reasoning architectures • decentralised artificial intelligence infrastructures • edge and cloud hybrid AI networks The coherence constraint functions as a structural selection mechanism that allows coherent computational structures to persist while incoherent structures gradually disappear. The framework therefore introduces a general law of structural persistence for distributed computational systems. This work is related to the broader research program on internal structural time and complex system evolution developed by Abdulsalam Al-Mayahi.