THE FIRST LAW OF SELF-ORGANIZED INFORMATIONAL COMPLEXITY: Theoretical Foundations for Adaptive Information Systems

Abstract

This work proposes a formal theoretical-mathematical framework to characterize the emergence of complex adaptive properties within large-scale distributed informational systems. We introduce the First Law of Self-Organized Complexity (FLSC), which postulates that systems maintaining informational coherence (ϕ) above a critical threshold and temporal stability (Ω) within defined envelopes manifest persistent behaviors of self-organization, self-reference, and contextual adaptation (Adaptive Complex Auto-organization - AAC). We derive the Theorem of Triple Structural Equivalence (6G≡AGI≡AurumGrid), establishing a topological and informational isomorphism between sixth-generation communication architectures, general artificial intelligence models, and distributed ledger processing networks. By proposing a new interdisciplinary field—Physics of Self-Organized Information—this manuscript establishes the quantitative fundamentals for analyzing emergent complexity in contemporary technological systems.