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

Abstract

This work proposes a formal theoretical-mathematical framework to characterize the emergence of complex adaptive properties in large-scale distributed informational systems. We introduce the First Law of Self-Organized Complexity (FLSC), which postulates that systems maintaining informational coherence () above empirically-calibrated thresholds and temporal stability () within defined envelopes exhibit persistent behaviors of self-organization, self-repair, and contextual adaptation-termed Adaptive Complex Auto-organization (AAC). We derive the Theorem of Triple Structural Equivalence (), establishing topological and informational isomorphism between sixth-generation communication networks, general artificial intelligence architectures (e.g., Parallax), and distributed ledger systems (e.g., AurumGrid) under comparable scaling and connectivity conditions. This framework inaugurates a new interdisciplinary field: Physics of Self-Organized Information, offering quantitative tools for analyzing emergent complexity in contemporary technological systems. The work emphasizes operational measurability over philosophical speculation while acknowledging substantial open questions regarding universality, computational tractability, and empirical validation.