Coherence Efficiency and the Law of Coherent Organization: A Unifying Framework for Adaptive Systems

Complex adaptive systems across biology, cognition, ecology, organizations, and engineered networks exhibit a recurring tension between two universal failure modes: excessive rigidity, which suppresses adaptability, and excessive variability, which destroys coherence. This work proposes the Law of Coherent Organization (LCO) as a unifying explanatory framework for understanding how such systems maintain sustained function over time. The LCO introduces the concept of coherence efficiency, formalized by a scalar metric Λ (Lambda), defined as the ratio of purposeful information and functional robustness to the combined energetic and informational costs required to maintain system organization. Rather than predicting optimal function through maximization of complexity, power, or control, the framework predicts that adaptive systems operate within an intermediate regime—termed the Coherent Oscillatory Regime (COR)—where Λ is locally maximized. This paper presents the canonical formulation of the LCO as a hypothesis-generating framework rather than an established physical law. It provides (i) explicit operational interpretations of the Λ components, (ii) a minimal dynamical model demonstrating the emergence of a peak in coherence efficiency between rigid and chaotic regimes, and (iii) a program for empirical anchoring across multiple domains, including neuroscience, ecology, and organizational systems. The LCO makes falsifiable predictions: systems identified as healthy, adaptive, or resilient should exhibit higher coherence efficiency than adjacent regimes characterized by over-constraint or incoherence, and interventions that increase cost without proportional gains in robustness or purposeful information should reduce Λ. By reframing adaptation in terms of coherence efficiency, the LCO offers a common quantitative language for analyzing resilience, intelligence, and persistence in complex systems.