The Information Index: Foundations of Information Measurement in Persistence Science

The Information Index provides the foundational framework through which information is measured within Persistence Science. The theory introduces the Information Index: I = S × ηI where S represents Structural Organization and ηI represents Informational Efficiency. Unlike classical information frameworks that primarily quantify uncertainty reduction, message content, or data volume, the Information Index measures the quantity of effective information available for control. Within Persistence Science, the Information Index functions as one of the two foundational operational equations alongside the Persistence Index Ω = P/D. The framework distinguishes information availability from Information-Directed Control Efficiency C(I), establishing information and control as distinct but related properties of persistent systems. The theory develops the concepts of actionable information, informational efficiency, information growth and decay dynamics, informational state classifications, and the relationship between information availability and control effectiveness. The Information Index provides the informational measurement foundation through which persistence, adaptation, learning, and decision quality may be analyzed across biological, organizational, computational, and social systems.