The Decay Index: Foundations of Decay Measurement in Persistence Science

Persistence Science explains survival through the interaction of information, control, energy, and decay. While the Information Index provides a framework for measuring information and the Persistence Index provides a framework for measuring persistence, Persistence Science currently lacks a dedicated normalized framework for measuring total decay, its constituent channels, and its dynamic trajectory as a unified construct. This paper introduces the Decay Index, a unified framework for measuring the magnitude, composition, trajectory, and acceleration of decay across adaptive systems. Decay is decomposed into four primary channels: D = Dᶠ + Dᵉ + Dˢ + Dᶜ where Dᶠ represents frictional decay, Dᵉ represents entropic decay, Dˢ represents structural decay, and Dᶜ represents conflict and external-shock decay. The framework introduces a canonical normalized Decay Index: Δ = D / Dᵣₑ𝒻 together with a weighted domain-specific extension, decay state classifications, Decay Velocity (δ), Decay Acceleration (ζ), the Decay State Vector Φᴰ(t), the Decay Horizon (Tᵈ), and the Political Decay Damper (kₚ). By distinguishing raw Total Decay from normalized decay intensity, the framework enables deterioration to be measured, compared, and tracked across biological, organizational, computational, economic, political, and civilizational systems. The Decay Index completes the foundational measurement trilogy of Persistence Science alongside the Information Index and Persistence Index, providing a unified framework for analyzing deterioration, resilience, persistence decline, and systemic collapse.