The Human Moral Archive Framework – Addendum II: Moral Distribution Indexing (MDI)

This paper constitutes the second formal extension of The Human Moral Archive Framework (HMAF), introducing the construct of Moral Distribution Indexing (MDI) as the empirical and temporal layer of moral data analytics. It defines a system for quantifying moral drift, coherence, and stability through information-theoretic principles derived from Shannon (1948), Kullback & Leibler (1951), Fisher (1922), and Cover & Thomas (2006). MDI introduces a family of new analytic measures—Moral Drift (ΔI), Ethical Stability (σᴇ), Moral Entropy (Sₘ), Ethical Coherence (Cₑ), Moral Inertia (μᴍ), and Ethical Resonance (Rₑ)—each formalizing dynamic moral relationships within multi-agent systems. Together, these constructs transform HMAF from a descriptive archive of moral distributions into an operational architecture capable of longitudinal measurement, comparative calibration, and predictive inference. Addendum II – Moral Distribution Indexing (MDI) directly extends Addendum I – Formalizing the Moral Distribution Model (MDM) and provides the mathematical foundation for Addendum III – Predictive Moral Analytics (MDP), establishing a coherent theoretical continuum across the HMAF moral analytics series.