Exam Readiness Index (ERI): A Theoretical Framework for a Composite, Explainable Index

Abstract: We present a theoretical framework for an Exam Readiness Index (ERI): a composite, blueprint-aware score R in [0,100] that summarizes a learner's readiness for a high-stakes exam while remaining interpretable and actionable. The ERI aggregates six signals -- Mastery (M), Coverage (C), Retention (R), Pace (P), Volatility (V), and Endurance (E) -- each derived from a stream of practice and mock-test interactions. We formalize axioms for component maps and the composite, prove monotonicity, Lipschitz stability, and bounded drift under blueprint re-weighting, and show existence and uniqueness of the optimal linear composite under convex design constraints. We further characterize confidence bands via blueprint-weighted concentration and prove compatibility with prerequisite-admissible curricula (knowledge spaces / learning spaces). The paper focuses on theory; empirical study is left to future work.