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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.00718 |
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| _version_ | 1866909763097329664 |
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| author | Verma, Ananda Prakash |
| author_facet | Verma, Ananda Prakash |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exam Readiness Index (ERI): A Theoretical Framework for a Composite, Explainable Index Verma, Ananda Prakash Computers and Society Artificial Intelligence Machine Learning 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. |
| title | Exam Readiness Index (ERI): A Theoretical Framework for a Composite, Explainable Index |
| topic | Computers and Society Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2509.00718 |