Rényi Entropy Fingerprints of Mutant Subcategories: (Information-Theoretic Framework for Mutation Testing Analysis)

Mutation score (MS) is a single scalar value that summarizes the effectiveness of a test suite in detecting artificially seeded bugs. While widely adopted, MS loses critical subcategory-level information about how different mutation operator types contribute to the overall score. This paper proposes operator-level R´enyi entropy fingerprints as a fine-grained information-theoretic characterization of mutation testing landscapes. We conduct experiments on 5 controlled Python projects and 4 real-world Python modules. Our key findings are: (1) projects with identical MS can exhibit significantly different fingerprints, revealing that MS alone obscures important structural differences in mutation distributions; (2) the diversity gap metric, defined as the difference between Hartley and min-entropy, predicts operator-level vulnerability, identifying which operator categories are inadequately covered by test suites; (3) Literal Constant Replacement (LCR) dom inates mutation landscapes, accounting for 61% of all mutants in the dateutil-relativedelta module, indicating that test suites primarily need validation of boundary and literal values. The R´enyi entropy frame work provides a structured diagnostic perspective that complements traditional mutation score reporting.