Are the Majority of Public Computational Notebooks Pathologically Non-Executable?

Computational notebooks are the de facto platforms for exploratory data science, offering an interactive programming environment where users can create, modify, and execute code cells in any sequence. However, this flexibility often introduces code quality issues, with prior studies showing that approximately 76% of public notebooks are non-executable, raising significant concerns about reusability. We argue that the traditional notion of executability - requiring a notebook to run fully and without error - is overly rigid, misclassifying many notebooks and overestimating their non-executability. This paper investigates pathological executability issues in public notebooks under varying notions and degrees of executability. Even partially improving executability can improve code comprehension and offer a pathway for dynamic analyses. With this insight, we first categorize notebooks into potentially restorable and pathological non-executable notebooks and then measure how removing misconfiguration and superficial execution issues in notebooks can improve their executability (i.e., additional cells executed without error). In a dataset of 42,546 popular public notebooks containing 34,659 non-executable notebooks, only 21.3% are truly pathologically non-executable. For restorable notebooks, LLM-based methods fully restore 5.4% of previously non-executable notebooks. Among the partially restored, the executability of notebooks improves by 42.7% and 28% by installing the correct modules and generating synthetic data. These findings challenge prior assumptions, suggesting that notebooks have higher executability than previously reported, many of which offer valuable partial execution, and that their executability should be evaluated within the interactive notebook paradigm rather than through traditional software executability standards.