Introducing Repository Stability

Abstract: Drawing from engineering systems and control theory, we introduce a framework to understand repository stability, which is a repository activity capacity to return to equilibrium following disturbances - such as a sudden influx of bug reports, key contributor departures, or a spike in feature requests. The framework quantifies stability through four indicators: commit patterns, issue resolution, pull request processing, and community engagement, measuring development consistency, problem-solving efficiency, integration effectiveness, and sustainable participation, respectively. These indicators are synthesized into a Composite Stability Index (CSI) that provides a normalized measure of repository health proxied by its stability. Finally, the framework introduces several important theoretical properties that validate its usefulness as a measure of repository health and stability. At a conceptual phase and open to debate, our work establishes mathematical criteria for evaluating repository stability and proposes new ways to understand sustainable development practices. The framework bridges control theory concepts with modern collaborative software development, providing a foundation for future empirical validation.