A Generalized Algorithmic Framework for Detecting Faraday Rotation Measure Flares in Repeating Fast Radio Bursts

Variations in the Faraday rotation measure (RM) of repeating fast radio bursts (FRBs) provide critical diagnostics of the dynamically evolving magneto-ionic environments surrounding their progenitors. Sudden, transient ``RM flares'' can trace the passage of discrete magneto-ionic structures, such as stellar coronal mass ejections from the companion or other dense plasma clumps, across the line of sight. However, identifying these rare events is difficult because RM evolution manifests a wide range of complex behaviors, from smooth, long-term trends to chaotic stochasticity, further complicated by highly non-uniform temporal sampling. This complexity makes it a non-trivial challenge to distinguish localized ``flares'' from intrinsic environmental volatility. We present a generalized algorithmic framework that establishes a robust methodology for the automated detection and characterization of RM flares. By isolating discrete transient perturbations from quiescent backgrounds, this pipeline enables the uniform census of environmental variability across the FRB population. Applying this framework to 15 repeating FRBs, we find that distinct RM flares are rare, with FRB 20220529A being the only source to exhibit an algorithmic detection under standardized parameters. Most of other active repeaters instead display high-level intrinsic fluctuations or secular evolution. This work provides a rigorous foundation for distinguishing between different modes of local plasma dynamics, offering a crucial diagnostic tool for identifying the diverse progenitor systems and local environments of FRBs.