Sigmoid-Parameterized Lifepaths: A Dynamic Framework for Analyzing Research Trajectories in Scholarly Ecosystems

Traditional bibliometric methods cannot track dynamic research trajectories—they provide static snapshots (h-index), apply single-pass sigmoid fitting to entire datasets, or categorize discrete regimes, missing transitions and non-monotonic disruptions. We introduce sigmoidparameterized lifepaths: iteratively fitting sigmoid curves at regular intervals and plotting evolving parameters as trajectories through dynamic space. This identifies saturation dynamics—tracking entities' positions relative to ultimate capacity limits (acceleration, inflection, deceleration, deactivation), transition timing between saturation phases, and “time folds”—backward-moving saturation projections indicating downward capacity revisions from policy shocks or unsustainable growth recognition, and forward jumps indicating re-acceleration or capacity expansion. Bibliometric validation used carbon footprint research (2007-2023, 16,103 records, n=114 countries, n=7,960 authors): significant correspondence with independent regime classification (χ2=44.99, p<0.001), demonstrating convergent validity while revealing transitional saturation dynamics regime analysis cannot detect, country analysis showing saturation midpoints concentrated in 2015–2022, with backward capacity revisions showing a temporal concentration around the Paris Agreement ratification period consistent across window sizes and fitting designs, and forward jumps occurring at approximately one-sixth the rate of backward folds throughout the observation period, and author analysis revealing diverse career trajectories including sustained acceleration, premature saturation, and topic abandonment patterns that lifepaths capture through saturation dynamics unavailable in cumulative metrics.