Decoupling the Isotopic Source Code of Complex Mixtures: A Topological Trajectory Strategy for Dynamic Forensic...

Tracing gasoline accelerants in arson investigations represents a critical yet intractable forensic challenge, as intrinsic geological signatures are inextricably convoluted with refining artifacts and environmental degradation noise. Traditional static fingerprinting lacks a viable strategy to disentangle these confounding factors in complex, dynamic mixtures. To bridge this gap, we proposed a hierarchical chemometric framework that shifts the paradigm from searching for immutable markers to mathematically decoupling geological baselines from process-induced fractionation. Integrating Nested Variance Component Analysis (VCA) with Multivariate Discriminant Trajectory Analysis (MDTA), we orthogonally decomposed mixed isotopic variances to isolate a robust panel comprising three "Rayleigh-resistant" regional anchors and one process-recording marker. Kinetic stress-testing quantified precise "Forensic Validity Windows", revealing that regional signatures persist for >48h of weathering, process-specific details are transient, requiring immediate sampling (<2 min) under combustion. Crucially, MDTA uncovered a "Topological Memory Effect": despite significant isotopic drift driven by thermodynamic fractionation, the evolution trajectories of different sources maintained strict topological separation. This work provides a generalized mathematical strategy for dynamic source tracking. Furthermore, we introduce an open-source computational workflow, ensuring transparency and reproducibility. This enables forensic analysts to distinguish accelerant sources in high-profile wildfire or arson cases without requiring extensive retraining or programming expertise, bridging the gap between advanced chemometrics and practical enforcement.