Assessing trace metal(loid)s in mining-affected soils: Vector-based contamination patterns derived from interval...

This study addresses the spatial, temporal, and structural limitations inherent in conventional approaches to evaluating multi-metal soil contamination. Traditional indices, including the pollution load index (PLI), rely on the scalar aggregation of metal concentrations, often obscuring inter-element relationships such as relative dominance and co-occurrence structures. To overcome this limitation, we introduce a structure-preserving framework based on interval number sorting (INS), which transforms multi-metal data into discrete vector configurations while retaining compositional dependencies among elements. To account for geochemical heterogeneity and temporal dynamics, site-specific background concentrations (B_n) are incorporated to control for localized geogenic variations, and an entropy-weighted temporal model is applied to enhance sensitivity to recent environmental conditions. Application of this framework to 3849 soil samples from mining-impacted agricultural regions in Korea demonstrates that site-specific B_n thresholds stabilize baseline estimation, while temporal weighting prevents recent contamination signals from being mathematically diluted by historical observations. The INS-based topological analysis reveals an extreme structural sparsity of 0.33% within the theoretical state space, indicating that regional multi-metal co-occurrence is governed by coordinated constraints rather than stochastic accumulation processes. This structural control aligns closely with the primary mineralogical controls, which regulate geochemical mobilization and results elemental distributions in near-surface environments. Moreover, contamination progression exhibits a distinct binary bifurcation, evolving along either a Cd-dominant or an As-dominant pathway as contamination severity increases. These findings suggest that soil contamination evolves through constrained geochemical pathways rather than random accumulation processes. By preserving relative magnitude relationships among trace metals, the proposed framework enables the identification of dominant contamination configurations and their evolutionary trajectories, thereby advancing soil contamination assessment from magnitude-based evaluation toward pathway-based interpretation.