Measuring Activity-Space Segregation with Multi-Source Big Data: A Physical-Digital Framework with Simulation Validation and a Real-Data Proof of Concept

Segregation research increasingly measures who people encounter beyond home, yet physical mobility, place semantics, and digital activity are often combined without clear construct boundaries. This study develops a physical-digital activity-space framework that distinguishes co-presence, digital exposure, and digital interaction, and represents physical and digital segregation as separate components rather than a forced composite. Validation is deliberately split by evidentiary role. A public Washington--Baltimore Foursquare check-in subset tests the computational feasibility and robustness of a discrete group co-visitation statistic; it does not validate continuous socioeconomic exposure because the dataset lacks individual socioeconomic status. Monte Carlo experiments separately test layer-selective construct response and sensitivity to trace missingness, spatial aggregation, socioeconomic measurement error, and cross-layer coupling. The results show that the proposed calculations are executable and that the synthetic physical and digital components respond selectively to their generating mechanisms, while also revealing important measurement attenuation. No real-data estimate of income segregation, digital exposure, physical--digital coupling, or the causal effect of inequality is reported. The framework therefore combines bounded validation with a falsifiable comparative and causal research agenda.