Unpacking spatial-digital coupling: nonlinear morphological association ranges and spatially heterogeneous built-environment relationships in Beijing

Digital infrastructure usage in historic urban cores is shaped by a fine-grained interaction among commercial service quality, spatial permeability, heritage agglomeration, and environmental comfort. Using anonymized operator-side cellular records from Beijing's Capital Core Functional Area, this study constructs Digital Infrastructure Usage Intensity (DIUI) as a grid-level indicator that combines passive ambient population presence with active foreground cellular traffic. An interpretable modelling framework integrating XGBoost, SHAP, and geographically weighted regression is then used to identify dominant correlates, nonlinear association ranges, and spatially varying local relationships. The results indicate that commercial service quality and block openness are the most influential predictors, but their associations with DIUI are conditional rather than monotonic: commercial upgrading is associated with higher DIUI only when the surrounding morphology provides sufficient permeability and visibility, whereas overly enclosed or over-saturated settings weaken this relationship. Heritage concentration shows an inverted-U association with DIUI, suggesting that moderate agglomeration may support digital activity more effectively than excessive clustering. Spatially, transitional historic neighborhoods show stronger associations with commercial improvement than already saturated core areas, while street-level greenery appears to amplify digital activity in permeable settings. Overall, the results support a context-specific interpretation of spatial-digital coupling and caution against translating model-derived ranges into universal planning prescriptions without local validation.