Intra-settlement scaling across the urban-rural continuum: material stocks, service provisioning, and greenhouse gas emissions in the contiguous United States.

Research on urban scaling laws suggests that cities with larger populations tend to be more resource-efficient, yet whether these findings hold across spatial scales, varying definitions of 'urban' and the entire rural-urban continuum remains unresolved. Herein, we leverage high-resolution maps for the entire contiguous United States of America to examine how built environment material stocks, service provisioning, and operational greenhouse gas (GHG) emissions scale with population size across the country. Results show that residential building footprints, i.e., the ground area covered by buildings, useful floor area, and material stocks scale moderately sub-linearly (scaling exponent Supplementary Information: The online version contains supplementary material available at 10.1007/s44498-026-00125-w. Supplementary Information SI1. This Supplementary Information contains supplementary methodological details, additional explanations, robustness tests, figures, and results, including Supplementary Notes S1, S20, Supplementary Figures S1, S18, Supplementary Tables S1, S24, and Supplementary References. Supplementary Information SI2. This Supplementary Information file provides the numerical data underlying Tables S3, S4, S10, S11, S19, and S23 reported in Supplementary Information SI1.