Network-based Spatial Context Retrieval for Open-weight LLMs: A Faithfulness Benchmark for Grounded Geographic Reasoning

Large language models (LLMs) encode substantial latent geographic knowledge, yet they reason poorly over space and are unreliable when queried from coordinates alone. Useful behaviour emerges only when structured spatial context is supplied in the prompt. This raises a question geographic evaluation has left unexamined: once the right context is supplied, does the model reason from it, or override it with its own parametric recall? We take up this question with an open pipeline for network-based spatial context retriev-al. In it, the surroundings of a selected point are defined by the pedestrian street network, the area actually reachable on foot. Using only open data and open-weight models, the pipeline retrieves features from OpenStreetMap and the GHS-POP population grid, computes indicators over the network catchment in code, and injects them as a compact spatial brief. On this basis we build a faithfulness benchmark. It labels every claim a model makes by its source (grounded in the brief, or drawn from training knowledge) and its correctness, and it probes each case with a planted false premise that the brief refutes. We evaluate sixteen open-weight model configurations across three families (Qwen, Gemma and Llama, with Gemma in two generations), four size classes and, where available, both thinking and non-thinking modes, on three con-trasting cities, resampling every case over ten seeds. The results show that resistance to the planted premise varies more strongly by model family and generation than by scale, while brief-reading competence forms a partly separate dimension. These behaviours are not captured by conventional world-correctness scores or single-shot evaluation. We release the implementation, spatial briefs, model outputs, and claim-level labels as a reproducible workflow at github.com/perezjoan/NSCR-LLM.