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The verbose context problem occurs when structured concepts have token-inefficient textual representations. This bottleneck is acute in population health: cohort-level analysis of longitudinal patient records requires reasoning over thousands of medically-coded events, often exceeding 400K tokens in total. We present PopMedQA, a benchmark isolating this problem through computational tasks on groups of longitudinal patient records. We construct the benchmark using neopatient, a new library for language-controlled generation of artificial patient records. Through extensive ablations -- including prompting strategies, prompt compression, and agentic decomposition -- we find that domain-independent methods fail to alleviate the verbose context problem. There remains significant opportunity to exploit domain-specific structure in language model inputs for population-scale reasoning.