Compression Over Retrieval: A Verification Gate for Structural Abstraction in Language Models

When we ask a language model a hard question, it typically does one of two things: it retrieves what it knows, or it reasons about structure. These are different operations, and we find they produce fundamentally different outputs. This paper introduces the compression scaffold: a prompting method that forces models to strip a problem down to its bare logical skeleton, verify that skeleton is genuinely abstract, transfer it to a completely unrelated domain, and generate a prediction from that transfer alone. Across experiments involving six models ranging from 0.8 billion to 100+ billion parameters and five problem domains, we observe three consistent findings. First, compression prompting produces novel predictions not present in standard retrieval outputs. Second, a single verification step — requiring the model to confirm its skeleton maps onto two unrelated real-world systems before proceeding — eliminates a specific failure mode we call shallow formalization, where models produce abstract-looking output that secretly preserves domain-specific content. Third, smaller models above a minimum size threshold produce structurally purer skeletons than larger models on abstract problems, suggesting that for this specific operation, the capability gap between small and large models is determined more by prompting architecture than by parameter count. We release the full prompt scaffold (and scoring rubric) to enable replication.