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Hill Sampling is a simple test-time scaling method that repeatedly samples edits to the best verified program using frozen LLMs, achieving state-of-the-art results on algorithmic problems like circle packing and Erdős' minimum-overlap problem.
An individual used their OpenClaw AI agent to solve circle packing problems, resulting in 10 new packings that beat existing records, and the agent was cited on a math records page alongside professional researchers.