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This work organizes 82 reusable methods from Putnam 2000-2014 as Method Contracts, which pair applicability descriptions with Mathlib anchors, a checked example or scaffold, and expected proof obligations, and analyzes when similarity-based representations cannot distinguish methods with different applicability, how er...
Large language models (LLMs) have reached expert-level performance on competition mathematics largely through the volume of search placed around them: candidate solutions are sampled in quantity and retained only when an external criterion accepts them. Such a procedure improves the outcome that survives it while leavi...
This work introduces Tool Primitives, a design that replaces rigid API schema-based invocation with natural language as the interface for tool calling, where each tool is wrapped with an LLM interface that handles schema resolution and execution internally, enabling natural inter-tool communication for nested and multi...
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