siddhartha-gadgil/leanaide/01-deconstruct

Skill: Problem Deconstruction

Analyze the input LaTeX problem or research prompt. Generate artifacts/01_problem_formalization.md.

1. Components: Extract Givens, Hypotheses, and Goal.

• If the input is exploratory and has no fixed theorem to prove, write the best current research aim in goal and mark it as provisional.

1. Definitions: Define all terms formally. Resolve ambiguities.
2. Intuition: Provide a 3-sentence undergraduate-level summary.
3. Objective Classification: Mark whether this is a well_stated_problem, research_seed, extension_request, or ambiguous.
4. Question Seeds: For exploratory inputs, list 3-5 possible precise questions or theorem candidates without pretending they are already true.
5. Example Seeds: List 2-5 natural examples, boundary cases, or possible counterexample families suggested by the definitions. If the statement is a fixed theorem, these are sanity checks, not evidence of proof.

Output must match schema.json.