siddhartha-gadgil/leanaide/02-inspect-triage

Skill: Problem Inspection & Triage

Goal: Decide if the agent should begin proof strategizing, study literature, or branch into exploratory research.

Instructions:

1. Review artifacts/01_problem_formalization.md.
2. Assess objective type and complexity:

• Is there a precise claim with fixed hypotheses and a fixed goal?
• Is the request instead to extend, generalize, formulate questions, or look for conjectures?
• Does it invoke advanced, highly specific machinery requiring source study?
• Are there obvious small, degenerate, or boundary examples that could immediately refute or clarify the statement?

1. Decision:

• Return DIRECT_PROOF if the hypotheses and goal use standard definitions that can be manipulated directly.
• Return SOURCE_STUDY if the problem requires adapting a complex known theorem. Suggest keywords or specific papers to search.
• Return EXPLORATORY_RESEARCH if there is no fixed theorem to prove, or the user asks for extensions, questions, conjectures, examples, or research directions.

1. Auxiliary Example Check: If the statement's truth is uncertain, hypotheses seem sharp, or definitions are ambiguous, request skills/12_example_counterexample/SKILL.md before strategy generation. This is an auxiliary action, not a separate terminal triage decision.

Regression Rule: If the input is a normal theorem/exercise with an explicit goal, do not route to exploratory research merely because generalizations might be interesting.