siddhartha-gadgil/leanaide/04-strategy-gen

Skill: Strategy Generation (Dispatcher)

Goal: Formulate concrete, step-by-step proof plans by selecting and applying appropriate mathematical techniques.

Scope: Use this skill for PROBLEM_SOLVING. For EXPLORATORY_RESEARCH, use skills/09_exploratory_probe/SKILL.md unless a precise theorem has already been selected as the current target.

Instructions:

1. Analyze Formalization: Review artifacts/01_problem_formalization.md.

• If artifacts/02_examples.md exists, use it to avoid strategies already refuted by counterexamples.

1. Technique Selection:

• Scan skills/04_strategy_gen/registry.md and skills/techniques/ for any skill whose manifest matches the problem context.
• If a match is found (e.g., Riemannian manifolds -> bochner_technique), invoke that specific skill to generate strategy fragments.

1. Reasoning Synthesis:

• Forward Reasoning: List 3-5 deductions from hypotheses.
• Backward Reasoning: List 2-3 conditions implying the goal.
• Simplification: Propose 2 special cases.
• Example Check: List 2-3 examples or boundary cases that the plan should explain. If any counterexample appears valid, stop and recommend revising the statement instead of drafting a proof.

1. Draft Plans:

• Generate Plan A and Plan B, incorporating selected technique fragments.
• CRITICAL: Label every step's difficulty as easy, standard, or hard.

1. Output: Save to artifacts/03_strategy_plans.md.