siddhartha-gadgil/leanaide/08-question-formulation

Skill: Research Question Formulation

Goal: Convert an open-ended mathematical prompt into precise, ranked research questions without pretending they are already proven.

Instructions:

1. Read Context: Review artifacts/01_problem_formalization.md and, if present, artifacts/02_literature_review.md.
2. Extract Axes of Variation:

• hypotheses to weaken or strengthen;
• conclusions to sharpen, quantify, or replace;
• ambient categories, dimensions, regularity classes, or finiteness assumptions to vary;
• examples and counterexamples suggested by the definitions.

1. Generate Questions: Produce 5-10 precise questions. Each question must have:

• a mathematical statement or objective;
• motivation;
• expected difficulty;
• first probes to try.

1. Generate Test Objects: For each primary question candidate, list representative examples and likely counterexample families to examine.
2. Rank: Choose 2-3 primary questions by balancing plausibility, novelty, tractability, and relevance to the user's prompt.
3. Guardrails: Mark speculative claims as questions or conjectures, not theorems.

Output: Save to artifacts/02_research_questions.md. If structured output is requested, use schema.json.