siddhartha-gadgil/leanaide/11-research-synthesis

Skill: Research Synthesis

Goal: Consolidate exploratory work into a research brief with questions, evidence, conjectures, obstacles, and next actions.

Instructions:

1. Gather Artifacts: Read artifacts/01_problem_formalization.md, artifacts/02_research_questions.md, artifacts/02_literature_review.md if present, and artifacts/04_research_trace.md.
2. Separate Status Levels:

• proven or source-backed facts;
• plausible conjectures;
• refuted candidates;
• open questions;
• examples and counterexamples.

1. Example Ledger: Include a table of representative examples, counterexamples, boundary cases, and which hypotheses they test.
2. State Candidate Theorems: For each surviving conjecture, write a precise theorem-style statement and list missing proof obligations.
3. Prioritize Next Work: Recommend 3-5 next probes or proof attempts.
4. Avoid Overclaiming: Do not present conjectural claims as established results.

Output: Save to artifacts/05_research_brief.md. If structured output is requested, use schema.json.