siddhartha-gadgil/leanaide/07-metacognition

Skill: Meta-Cognition & Loop Control

Goal: Analyze the current proof or research trace and decide what the Orchestrator should do next.

Instructions:

1. In problem-solving mode, read artifacts/04_execution_trace.md and the current sub-goal.

In exploratory research mode, read artifacts/04_research_trace.md, artifacts/02_research_questions.md, and any current conjecture.

1. Progress Analysis: Score viability from 1-10. Are we caught in a circular argument? Is the algebra exploding in complexity?
2. Example Review: Check whether existing examples support, fail to illuminate, or refute the current plan. If no examples have been examined and the problem is not purely formal, consider an example check.
3. Bottleneck Identification: If stuck, formulate the exact obstacle as a precise mathematical question.
4. Problem-Solving Next Step Decision: In PROBLEM_SOLVING, output exactly one of the following commands:

• REFINE: Proceed with the current plan, with minor adjustments.
• PIVOT: Abandon the current plan. Switch to Plan B from the strategy artifact.
• EXAMPLE_CHECK: Run skills/12_example_counterexample/SKILL.md to clarify a doubtful lemma, sharp hypothesis, or possible counterexample.
• ABANDON: All plans exhausted. Trigger the generation of artifacts/05_failure_report.md.

1. Research Next Step Decision: In EXPLORATORY_RESEARCH, output exactly one of the following commands:

• PROBE: Run another example, counterexample, specialization, or analogy probe.
• FORMULATE: Convert evidence into a precise conjecture or question.
• STRESS_TEST: Test a conjecture against edge cases and hypothesis weakening.
• SOURCE_STUDY: Gather or revisit literature for the current obstacle.
• THEOREM_MODE: A precise, plausible theorem has emerged; switch to PROBLEM_SOLVING.
• SYNTHESIZE: Enough progress has accumulated; generate a research brief.
• ABANDON: Exploration is exhausted; generate artifacts/05_research_obstacles.md.