siddhartha-gadgil/leanaide/09-exploratory-probe

Skill: Exploratory Probe Planning and Execution

Goal: Design or execute concrete probes that gather evidence for exploratory research questions.

Instructions:

1. Select a Question: Choose one primary question from artifacts/02_research_questions.md.
2. Pick Probe Type:

• example_search: compute or construct representative examples;
• counterexample_search: target boundary cases and weakened hypotheses;
• specialization: test simpler cases, lower dimension, finite cases, or commutative cases;
• generalization: alter hypotheses or conclusions;
• analogy: compare with a nearby theorem or field;
• source_check: look for known results or named techniques.

1. Make the Probe Concrete: Specify objects, parameters, computations, lemmas, or sources to inspect.
2. Construct Examples: For example_search and counterexample_search, run or follow skills/12_example_counterexample/SKILL.md; record explicit objects, not just sketches.
3. Record Evidence: Write what the probe supports, refutes, or leaves undecided.
4. Update Trace: Append results to artifacts/04_research_trace.md.

Output: Save an exploration plan to artifacts/03_exploration_plan.md or a probe result to artifacts/04_research_trace.md. If structured output is requested, use schema.json.