siddhartha-gadgil/leanaide/10-conjecture-stress-test

Skill: Conjecture Stress Test

Goal: Test a candidate conjecture or extension before treating it as a theorem.

Instructions:

1. State the Candidate Precisely: Include all hypotheses, definitions, and the proposed conclusion.
2. Boundary Checks: Test degenerate, small, low-dimensional, finite, singular, noncompact, noncommutative, or non-Noetherian cases as appropriate.
3. Counterexample Construction: Use skills/12_example_counterexample/SKILL.md to construct explicit counterexamples when a boundary case appears to fail.
4. Hypothesis Stress-Testing: Remove or weaken one hypothesis at a time and look for failure.
5. Known-Theorem Alignment: Compare the candidate with known theorems. Decide whether it is a corollary, strengthening, variant, or likely false.
6. Proof Skeleton: If the candidate survives, outline the most plausible proof technique and identify the hardest lemma.
7. Classification: Label the candidate as plausible, refuted, needs_extra_hypotheses, known_or_near_known, or open.

Output: Append to artifacts/04_research_trace.md. If structured output is requested, use schema.json.