Individual skill
numerical-check
Numerically stress-test a self-authored mathematical claim over its parameter space to seek counterexamples or characterize violations. Use when checking monotonicity, thresholds, inequalities, comparative statics, or limits computationally. For algebraic proof or Lean formalization, use $symbolic-check or $lean-check.
skills/numerical-check/SKILL.md
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# Numerical Check: Falsify a Self-Authored Math Claim by Sweep
Empirically stress-test a mathematical claim you wrote but have not proven. The goal is **falsification**: throw many random instances at the claim and try to break it. A single genuine counterexample kills the claim; a large clean sweep is *evidence*, never proof.
## When to Use
- You wrote a **Proposition / Theorem / Conjecture** (monotonicity, threshold, comparative-static, inequality, closed-form, limit) and want to know if it's actually true before claiming it.
- `numerical-check`, "stress-test my conjecture", "find a counterexample to X", "is Q(ρ) really monotone", "does the threshold hold for all …".
- The write-time empirical arm of the `mark-unverified` rule (self-authored math must be checked before assertion).
## When NOT to Use
| Situation | Use instead |
|---|---|