numerical-check

# 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 | |---|---| | Verify an algebra / derivative / limit / closed-form identity | `symbolic-check` (R2) | | Machine-prove a lemma (want a proof, not a stress-test) | `lean-check` (R3) | | Re-verify a computed empirical result in another language | `cross-language-check` | | Conceptual / assumption-completeness review | `domain-reviewer` (agent) | ## Position in the verification spectrum **R1 — numerical falsification.** Can **FALSIFY** definitively (a confirmed counterexample refutes the claim) but can **never VERIFY** (no counterexample ≠ proof). The strongest positive result is `INCONCLUSIVE (supported): no counterexample in N draws`. Pair with `le...