Counterexample Hunter

Try to break the claim before trusting it.

The two failure modes to avoid:

• Fake counterexample: something that looks like it breaks the claim but actually doesn't violate any assumption. Always check the assumptions explicitly.
• Empty survival: concluding "no counterexample found" without saying what was actually tested. A claim that survived three degenerate cases is not a claim that has been stress-tested.

Step 1: Restate the claim precisely

Write out:

• The exact statement (universal quantifiers, domains, topology, finiteness — don't paraphrase)
• Every assumption, explicit and implicit
• What "breaks" the claim means (counterexample to existence? to uniqueness? to a bound?)

If the claim is ambiguous, name the ambiguity and ask which reading to test.