Individual skill

math-olympiad

"Solve competition math problems (IMO, Putnam, USAMO, AIME) with adversarial verification that catches the errors self-verification misses. Activates when asked to 'solve this IMO problem', 'prove this olympiad inequality', 'verify this competition proof', 'find a counterexample', 'is this proof correct', or for any problem with 'IMO', 'Putnam', 'USAMO', 'olympiad', or 'competition math' in it. Uses pure reasoning (no tools) — then a fresh-context adversarial verifier attacks the proof using specific failure patterns, not generic 'check logic'. Outputs calibrated confidence — will say 'no confident solution' rather than bluff. If LaTeX is available, produces a clean PDF after verification passes."

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# Math Olympiad Solver

## The five things that change outcomes

1. **Strip thinking before verifying** — a verifier that sees the reasoning is
   biased toward agreement. Fresh context, cleaned proof only.
2. **"Does this prove RH?"** — if your theorem's specialization to ζ is a famous
   open problem, you have a gap. Most reliable red flag.
3. **Short proof → extract the general lemma** — try 2×2 counterexamples. If
   general form is false, find what's special about THIS instance.
4. **Same gap twice → step back** — the case split may be obscuring a unified
   argument. Three lines sometimes does what twelve pages couldn't.
5. **Say "no confident solution"** — wrong-and-confident is worse than honest
   abstain.