math-olympiad

To prove olympiad inequalities with rigor, this Skill drafts a full solution and then runs fresh-context adversarial verification using pattern-specific failure modes to catch reasoning holes. It outputs a calibrated confidence score or abstains if verification fails.

Yes, you can check an alleged proof for IMO, Putnam, or USAMO problems. The Skill applies adversarial reasoning and counterexample search in a fresh context to attack the provided proof and identify any logical holes or invalid steps.

Adversarial verification for competition math proofs is a process that attacks a drafted solution using pattern-armed checks for specific failure modes. It reduces the risk of subtle but fatal reasoning errors by independently testing the proof's logic in a fresh context.

To find a counterexample to a competition math statement, the Skill applies pure-reasoning workflow constraints and adversarial checks. If it successfully refutes the statement, it outputs the counterexample; otherwise, it provides a verified full proof or a calibrated abstention.

Yes, when LaTeX is available and adversarial verification passes, the approach formats the verified full proof into a clean LaTeX output. This ensures the final competition math solution is both rigorous and properly typeset.

When a competition math proof cannot be confidently verified, the Skill outputs a calibrated "no confident solution" abstention. This prevents wrong-and-confident answers by ensuring only fully verified proofs are returned to the user.