/math-olympiad

name: math-olympiad
description:
  "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."
version: 0.1.0

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.

---

**Tool policy**: Solvers and verifiers use THINKING ONLY in the tight-budget workflow. Competition math is reasoning. Computation is for deep mode (§6c), and even then bounded — a recurrence that's doubly-exponential can't be computed past n~30, work mod 2^m instead.

---

When to use which approach

| Problem | Approach | Verification | | ---------------------------------------------------- | ------------------------------------------------------------------------------ | ------------------------- | | AIME numeric answer | Best-of-N → majority vote | Answer check only | | Olympiad proof (IMO/Putnam/USAMO) | Full workflow below | 5-pass adversarial | | "Is this proof correct?" | Skip to verification (step 4) | Adversarial + spec-gaming | | **Full problem set** (e.g. all 6 from a competition) | Sequential: one full workflow per problem, collect results, compile single PDF | Per-problem adversarial |

**Batch in one Workflow**: Set `opts.label` on every `agent()` call to include the problem ID (e.g., `label: "P3:solver:2"`). Without labels, 36 results come back with no problem association. Run problems in parallel — the label is what matters, not ordering.

For a full problem set

Launch one solver workflow per problem (same VERBATIM prompt, different statement). Run them in parallel. When all return, run adversarial verification per problem. Problems that pass get their proof in the PDF; problems that abstain get "No confident solution" with partial notes.

Don't try to solve all N problems in one agent's context — each problem needs its own thinking budget and its own fresh-context verifier. The composition is mechanical: collect the per-problem outputs, fill in LaTeX sections, compile once. | "Simplify this proof" | Skip to presentation (step 8) | — |

---

The Workflow

1. Interpretation check (30 seconds, catches 50/63 of one class of errors)

Before solving anything, identify the interpretation.

> Read the problem statement. List 2-3 ways it could be interpreted. For each: > is this reading TRIVIAL? If one reading makes the problem easy and another > makes it hard, the hard one is almost certainly intended. State which > interpretation you're solving and WHY you believe it's the intended one.

The Aletheia case study found 50 of 63 "technically correct" solutions were for the wrong interpretation. Olympiad problems often have a trap easy reading.

2. Generate candidates with internal refinement (parallel, thinking only)

Launch 8-12 attempt agents in parallel. **Each agent internally iterates** — solve → self-improve → self-verify → correct → repeat. This is the Yang-Huang structure that achieves 85.7% on IMO: one-shot solving isn't enough; per-attempt refinement matters.

**The Agent tool cannot enforce tool restriction.** Subagents get the full tool set. The only mechanism is the prompt. Use this prompt VERBATIM — do not summarize, do not synthesize your own:

NO COMPUTATION. Do not use Bash, Python, WebSearch, Read, Write, or any tool that runs code or fetches data. Numerical verification is not a proof step. "I computed n=1..10 and the pattern holds" is not a proof.

(If your agent harness requires a StructuredOutput or similar return-mechanism tool call, that is NOT a computation tool — call it to return your answer. The restriction is on tools that DO work, not tools that REPORT work.)

Your internal process (iterate until done):
- Solve: Complete rigorous solution.
- Self-improve: Reread. Fix gaps before a grader sees it.
- Self-verify: Strict grader mode. Every step justified?
- Correct: Fix and re-verify. Up to 5 rounds.
- Stop: Self-verify passes twice clean, OR 5 rounds, OR approach fundamentally wrong.

A correct answer from flawed reasoning is a failure. If incomplete, say so honestly. Never hide gaps.

PROBLEM: <insert the problem statement here>
ANGLE: <insert one starting angle here>

The first two paragraphs are load-bearing. A session that writes its own prompt and omits them will produce subagents that grind Python for 30 iterations and confidently get wrong answers — a patt