Upload PROMPTS.md

PROMPTS.md

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+# RoJBMO Prompt Templates
+
+The exact prompt templates used in the RoJBMO evaluation pipeline: solution
+generation, pointwise judging, and pairwise judging. Referenced from the
+paper ("*RoJBMO: Evaluating Large Language Models on Junior Balkan
+Mathematical Olympiad Problems*", SYNASC 2026), Section IV-C.
+
+Placeholders in `{curly braces}` are filled in per problem at runtime; the
+rest of the text is sent to the model unmodified.
+
+---
+
+## 1. Generation prompt
+
+Elicits a candidate solution from each generation model.
+
+```text
+You are an expert mathematician participating in the Junior Balkan Mathematical Olympiad (JBMO).
+
+Solve the following {domain} problem completely, showing all steps clearly.
+Write your solution in a clean, rigorous mathematical style.
+
+PROBLEM ({year} · {domain}):
+{statement}
+
+Provide a complete, step-by-step solution:
+```
+
+- `{domain}` — one of Algebra / Combinatorics / Geometry / Number Theory.
+- `{year}` — the competition year of the source problem.
+- `{statement}` — the problem statement, LaTeX, English.
+
+Sampling: temperature 0.2, single user-turn message, no system prompt.
+
+---
+
+## 2. Pointwise judge prompt
+
+Scores a single candidate solution against the reference solution across
+five dimensions.
+
+```text
+You are an expert JBMO (Junior Balkan Mathematical Olympiad) grader.
+Evaluate the candidate solution below against the reference solution.
+
+═══ PROBLEM ({year} · {domain}) ═══
+{statement}
+
+═══ REFERENCE SOLUTION ═══
+{reference_solution}
+
+═══ CANDIDATE SOLUTION (by {model_label}) ═══
+{candidate_solution}
+
+═══ SCORING INSTRUCTIONS ═══
+Score each dimension 1–10. Be strict: a single unjustified logical step or gap in correctness
+should cap that dimension at ≤ 6. Only award 9–10 when the solution is virtually flawless.
+
+Dimensions:
+• correctness (1–10): Every logical step valid, no hidden assumptions, conclusion fully justified.
+• clarity (1–10): Notation clean, argument easy to follow, well-organised.
+• completeness (1–10): All cases covered, no steps skipped, final answer clearly stated.
+• elegance (1–10): Approach is clean, insightful, or avoids unnecessary computation.
+• overall (1–10): Holistic quality — not necessarily the average of the above.
+
+Respond ONLY with valid JSON (no markdown fences, no extra text):
+{
+  "correctness": <int 1-10>,
+  "clarity": <int 1-10>,
+  "completeness": <int 1-10>,
+  "elegance": <int 1-10>,
+  "overall": <int 1-10>,
+  "reasoning": "<3-4 sentences: key strengths, key flaws, and whether the solution is correct>"
+}/no_think
+```
+
+- `{model_label}` — human-readable name of the model being judged (excluded
+  from the judge's own generation pool to avoid self-preference).
+- The trailing `/no_think` suppresses extended-thinking preambles on models
+  that support the convention, so the response stays pure JSON.
+
+Judge: GPT-4o, temperature 0.0, single user-turn message.
+
+---
+
+## 3. Pairwise judge prompt
+
+Directly compares two candidate solutions on the same problem, using a
+four-class verdict scheme. Each pair is judged in both orders (A/B and B/A)
+to measure position bias.
+
+```text
+You are an expert JBMO (Junior Balkan Mathematical Olympiad) grader.
+Two candidate solutions are provided below. Determine whether each is mathematically correct.
+
+═══ PROBLEM ({year} · {domain}) ═══
+{statement}
+
+═══ REFERENCE SOLUTION ═══
+{reference_solution}
+
+═══ SOLUTION A (by {label_a}) ═══
+{solution_a}
+
+═══ SOLUTION B (by {label_b}) ═══
+{solution_b}
+
+═══ INSTRUCTIONS ═══
+Classify into exactly one of four cases:
+• "both_correct"    — both solutions reach the correct answer by a valid mathematical argument
+• "A_correct"       — only Solution A is mathematically correct
+• "B_correct"       — only Solution B is mathematically correct
+• "neither_correct" — neither solution is correct
+
+Respond ONLY with valid JSON (no markdown fences, no extra text):
+{
+  "verdict": "<both_correct|A_correct|B_correct|neither_correct>",
+  "reasoning": "<2-3 sentences explaining which solution is correct and why>"
+}/no_think
+```
+
+Judge: same as the pointwise prompt above.