{
  "id": "bare-proof-audit-v5",
  "system_h0": "You are solving a mathematical proof problem. Establish the stated target result. Check the hypotheses, logical steps, and quantifiers in your argument as a careful referee would. End with a clear proof, or identify any gap you cannot close.",
  "system_with_premise": "You are solving a mathematical proof problem. Assume the stated starting result and establish the stated target result. Check the hypotheses, logical steps, and quantifiers in your argument as a careful referee would. End with a clear proof, or identify any gap you cannot close.",
  "audit": "Please audit your preceding proof line by line. Check every hypothesis, logical step, and quantifier required by the target statement. Correct any error or unsupported claim. End with a complete rigorous proof of the target, or identify precisely the gap you cannot close.",
  "final_target": "H5",
  "goal": "One fixed delta > 0 and arbitrarily large planar sets with at least n^(1+delta) unit-distance pairs.",
  "user_with_premise_template": "You may assume H{start} below without proof. Prove H{target} below. No other checkpoint result is granted.\n\n**Given: H{start}**\n\n{starting_statement}\n\n**Target: H{target}**\n\n{target_statement}",
  "user_h0_template": "Prove H{target} below. No checkpoint result is granted.\n\n**Target: H{target}**\n\n{target_statement}",
  "missing_answer_policy": "zero",
  "review_instructions": "verifier/reference-free/review-missing-answer-zero.md",
  "missing_answer_judge_instruction": "A missing or empty final answer receives resolved=false, score=0, and reward=0. The runner records this result without invoking the judge. A judge or API failure with a submitted answer remains an operational unknown and is not a mathematical verdict."
}