{
  "schema": "diskcover-public-problem-v2",
  "problem_id": "diskcover-n12",
  "n": 12,
  "title": "单位圆盘的 12 圆最优覆盖问题",
  "language": "zh-CN",
  "page_url": "n12.zh.html",
  "prompt_url": "prompts/n12.md",
  "alternate_pages": {
    "zh-CN": "n12.zh.html",
    "en": "n12.html"
  },
  "protocol": "diskcover-minpoly-v1",
  "protocol_url": "protocol.txt",
  "fingerprint_script_url": "diskcover_answer.py",
  "report_prompt_url": "report-prompt.txt",
  "reference_sha256": "35d604a5ea1b1fe5c52c30337743c1a8142b69827023284f9597e1ca9cb8f947",
  "reference_status": "published",
  "reference_note": "参考指纹已发布；指纹匹配不等于证明通过。",
  "reference_time_seconds": "21600",
  "scoring_version": "diskcover-log-score-v1",
  "score_formula": "round_half_up(200 + 100 * log2(reference_time_seconds / elapsed_seconds))",
  "score_rounding": "decimal_ROUND_HALF_UP_integer",
  "score_direction": "higher_is_better",
  "time_limit_seconds": "43200",
  "deadline_inclusive": true,
  "timeout_score": "0",
  "late_completion_score": "0",
  "not_tested_score": null,
  "scoring_rule": "本题时限为12小时（43200秒）。超过12小时仍未取得符合本题验收要求的有效结果，计0分；超时后完成仍计0分。12小时内完成（含截止时刻），按 S = round(200 + 100 × log₂(参考用时 / 实际用时))计分，越高越好。未测试不计作0分。",
  "scoring_status": "demo_reference_not_frozen",
  "public_record_submissions": "closed",
  "answer_disclosure": "fingerprint_only",
  "configuration": {
    "image": "assets/n12.svg",
    "caption": "覆盖示意图：非最优构型，仅作展示"
  },
  "records_note": "2026-10-01 的两次事后测试使用公开已有证明，来源见报告；发布者已明确仅禁止测试前已有本地资料，本次新下载、新生成文件允许读取。2026-10-03（UTC）的 DeepSeek 单次测试提交了错误最优值，经精确更优覆盖反例判零分。各次测试非从零自主发现能力认证，非正式排名。",
  "records": [
    {
      "model": "gpt-6 astra/max",
      "model_id": "gpt-6-astra",
      "reasoning_effort": "max",
      "elapsed_seconds": "3175.402",
      "score": "477",
      "runs": 1,
      "status": "reported",
      "timing_scope": "first_complete_problem_received_to_final_answer_fully_recorded",
      "model_identity_status": "verified_original_solver_turn_context",
      "verification_status": "reference_hash_match_and_historical_exact_replays; resource_rule_clarified; no_external_proof_review",
      "report_url": "record-n12-astra-20261001.zh.html",
      "report_url_en": "record-n12-astra-20261001.html",
      "test_date_utc": "2026-10-01",
      "score_scope": "benchmark_score",
      "acceptance_status": "accepted_on_reviewed_evidence_under_clarified_resource_rule",
      "within_time_limit": true,
      "score_source": "elapsed_time_formula"
    },
    {
      "model": "gpt-6.1 sol/max",
      "model_id": "gpt-6.1-sol",
      "reasoning_effort": "max",
      "elapsed_seconds": "5457.272",
      "score": "398",
      "runs": 1,
      "status": "historical",
      "timing_scope": "full_original_prompt_receipt_to_final_mathematical_delivery_response",
      "model_identity_status": "conversation_configuration_not_independent_server_authentication",
      "verification_status": "reference_hash_match_and_historical_exact_replays; resource_rule_clarified; no_external_proof_review",
      "score_scope": "benchmark_score",
      "acceptance_status": "accepted_on_reviewed_evidence_under_clarified_resource_rule",
      "report_url": "record-n12-sol-20261001.zh.html",
      "report_url_en": "record-n12-sol-20261001.html",
      "test_date_utc": "2026-10-01",
      "within_time_limit": true,
      "score_source": "elapsed_time_formula"
    },
    {
      "model": "deepseek-v4-pro/max",
      "model_id": "deepseek-v4-pro",
      "reasoning_effort": "max",
      "elapsed_seconds": "8015.612",
      "score": "0",
      "runs": 1,
      "status": "not_completed",
      "timing_scope": "first_goal_create_to_final_substantive_assistant_message_includes_recovery_and_blocked_waiting",
      "model_identity_status": "verified_original_request_headers",
      "verification_status": "independent_exact_strictly_better_continuous_cover; optimum_refuted",
      "score_scope": "benchmark_failure_score",
      "acceptance_status": "failed_incorrect_optimal_radius_exact_better_cover",
      "report_url": "record-n12-deepseek-v4-pro-max-20261002.zh.html",
      "report_url_en": "record-n12-deepseek-v4-pro-max-20261002.html",
      "test_date_utc": "2026-10-03",
      "within_time_limit": true,
      "score_source": "not_completed_zero"
    }
  ],
  "best_recorded_run": {
    "run_id": "joint-v15-overlap-gmp-24-n12",
    "elapsed_seconds": "37.49846543500001",
    "score": "1117",
    "logical_cores": 24,
    "proof_engine": "DGC v62-G",
    "minpoly_engine": "MinPoly v15",
    "sha256": "35d604a5ea1b1fe5c52c30337743c1a8142b69827023284f9597e1ca9cb8f947",
    "hash_matches": true,
    "score_scope": "benchmark_score",
    "label": "DGC v62-G · MinPoly v15",
    "report_url": "record-n12-algorithm-run-20261001.zh.html",
    "report_url_en": "record-n12-algorithm-run-20261001.html",
    "note": "",
    "note_en": ""
  }
}