{
  "schema": "diskcover-public-problem-v2",
  "problem_id": "diskcover-n15",
  "n": 15,
  "title": "Optimal Covering of the Unit Disk with 15 Disks",
  "language": "en",
  "page_url": "n15.html",
  "prompt_url": "prompts/n15.en.md",
  "alternate_pages": {
    "zh-CN": "n15.zh.html",
    "en": "n15.html"
  },
  "protocol": "diskcover-minpoly-v1",
  "protocol_url": "protocol.en.txt",
  "fingerprint_script_url": "diskcover_answer.py",
  "report_prompt_url": "report-prompt.en.txt",
  "reference_sha256": "27d58d1f801408165315e66d2d9fcc823b76aa5531581432c84c31dbbe163335",
  "reference_status": "published",
  "reference_note": "Reference fingerprint published; a match does not verify a proof.",
  "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": "Time limit: 12 hours (43200 seconds). If no valid result meeting this problem's acceptance criteria is obtained within 12 hours, the score is 0; completion after the deadline also scores 0. Completion within 12 hours, including the deadline, is scored as S = round(200 + 100 × log₂(reference time / elapsed time)); higher is better. An untested run is not scored as 0.",
  "scoring_status": "demo_reference_not_frozen",
  "public_record_submissions": "closed",
  "answer_disclosure": "fingerprint_only",
  "configuration": {
    "image": "assets/n15.svg",
    "caption": "Covering illustration: non-optimal configuration, display only"
  },
  "records_note": "This extended 24-hour test was incomplete and scores 0. The 24h label is a limit, not a completion time. No same-condition formal ranking.",
  "records": [
    {
      "model": "gpt-6.1 sol/max",
      "model_id": "gpt-6.1-sol",
      "reasoning_effort": "max",
      "model_identity_status": "verified_original_model_id; public_effort_max_as_clarified_by_user",
      "elapsed_seconds": null,
      "runs": 1,
      "status": "not_completed",
      "timing_scope": "24-hour extended-test limit; not a successful completion time",
      "score_scope": "incomplete_zero; extended_test_not_same_condition_ranking",
      "report_url": "record-n15-sol-24h-20261024.html",
      "report_url_en": "record-n15-sol-24h-20261024.html",
      "test_date_utc": "2026-10-24",
      "time_limit_label": "24h",
      "score": "0",
      "acceptance_status": "incomplete",
      "verification_status": "minimal_polynomial_missing; external_geometry_records_saved; no_new_math_replay",
      "within_time_limit": null,
      "score_source": "not_completed_zero"
    }
  ]
}