{
  "schema": "diskcover-public-problem-v2",
  "problem_id": "diskcover-n19",
  "n": 19,
  "title": "Optimal Covering of the Unit Disk with 19 Disks",
  "language": "en",
  "page_url": "n19.html",
  "prompt_url": "prompts/n19.en.md",
  "alternate_pages": {
    "zh-CN": "n19.zh.html",
    "en": "n19.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": "7ead184fdc6f594d545b571276c44c23a261d93d22f69d78e799f69d6b684e7a",
  "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/n19.svg",
    "caption": "Covering illustration: non-optimal configuration, display only"
  },
  "records_note": null,
  "records": [],
  "best_recorded_run": {
    "run_id": "joint-v15-overlap-gmp-24-n19",
    "elapsed_seconds": "36.0441555",
    "score": "1123",
    "logical_cores": 24,
    "proof_engine": "DGC v62-G",
    "minpoly_engine": "MinPoly v15",
    "sha256": "7ead184fdc6f594d545b571276c44c23a261d93d22f69d78e799f69d6b684e7a",
    "hash_matches": true,
    "score_scope": "benchmark_score",
    "label": "DGC v62-G · MinPoly v15",
    "report_url": "record-n19-algorithm-run-20261001.html",
    "report_url_en": "record-n19-algorithm-run-20261001.html",
    "note": "",
    "note_en": ""
  }
}