{
  "schema": "diskcover-public-problem-v2",
  "problem_id": "diskcover-n13",
  "n": 13,
  "title": "Optimal Covering of the Unit Disk with 13 Disks",
  "language": "en",
  "page_url": "n13.html",
  "prompt_url": "prompts/n13.en.md",
  "alternate_pages": {
    "zh-CN": "n13.zh.html",
    "en": "n13.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": null,
  "reference_status": "not_published",
  "reference_note": "Reference answer unknown; no reference fingerprint has been published.",
  "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/n13.svg",
    "caption": "Covering illustration: non-optimal configuration, display only"
  },
  "records_note": "Both incomplete runs scored 0: no complete valid result within 12 hours. Their own original-Goal metadata identifies gpt-6 astra/max and gpt-6.1 sol/max respectively. Each report records its own sources, tools, stages and timing; the Astra report is revised to the n=11 Astra format. No formal ranking.",
  "records": [
    {
      "model": "gpt-6 astra/max",
      "model_id": "gpt-6-astra",
      "reasoning_effort": "max",
      "elapsed_seconds": "43200",
      "score": "0",
      "runs": 1,
      "status": "not_completed",
      "timing_scope": "fixed_deadline_observation_window_not_completion_time",
      "model_identity_status": "verified_from_original_thread_runtime_metadata",
      "verification_status": "no_complete_valid_result_by_deadline; no_answer_fingerprint; no_new_mathematical_replay",
      "report_url": "record-n13-codex-20261001.html",
      "report_url_en": "record-n13-codex-20261001.html",
      "test_date_utc": "2026-10-01",
      "score_scope": "benchmark_failure_score",
      "acceptance_status": "failed_no_complete_valid_result_by_deadline",
      "within_time_limit": true,
      "score_source": "not_completed_zero"
    },
    {
      "model": "gpt-6.1 sol/max",
      "model_id": "gpt-6.1-sol",
      "reasoning_effort": "max",
      "elapsed_seconds": "43200",
      "score": "0",
      "runs": 1,
      "status": "not_completed",
      "timing_scope": "fixed_deadline_observation_window_not_completion_time",
      "model_identity_status": "verified_original_solver_turn_context",
      "verification_status": "incomplete_at_deadline; original_partial_exact_checks; no_answer_fingerprint; no_new_math_replay",
      "report_url": "record-n13-sol-20261001.html",
      "report_url_en": "record-n13-sol-20261001.html",
      "test_date_utc": "2026-10-01",
      "score_scope": "benchmark_failure_score",
      "acceptance_status": "failed_no_complete_valid_result_by_deadline",
      "within_time_limit": true,
      "score_source": "not_completed_zero"
    },
    {
      "model": "gpt-6.1 sol/max",
      "model_id": "gpt-6.1-sol",
      "reasoning_effort": "max",
      "elapsed_seconds": null,
      "score": "0",
      "runs": 1,
      "status": "not_completed",
      "timing_scope": "Extended 48h Goal research; scoring elapsed time is unspecified; separate cumulative Goal and natural time in report.",
      "model_identity_status": "verified_original_model_id; intended_public_effort_max_as_clarified_by_user",
      "verification_status": "minimal_polynomial_incomplete; original_geometry_records_saved; no_mathematical_replay_during_publication",
      "report_url": "record-n13-sol-48h-20261016.html",
      "report_url_en": "record-n13-sol-48h-20261016.html",
      "test_date_utc": "2026-10-16",
      "score_scope": "retrospective_incomplete_zero; extended_research_not_same_condition_ranking",
      "acceptance_status": "incomplete_paused_at_user_48h_goal_limit",
      "time_limit_label": "48h",
      "within_time_limit": null,
      "score_source": "not_completed_zero"
    }
  ]
}