{
  "schema": "xmse-forensic-collusion-roc/v2",
  "generated_at": "2026-08-20T16:11:18.183082+00:00",
  "definitions": {
    "correct_accusation": "Z를 넘은 지목 집합이 비어 있지 않고, 지목된 사람이 모두 공모자이며, 무고자가 한 명도 포함되지 않은 시행.",
    "false_accusation": "Z를 넘은 지목 집합에 공모자가 아닌 사람(무고자)이 한 명이라도 포함된 시행.",
    "no_accusation": "Z를 넘는 사람이 한 명도 없어 아무도 지목하지 않은 시행.",
    "colluder_caught_any": "지목 집합에 공모자가 한 명이라도 포함된 시행. 무고자 동반 지목과 겹칠 수 있음.",
    "false_accusation_scope": "trial_any_innocent",
    "false_accusation_per_innocent": 0.0112,
    "false_accusation_per_innocent_source": "scripts/ops/test_tardos_skoric.py"
  },
  "false_accusation_scope": "trial_any_innocent",
  "false_accusation_per_innocent": 0.0112,
  "false_accusation_per_innocent_source": "scripts/ops/test_tardos_skoric.py",
  "z_scope": "per_innocent_per_cover",
  "pixel_fixtures_used": false,
  "familywise_bound_formula": "100*(1-(1-0.0112)^(n_users-1))",
  "familywise_bound_pct_by_n_users": {
    "32": 29.5,
    "64": 50.8
  },
  "familywise_bound_violations": [
    {
      "cell_id": "tardos-p-draw-0|n32|c2|max",
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 2,
      "attack": "max",
      "false_accusation_rate_pct": 44.0,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-0|n32|c3|mean",
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 3,
      "attack": "mean",
      "false_accusation_rate_pct": 33.7,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-0|n32|c3|max",
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 3,
      "attack": "max",
      "false_accusation_rate_pct": 38.6,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-0|n32|c3|median",
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 3,
      "attack": "median",
      "false_accusation_rate_pct": 35.2,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-0|n32|c5|mean",
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 5,
      "attack": "mean",
      "false_accusation_rate_pct": 39.6,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-0|n32|c5|median",
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 5,
      "attack": "median",
      "false_accusation_rate_pct": 38.0,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-0|n32|c10|mean",
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 10,
      "attack": "mean",
      "false_accusation_rate_pct": 33.1,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-0|n32|c10|median",
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 10,
      "attack": "median",
      "false_accusation_rate_pct": 33.4,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-0|n64|c5|min",
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "min",
      "false_accusation_rate_pct": 55.9,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-0|n64|c10|min",
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 10,
      "attack": "min",
      "false_accusation_rate_pct": 81.4,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-1|n32|c2|mean",
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "n_colluders": 2,
      "attack": "mean",
      "false_accusation_rate_pct": 30.2,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-1|n32|c3|mean",
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "n_colluders": 3,
      "attack": "mean",
      "false_accusation_rate_pct": 36.6,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-1|n32|c3|median",
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "n_colluders": 3,
      "attack": "median",
      "false_accusation_rate_pct": 36.2,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-1|n32|c5|mean",
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "n_colluders": 5,
      "attack": "mean",
      "false_accusation_rate_pct": 43.2,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-1|n32|c5|min",
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "n_colluders": 5,
      "attack": "min",
      "false_accusation_rate_pct": 37.8,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-1|n32|c5|median",
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "n_colluders": 5,
      "attack": "median",
      "false_accusation_rate_pct": 42.8,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-1|n32|c10|mean",
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "n_colluders": 10,
      "attack": "mean",
      "false_accusation_rate_pct": 44.0,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-1|n32|c10|min",
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "n_colluders": 10,
      "attack": "min",
      "false_accusation_rate_pct": 45.8,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-1|n32|c10|median",
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "n_colluders": 10,
      "attack": "median",
      "false_accusation_rate_pct": 43.6,
      "familywise_bound_pct": 29.5
    },
    {
      "cell_id": "tardos-p-draw-1|n64|c2|min",
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "n_colluders": 2,
      "attack": "min",
      "false_accusation_rate_pct": 51.6,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-1|n64|c2|max",
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "n_colluders": 2,
      "attack": "max",
      "false_accusation_rate_pct": 64.3,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-1|n64|c3|min",
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "n_colluders": 3,
      "attack": "min",
      "false_accusation_rate_pct": 52.2,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-1|n64|c3|max",
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "n_colluders": 3,
      "attack": "max",
      "false_accusation_rate_pct": 85.2,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-1|n64|c5|min",
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "min",
      "false_accusation_rate_pct": 54.7,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-1|n64|c5|max",
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "max",
      "false_accusation_rate_pct": 93.5,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-1|n64|c10|max",
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "n_colluders": 10,
      "attack": "max",
      "false_accusation_rate_pct": 92.9,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-2|n64|c2|min",
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 2,
      "attack": "min",
      "false_accusation_rate_pct": 60.5,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-2|n64|c3|min",
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 3,
      "attack": "min",
      "false_accusation_rate_pct": 72.4,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-2|n64|c3|max",
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 3,
      "attack": "max",
      "false_accusation_rate_pct": 51.9,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-2|n64|c5|min",
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "min",
      "false_accusation_rate_pct": 87.4,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-2|n64|c5|max",
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "max",
      "false_accusation_rate_pct": 55.3,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-2|n64|c10|min",
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 10,
      "attack": "min",
      "false_accusation_rate_pct": 94.2,
      "familywise_bound_pct": 50.8
    },
    {
      "cell_id": "tardos-p-draw-2|n64|c10|max",
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 10,
      "attack": "max",
      "false_accusation_rate_pct": 60.0,
      "familywise_bound_pct": 50.8
    }
  ],
  "monotonicity_inversions": [
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "attack": "min",
      "n_from": 1,
      "correct_from_pct": 78.9,
      "n_to": 2,
      "correct_to_pct": 90.3
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "attack": "min",
      "n_from": 2,
      "correct_from_pct": 90.3,
      "n_to": 3,
      "correct_to_pct": 93.7
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "attack": "max",
      "n_from": 2,
      "correct_from_pct": 56.0,
      "n_to": 3,
      "correct_to_pct": 61.4
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "attack": "max",
      "n_from": 3,
      "correct_from_pct": 61.4,
      "n_to": 5,
      "correct_to_pct": 73.6
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "attack": "mean",
      "n_from": 1,
      "correct_from_pct": 55.0,
      "n_to": 2,
      "correct_to_pct": 60.5
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "attack": "mean",
      "n_from": 2,
      "correct_from_pct": 60.5,
      "n_to": 3,
      "correct_to_pct": 67.8
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "attack": "min",
      "n_from": 1,
      "correct_from_pct": 53.1,
      "n_to": 2,
      "correct_to_pct": 65.9
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "attack": "max",
      "n_from": 1,
      "correct_from_pct": 57.4,
      "n_to": 2,
      "correct_to_pct": 64.4
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "attack": "max",
      "n_from": 2,
      "correct_from_pct": 64.4,
      "n_to": 3,
      "correct_to_pct": 65.2
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "attack": "median",
      "n_from": 1,
      "correct_from_pct": 55.2,
      "n_to": 2,
      "correct_to_pct": 64.6
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "attack": "median",
      "n_from": 2,
      "correct_from_pct": 64.6,
      "n_to": 3,
      "correct_to_pct": 68.0
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "attack": "median",
      "n_from": 3,
      "correct_from_pct": 68.0,
      "n_to": 5,
      "correct_to_pct": 69.9
    },
    {
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "attack": "min",
      "n_from": 1,
      "correct_from_pct": 71.8,
      "n_to": 2,
      "correct_to_pct": 73.7
    },
    {
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "attack": "max",
      "n_from": 1,
      "correct_from_pct": 71.2,
      "n_to": 2,
      "correct_to_pct": 76.5
    },
    {
      "cover_id": "tardos-p-draw-1",
      "n_users": 32,
      "attack": "max",
      "n_from": 2,
      "correct_from_pct": 76.5,
      "n_to": 3,
      "correct_to_pct": 83.0
    },
    {
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "attack": "mean",
      "n_from": 2,
      "correct_from_pct": 53.6,
      "n_to": 3,
      "correct_to_pct": 61.6
    },
    {
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "attack": "mean",
      "n_from": 3,
      "correct_from_pct": 61.6,
      "n_to": 5,
      "correct_to_pct": 70.3
    },
    {
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "attack": "max",
      "n_from": 5,
      "correct_from_pct": 6.2,
      "n_to": 10,
      "correct_to_pct": 6.9
    },
    {
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "attack": "median",
      "n_from": 2,
      "correct_from_pct": 51.7,
      "n_to": 3,
      "correct_to_pct": 64.1
    },
    {
      "cover_id": "tardos-p-draw-1",
      "n_users": 64,
      "attack": "median",
      "n_from": 3,
      "correct_from_pct": 64.1,
      "n_to": 5,
      "correct_to_pct": 69.5
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "attack": "mean",
      "n_from": 1,
      "correct_from_pct": 74.4,
      "n_to": 2,
      "correct_to_pct": 77.5
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "attack": "mean",
      "n_from": 2,
      "correct_from_pct": 77.5,
      "n_to": 3,
      "correct_to_pct": 88.3
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "attack": "mean",
      "n_from": 3,
      "correct_from_pct": 88.3,
      "n_to": 5,
      "correct_to_pct": 91.8
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "attack": "min",
      "n_from": 1,
      "correct_from_pct": 77.2,
      "n_to": 2,
      "correct_to_pct": 87.2
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "attack": "min",
      "n_from": 2,
      "correct_from_pct": 87.2,
      "n_to": 3,
      "correct_to_pct": 93.3
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "attack": "max",
      "n_from": 1,
      "correct_from_pct": 76.6,
      "n_to": 2,
      "correct_to_pct": 76.7
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "attack": "max",
      "n_from": 3,
      "correct_from_pct": 76.3,
      "n_to": 5,
      "correct_to_pct": 84.5
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "attack": "median",
      "n_from": 1,
      "correct_from_pct": 73.2,
      "n_to": 2,
      "correct_to_pct": 78.0
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "attack": "median",
      "n_from": 2,
      "correct_from_pct": 78.0,
      "n_to": 3,
      "correct_to_pct": 86.0
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "attack": "median",
      "n_from": 3,
      "correct_from_pct": 86.0,
      "n_to": 5,
      "correct_to_pct": 90.9
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "attack": "mean",
      "n_from": 2,
      "correct_from_pct": 52.7,
      "n_to": 3,
      "correct_to_pct": 63.5
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "attack": "mean",
      "n_from": 3,
      "correct_from_pct": 63.5,
      "n_to": 5,
      "correct_to_pct": 65.3
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "attack": "max",
      "n_from": 1,
      "correct_from_pct": 54.2,
      "n_to": 2,
      "correct_to_pct": 56.1
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "attack": "median",
      "n_from": 2,
      "correct_from_pct": 55.9,
      "n_to": 3,
      "correct_to_pct": 63.7
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "attack": "median",
      "n_from": 3,
      "correct_from_pct": 63.7,
      "n_to": 5,
      "correct_to_pct": 69.6
    }
  ],
  "eta_locked_a_priori": true,
  "method_ko": "Škorić 대칭 Tardos 부호 + 무고자 점수 (1-η) 분위수 임계 Z. Z 초과자만 지목. argmax 강제 지목 없음. 법정 포렌식·귀속 확정 아님.",
  "v1_archive": "/benchmarks/archive/forensic-collusion-roc-v1-naive-argmax.json",
  "v1_live_untouched": "/benchmarks/forensic-collusion-roc.json",
  "ssot": "data/registry/xmse-forensic-tardos-ssot.json",
  "eta_false_accusation_per_innocent": 0.01,
  "payload_bits": 256,
  "payload_evidence": [
    {
      "path": "apps/c2pa/public/benchmarks/s2-pilot-videoseal-msgs.json",
      "field": "n",
      "value": 256,
      "bits_len": 256
    },
    {
      "path": "scripts/ops/xmse-videoseal-embed-image.py",
      "slice": "preds[1:257]",
      "len": 256
    }
  ],
  "capacity_gap": [
    {
      "n_users": 32,
      "eta": 0.01,
      "m_needed_for_c0_3": 717,
      "bits_available": 256,
      "c0_max_at_available_bits": 1.7927,
      "guarantee_ko": "n=32·η=0.01에서 c0=3에 필요한 m=717비트, 가용 B=256비트. 역산 c0_max≈1.793. 이 값을 넘는 공모 규모는 보증 밖."
    },
    {
      "n_users": 64,
      "eta": 0.01,
      "m_needed_for_c0_3": 779,
      "bits_available": 256,
      "c0_max_at_available_bits": 1.7204,
      "guarantee_ko": "n=64·η=0.01에서 c0=3에 필요한 m=779비트, 가용 B=256비트. 역산 c0_max≈1.720. 이 값을 넘는 공모 규모는 보증 밖."
    }
  ],
  "trials_per_cell": 1000,
  "covers": [
    "tardos-p-draw-0",
    "tardos-p-draw-1",
    "tardos-p-draw-2"
  ],
  "cover_note_ko": "픽셀 픽스처 3장이 이 체크아웃에 없어, 표지 대신 독립 arcsine p-벡터 3회 추첨을 사용한다. 부호 계층 공모는 표지 픽셀을 쓰지 않는다.",
  "n_users_conditions": [
    32,
    64
  ],
  "n_colluders_conditions": [
    1,
    2,
    3,
    5,
    10
  ],
  "attacks": [
    "mean",
    "min",
    "max",
    "median"
  ],
  "axis_status_ko": "해당없음 — 오늘은 확인 승격 없음",
  "argmax_forced_accusations_total": 0,
  "cells": [
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 1,
      "attack": "mean",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.534236,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": 0.602382184021688,
        "innocent_std": 14.70617060191329
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 779,
        "trials": 1000,
        "rate_pct": 77.9,
        "ci95_wilson_low_pct": 75.2242,
        "ci95_wilson_high_pct": 80.3622,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 221,
        "trials": 1000,
        "rate_pct": 22.1,
        "ci95_wilson_low_pct": 19.6378,
        "ci95_wilson_high_pct": 24.7758,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 1.247,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": true,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 1,
      "attack": "min",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.534236,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": 0.602382184021688,
        "innocent_std": 14.70617060191329
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 789,
        "trials": 1000,
        "rate_pct": 78.9,
        "ci95_wilson_low_pct": 76.2629,
        "ci95_wilson_high_pct": 81.3159,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 211,
        "trials": 1000,
        "rate_pct": 21.1,
        "ci95_wilson_low_pct": 18.6841,
        "ci95_wilson_high_pct": 23.7371,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 1.236,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": true,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 1,
      "attack": "max",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.534236,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": 0.602382184021688,
        "innocent_std": 14.70617060191329
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 798,
        "trials": 1000,
        "rate_pct": 79.8,
        "ci95_wilson_low_pct": 77.1996,
        "ci95_wilson_high_pct": 82.1723,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 202,
        "trials": 1000,
        "rate_pct": 20.2,
        "ci95_wilson_low_pct": 17.8277,
        "ci95_wilson_high_pct": 22.8004,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 1.235,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": true,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 1,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.534236,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": 0.602382184021688,
        "innocent_std": 14.70617060191329
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 795,
        "trials": 1000,
        "rate_pct": 79.5,
        "ci95_wilson_low_pct": 76.8872,
        "ci95_wilson_high_pct": 81.887,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 205,
        "trials": 1000,
        "rate_pct": 20.5,
        "ci95_wilson_low_pct": 18.113,
        "ci95_wilson_high_pct": 23.1128,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 1.233,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": true,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 2,
      "attack": "mean",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.534236,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": 0.602382184021688,
        "innocent_std": 14.70617060191329
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 721,
        "trials": 1000,
        "rate_pct": 72.1,
        "ci95_wilson_low_pct": 69.2396,
        "ci95_wilson_high_pct": 74.7913,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 279,
        "trials": 1000,
        "rate_pct": 27.9,
        "ci95_wilson_low_pct": 25.2087,
        "ci95_wilson_high_pct": 30.7604,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.316,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 2,
      "attack": "min",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.534236,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": 0.602382184021688,
        "innocent_std": 14.70617060191329
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 903,
        "trials": 1000,
        "rate_pct": 90.3,
        "ci95_wilson_low_pct": 88.3084,
        "ci95_wilson_high_pct": 91.9831,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 97,
        "trials": 1000,
        "rate_pct": 9.7,
        "ci95_wilson_low_pct": 8.0169,
        "ci95_wilson_high_pct": 11.6916,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.102,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 2,
      "attack": "max",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.534236,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": 0.602382184021688,
        "innocent_std": 14.70617060191329
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 560,
        "trials": 1000,
        "rate_pct": 56.0,
        "ci95_wilson_low_pct": 52.9062,
        "ci95_wilson_high_pct": 59.0479,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 440,
        "trials": 1000,
        "rate_pct": 44.0,
        "ci95_wilson_low_pct": 40.9521,
        "ci95_wilson_high_pct": 47.0938,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.506,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": false,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": false
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 2,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.534236,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": 0.602382184021688,
        "innocent_std": 14.70617060191329
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 728,
        "trials": 1000,
        "rate_pct": 72.8,
        "ci95_wilson_low_pct": 69.9586,
        "ci95_wilson_high_pct": 75.4669,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 272,
        "trials": 1000,
        "rate_pct": 27.2,
        "ci95_wilson_low_pct": 24.5331,
        "ci95_wilson_high_pct": 30.0414,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.305,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 32,
      "n_colluders": 3,
      "attack": "mean",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.534236,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": 0.602382184021688,
        "innocent_std": 14.70617060191329
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 663,
        "trials": 1000,
        "rate_pct": 66.3,
        "ci95_wilson_low_pct": 63.3128,
        "ci95_wilson_high_pct": 69.1624,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 337,
        "trials": 1000,
        "rate_pct": 33.7,
        "ci95_wilson_low_pct": 30.8376,
        "ci95_wilson_high_pct": 36.6872,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.055,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": false,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": false
    },
    {
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      "n_colluders": 3,
      "attack": "min",
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      "eta": 0.01,
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      "colluder_caught_any": {
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        "ci95_wilson_high_pct": 100.0,
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      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
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      "z_scope": "per_innocent_per_cover",
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      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
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      "within_guaranteed_c0": false,
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        "ci95_wilson_high_pct": 42.6655,
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        "ci95_wilson_low_pct": 1.2984,
        "ci95_wilson_high_pct": 3.069,
        "rule_of_three_upper_pct": null
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      "colluder_caught_any": {
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        "rate_pct": 96.3,
        "ci95_wilson_low_pct": 94.9417,
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      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
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    },
    {
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      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
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        "ci95_wilson_low_pct": 90.0442,
        "ci95_wilson_high_pct": 93.4351,
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        "ci95_wilson_low_pct": 6.2048,
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      "colluder_caught_any": {
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      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
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      "familywise_bound_union_pct": 31.0,
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    },
    {
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      "argmax_forced_accusations": 0,
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        "ci95_wilson_low_pct": 70.7813,
        "ci95_wilson_high_pct": 76.238,
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        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
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        "ci95_wilson_low_pct": 2.6961,
        "ci95_wilson_high_pct": 5.0583,
        "rule_of_three_upper_pct": null
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      "colluder_caught_any": {
        "count": 948,
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        "ci95_wilson_low_pct": 93.2444,
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      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
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      "familywise_bound_union_pct": 31.0,
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      "within_union_bound": true
    },
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        "ci95_wilson_high_pct": 63.5825,
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        "ci95_wilson_high_pct": 65.4474,
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    },
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        "ci95_wilson_low_pct": 63.5163,
        "ci95_wilson_high_pct": 69.3574,
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        "ci95_wilson_low_pct": 7.5614,
        "ci95_wilson_high_pct": 11.1509,
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      "c0_max_for_this_n": 1.79,
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      "familywise_bound_independent_pct": 29.5,
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      "accusation_rule": "score_gt_z_only",
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      "false_accusation": {
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        "ci95_wilson_low_pct": 30.5452,
        "ci95_wilson_high_pct": 36.3819,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
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        "trials": 1000,
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        "ci95_wilson_low_pct": 9.7605,
        "ci95_wilson_high_pct": 13.7334,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 749,
        "trials": 1000,
        "rate_pct": 74.9,
        "ci95_wilson_low_pct": 72.1208,
        "ci95_wilson_high_pct": 77.4887,
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      "mean_accused_count": 1.5,
      "false_accusation_familywise_bound_pct": 29.5,
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      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": false
    },
    {
      "cover_id": "tardos-p-draw-0",
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      "n_colluders": 1,
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        "ci95_wilson_low_pct": 51.9032,
        "ci95_wilson_high_pct": 58.0585,
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        "trials": 1000,
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        "ci95_wilson_high_pct": 48.0968,
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      "no_accusation": {
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        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
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        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
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      },
      "mean_accused_count": 1.582,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": true,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
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      "n_colluders": 1,
      "attack": "min",
      "m_bits_used": 256,
      "eta": 0.01,
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      "z_cal": {
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      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 531,
        "trials": 1000,
        "rate_pct": 53.1,
        "ci95_wilson_low_pct": 50.001,
        "ci95_wilson_high_pct": 56.1753,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
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        "trials": 1000,
        "rate_pct": 46.9,
        "ci95_wilson_low_pct": 43.8247,
        "ci95_wilson_high_pct": 49.999,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 1.588,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": true,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 1,
      "attack": "max",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
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        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
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      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 574,
        "trials": 1000,
        "rate_pct": 57.4,
        "ci95_wilson_low_pct": 54.3125,
        "ci95_wilson_high_pct": 60.4308,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 426,
        "trials": 1000,
        "rate_pct": 42.6,
        "ci95_wilson_low_pct": 39.5692,
        "ci95_wilson_high_pct": 45.6875,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 1.529,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": true,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 1,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 552,
        "trials": 1000,
        "rate_pct": 55.2,
        "ci95_wilson_low_pct": 52.1037,
        "ci95_wilson_high_pct": 58.2565,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 448,
        "trials": 1000,
        "rate_pct": 44.8,
        "ci95_wilson_low_pct": 41.7435,
        "ci95_wilson_high_pct": 47.8963,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 1.539,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": true,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 2,
      "attack": "mean",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 605,
        "trials": 1000,
        "rate_pct": 60.5,
        "ci95_wilson_low_pct": 57.4354,
        "ci95_wilson_high_pct": 63.4842,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 395,
        "trials": 1000,
        "rate_pct": 39.5,
        "ci95_wilson_low_pct": 36.5158,
        "ci95_wilson_high_pct": 42.5646,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.486,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 2,
      "attack": "min",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
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      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 659,
        "trials": 1000,
        "rate_pct": 65.9,
        "ci95_wilson_low_pct": 62.906,
        "ci95_wilson_high_pct": 68.7723,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 341,
        "trials": 1000,
        "rate_pct": 34.1,
        "ci95_wilson_low_pct": 31.2277,
        "ci95_wilson_high_pct": 37.094,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.398,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 2,
      "attack": "max",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 644,
        "trials": 1000,
        "rate_pct": 64.4,
        "ci95_wilson_low_pct": 61.3823,
        "ci95_wilson_high_pct": 67.3074,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 356,
        "trials": 1000,
        "rate_pct": 35.6,
        "ci95_wilson_low_pct": 32.6926,
        "ci95_wilson_high_pct": 38.6177,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.436,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 2,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 646,
        "trials": 1000,
        "rate_pct": 64.6,
        "ci95_wilson_low_pct": 61.5853,
        "ci95_wilson_high_pct": 67.5029,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 354,
        "trials": 1000,
        "rate_pct": 35.4,
        "ci95_wilson_low_pct": 32.4971,
        "ci95_wilson_high_pct": 38.4147,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.447,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
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      "n_colluders": 3,
      "attack": "mean",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
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        "innocent_mean": 0.11151130435048687,
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      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
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        "trials": 1000,
        "rate_pct": 67.8,
        "ci95_wilson_low_pct": 64.8406,
        "ci95_wilson_high_pct": 70.6231,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
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        "trials": 1000,
        "rate_pct": 32.2,
        "ci95_wilson_low_pct": 29.3769,
        "ci95_wilson_high_pct": 35.1594,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.155,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 3,
      "attack": "min",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
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        "innocent_mean": 0.11151130435048687,
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      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
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        "trials": 1000,
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        "ci95_wilson_low_pct": 59.3557,
        "ci95_wilson_high_pct": 65.3494,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 376,
        "trials": 1000,
        "rate_pct": 37.6,
        "ci95_wilson_low_pct": 34.6506,
        "ci95_wilson_high_pct": 40.6443,
        "rule_of_three_upper_pct": null
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      "no_accusation": {
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        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 999,
        "trials": 1000,
        "rate_pct": 99.9,
        "ci95_wilson_low_pct": 99.4357,
        "ci95_wilson_high_pct": 99.9823,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.133,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 3,
      "attack": "max",
      "m_bits_used": 256,
      "eta": 0.01,
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      "z_cal": {
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        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
      },
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      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
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        "trials": 1000,
        "rate_pct": 65.2,
        "ci95_wilson_low_pct": 62.1946,
        "ci95_wilson_high_pct": 68.0891,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 348,
        "trials": 1000,
        "rate_pct": 34.8,
        "ci95_wilson_low_pct": 31.9109,
        "ci95_wilson_high_pct": 37.8054,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
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        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.034,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 3,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
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        "trials": 1000,
        "rate_pct": 68.0,
        "ci95_wilson_low_pct": 65.0446,
        "ci95_wilson_high_pct": 70.8176,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 319,
        "trials": 1000,
        "rate_pct": 31.9,
        "ci95_wilson_low_pct": 29.0851,
        "ci95_wilson_high_pct": 34.8534,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 1,
        "trials": 1000,
        "rate_pct": 0.1,
        "ci95_wilson_low_pct": 0.0177,
        "ci95_wilson_high_pct": 0.5643,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 999,
        "trials": 1000,
        "rate_pct": 99.9,
        "ci95_wilson_low_pct": 99.4357,
        "ci95_wilson_high_pct": 99.9823,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.157,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "mean",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 647,
        "trials": 1000,
        "rate_pct": 64.7,
        "ci95_wilson_low_pct": 61.6868,
        "ci95_wilson_high_pct": 67.6007,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 333,
        "trials": 1000,
        "rate_pct": 33.3,
        "ci95_wilson_low_pct": 30.4477,
        "ci95_wilson_high_pct": 36.2801,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
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        "trials": 1000,
        "rate_pct": 2.0,
        "ci95_wilson_low_pct": 1.2984,
        "ci95_wilson_high_pct": 3.069,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 972,
        "trials": 1000,
        "rate_pct": 97.2,
        "ci95_wilson_low_pct": 95.983,
        "ci95_wilson_high_pct": 98.0558,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.763,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "min",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
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        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 434,
        "trials": 1000,
        "rate_pct": 43.4,
        "ci95_wilson_low_pct": 40.3591,
        "ci95_wilson_high_pct": 46.4914,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 559,
        "trials": 1000,
        "rate_pct": 55.9,
        "ci95_wilson_low_pct": 52.8059,
        "ci95_wilson_high_pct": 58.949,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 7,
        "trials": 1000,
        "rate_pct": 0.7,
        "ci95_wilson_low_pct": 0.3395,
        "ci95_wilson_high_pct": 1.4378,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 980,
        "trials": 1000,
        "rate_pct": 98.0,
        "ci95_wilson_low_pct": 96.931,
        "ci95_wilson_high_pct": 98.7016,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.139,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": false,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "max",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 619,
        "trials": 1000,
        "rate_pct": 61.9,
        "ci95_wilson_low_pct": 58.8499,
        "ci95_wilson_high_pct": 64.859,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 357,
        "trials": 1000,
        "rate_pct": 35.7,
        "ci95_wilson_low_pct": 32.7903,
        "ci95_wilson_high_pct": 38.7191,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 24,
        "trials": 1000,
        "rate_pct": 2.4,
        "ci95_wilson_low_pct": 1.618,
        "ci95_wilson_high_pct": 3.5463,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 959,
        "trials": 1000,
        "rate_pct": 95.9,
        "ci95_wilson_low_pct": 94.4852,
        "ci95_wilson_high_pct": 96.9635,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.433,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 699,
        "trials": 1000,
        "rate_pct": 69.9,
        "ci95_wilson_low_pct": 66.9853,
        "ci95_wilson_high_pct": 72.6624,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 283,
        "trials": 1000,
        "rate_pct": 28.3,
        "ci95_wilson_low_pct": 25.5952,
        "ci95_wilson_high_pct": 31.1709,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 18,
        "trials": 1000,
        "rate_pct": 1.8,
        "ci95_wilson_low_pct": 1.1416,
        "ci95_wilson_high_pct": 2.8273,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 971,
        "trials": 1000,
        "rate_pct": 97.1,
        "ci95_wilson_low_pct": 95.8661,
        "ci95_wilson_high_pct": 97.9734,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.69,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 10,
      "attack": "mean",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": 0.11151130435048687,
        "innocent_std": 15.31612551305348
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 497,
        "trials": 1000,
        "rate_pct": 49.7,
        "ci95_wilson_low_pct": 46.6081,
        "ci95_wilson_high_pct": 52.7942,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 271,
        "trials": 1000,
        "rate_pct": 27.1,
        "ci95_wilson_low_pct": 24.4366,
        "ci95_wilson_high_pct": 29.9386,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 232,
        "trials": 1000,
        "rate_pct": 23.2,
        "ci95_wilson_low_pct": 20.6893,
        "ci95_wilson_high_pct": 25.9158,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 669,
        "trials": 1000,
        "rate_pct": 66.9,
        "ci95_wilson_low_pct": 63.9236,
        "ci95_wilson_high_pct": 69.7471,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 1.325,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-0",
      "n_users": 64,
      "n_colluders": 10,
      "attack": "min",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 35.449806,
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        "innocent_n": 12600,
        "innocent_mean": 0.11151130435048687,
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      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 164,
        "trials": 1000,
        "rate_pct": 16.4,
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      "colluder_caught_any": {
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        "ci95_wilson_low_pct": 99.6173,
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        "rule_of_three_upper_pct": null
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      "within_guaranteed_c0": false,
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      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
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    {
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      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
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      "within_guaranteed_c0": false,
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        "ci95_wilson_low_pct": 73.7737,
        "ci95_wilson_high_pct": 79.0235,
        "rule_of_three_upper_pct": null
      },
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        "trials": 1000,
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        "ci95_wilson_low_pct": 20.9765,
        "ci95_wilson_high_pct": 26.2263,
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        "rate_pct": 0.0,
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        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
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      "colluder_caught_any": {
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        "ci95_wilson_low_pct": 99.6173,
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      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
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      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
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    },
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      "attack": "median",
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      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
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      "colluder_caught_any": {
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      "colluder_caught_any": {
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      "colluder_caught_any": {
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      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
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      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
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      "colluder_caught_any": {
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      "colluder_caught_any": {
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        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
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      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": false
    },
    {
      "cover_id": "tardos-p-draw-1",
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      "colluder_caught_any": {
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        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
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      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
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    {
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        "ci95_wilson_low_pct": 67.3945,
        "ci95_wilson_high_pct": 73.0501,
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      },
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        "ci95_wilson_low_pct": 26.853,
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      "colluder_caught_any": {
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      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
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      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
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      },
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        "ci95_wilson_low_pct": 51.6026,
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      "colluder_caught_any": {
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        "ci95_wilson_low_pct": 95.8661,
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      "familywise_bound_union_pct": 63.0,
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    },
    {
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        "ci95_wilson_low_pct": 4.8664,
        "ci95_wilson_high_pct": 7.8688,
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        "ci95_wilson_low_pct": 91.7994,
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      "within_guaranteed_c0": false,
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      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": false
    },
    {
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      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
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        "rate_pct": 69.5,
        "ci95_wilson_low_pct": 66.5762,
        "ci95_wilson_high_pct": 72.2745,
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        "ci95_wilson_low_pct": 27.1437,
        "ci95_wilson_high_pct": 32.8101,
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      "colluder_caught_any": {
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      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-1",
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      "n_colluders": 10,
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      "eta": 0.01,
      "z": 32.591624,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": 0.3849079438501337,
        "innocent_std": 14.644799304013565
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
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        "rate_pct": 67.2,
        "ci95_wilson_low_pct": 64.2291,
        "ci95_wilson_high_pct": 70.0392,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 237,
        "trials": 1000,
        "rate_pct": 23.7,
        "ci95_wilson_low_pct": 21.1681,
        "ci95_wilson_high_pct": 26.4332,
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      "no_accusation": {
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        "ci95_wilson_low_pct": 7.4704,
        "ci95_wilson_high_pct": 11.0426,
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      "colluder_caught_any": {
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        "count": 767,
        "trials": 1000,
        "rate_pct": 76.7,
        "ci95_wilson_low_pct": 73.9807,
        "ci95_wilson_high_pct": 79.215,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 233,
        "trials": 1000,
        "rate_pct": 23.3,
        "ci95_wilson_low_pct": 20.785,
        "ci95_wilson_high_pct": 26.0193,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.257,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "n_colluders": 2,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.459386,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": -0.7715485554188566,
        "innocent_std": 17.42867355004248
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 780,
        "trials": 1000,
        "rate_pct": 78.0,
        "ci95_wilson_low_pct": 75.328,
        "ci95_wilson_high_pct": 80.4577,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 220,
        "trials": 1000,
        "rate_pct": 22.0,
        "ci95_wilson_low_pct": 19.5423,
        "ci95_wilson_high_pct": 24.672,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.24,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "n_colluders": 3,
      "attack": "mean",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.459386,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": -0.7715485554188566,
        "innocent_std": 17.42867355004248
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 883,
        "trials": 1000,
        "rate_pct": 88.3,
        "ci95_wilson_low_pct": 86.1597,
        "ci95_wilson_high_pct": 90.1472,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 116,
        "trials": 1000,
        "rate_pct": 11.6,
        "ci95_wilson_low_pct": 9.7605,
        "ci95_wilson_high_pct": 13.7334,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 1,
        "trials": 1000,
        "rate_pct": 0.1,
        "ci95_wilson_low_pct": 0.0177,
        "ci95_wilson_high_pct": 0.5643,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 999,
        "trials": 1000,
        "rate_pct": 99.9,
        "ci95_wilson_low_pct": 99.4357,
        "ci95_wilson_high_pct": 99.9823,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.776,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "n_colluders": 3,
      "attack": "min",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.459386,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": -0.7715485554188566,
        "innocent_std": 17.42867355004248
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 933,
        "trials": 1000,
        "rate_pct": 93.3,
        "ci95_wilson_low_pct": 91.5788,
        "ci95_wilson_high_pct": 94.6898,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 66,
        "trials": 1000,
        "rate_pct": 6.6,
        "ci95_wilson_low_pct": 5.2212,
        "ci95_wilson_high_pct": 8.311,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 1,
        "trials": 1000,
        "rate_pct": 0.1,
        "ci95_wilson_low_pct": 0.0177,
        "ci95_wilson_high_pct": 0.5643,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 999,
        "trials": 1000,
        "rate_pct": 99.9,
        "ci95_wilson_low_pct": 99.4357,
        "ci95_wilson_high_pct": 99.9823,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.64,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "n_colluders": 3,
      "attack": "max",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.459386,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": -0.7715485554188566,
        "innocent_std": 17.42867355004248
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 763,
        "trials": 1000,
        "rate_pct": 76.3,
        "ci95_wilson_low_pct": 73.5668,
        "ci95_wilson_high_pct": 78.8319,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 237,
        "trials": 1000,
        "rate_pct": 23.7,
        "ci95_wilson_low_pct": 21.1681,
        "ci95_wilson_high_pct": 26.4332,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.15,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "n_colluders": 3,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.459386,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": -0.7715485554188566,
        "innocent_std": 17.42867355004248
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 860,
        "trials": 1000,
        "rate_pct": 86.0,
        "ci95_wilson_low_pct": 83.7113,
        "ci95_wilson_high_pct": 88.0132,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 140,
        "trials": 1000,
        "rate_pct": 14.0,
        "ci95_wilson_low_pct": 11.9868,
        "ci95_wilson_high_pct": 16.2887,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.791,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "n_colluders": 5,
      "attack": "mean",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.459386,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": -0.7715485554188566,
        "innocent_std": 17.42867355004248
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 918,
        "trials": 1000,
        "rate_pct": 91.8,
        "ci95_wilson_low_pct": 89.9352,
        "ci95_wilson_high_pct": 93.3448,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 65,
        "trials": 1000,
        "rate_pct": 6.5,
        "ci95_wilson_low_pct": 5.1324,
        "ci95_wilson_high_pct": 8.2006,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 17,
        "trials": 1000,
        "rate_pct": 1.7,
        "ci95_wilson_low_pct": 1.0641,
        "ci95_wilson_high_pct": 2.7056,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 982,
        "trials": 1000,
        "rate_pct": 98.2,
        "ci95_wilson_low_pct": 97.1727,
        "ci95_wilson_high_pct": 98.8584,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.592,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "n_colluders": 5,
      "attack": "min",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.459386,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": -0.7715485554188566,
        "innocent_std": 17.42867355004248
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 815,
        "trials": 1000,
        "rate_pct": 81.5,
        "ci95_wilson_low_pct": 78.9743,
        "ci95_wilson_high_pct": 83.7846,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 25,
        "trials": 1000,
        "rate_pct": 2.5,
        "ci95_wilson_low_pct": 1.699,
        "ci95_wilson_high_pct": 3.6646,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 160,
        "trials": 1000,
        "rate_pct": 16.0,
        "ci95_wilson_low_pct": 13.8585,
        "ci95_wilson_high_pct": 18.4017,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 836,
        "trials": 1000,
        "rate_pct": 83.6,
        "ci95_wilson_low_pct": 81.1772,
        "ci95_wilson_high_pct": 85.7656,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 1.537,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "n_colluders": 5,
      "attack": "max",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.459386,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": -0.7715485554188566,
        "innocent_std": 17.42867355004248
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 845,
        "trials": 1000,
        "rate_pct": 84.5,
        "ci95_wilson_low_pct": 82.1253,
        "ci95_wilson_high_pct": 86.6107,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 153,
        "trials": 1000,
        "rate_pct": 15.3,
        "ci95_wilson_low_pct": 13.2019,
        "ci95_wilson_high_pct": 17.6637,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 2,
        "trials": 1000,
        "rate_pct": 0.2,
        "ci95_wilson_low_pct": 0.0549,
        "ci95_wilson_high_pct": 0.7263,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 998,
        "trials": 1000,
        "rate_pct": 99.8,
        "ci95_wilson_low_pct": 99.2737,
        "ci95_wilson_high_pct": 99.9451,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.487,
      "false_accusation_familywise_bound_pct": 29.5,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.79,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 29.5,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 31.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 32,
      "n_colluders": 5,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.459386,
      "z_cal": {
        "innocent_n": 6200,
        "innocent_mean": -0.7715485554188566,
        "innocent_std": 17.42867355004248
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      "trials": 1000,
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      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
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      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
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        "rate_pct": 39.5,
        "ci95_wilson_low_pct": 36.5158,
        "ci95_wilson_high_pct": 42.5646,
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        "ci95_wilson_low_pct": 57.4354,
        "ci95_wilson_high_pct": 63.4842,
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      "no_accusation": {
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        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.829,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": false,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
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      "n_colluders": 2,
      "attack": "max",
      "m_bits_used": 256,
      "eta": 0.01,
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      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
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        "ci95_wilson_high_pct": 59.1467,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
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        "ci95_wilson_low_pct": 40.8533,
        "ci95_wilson_high_pct": 46.9934,
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      },
      "no_accusation": {
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        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
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        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.583,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
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      "n_colluders": 2,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
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        "rate_pct": 55.9,
        "ci95_wilson_low_pct": 52.8059,
        "ci95_wilson_high_pct": 58.949,
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      },
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        "trials": 1000,
        "rate_pct": 44.1,
        "ci95_wilson_low_pct": 41.051,
        "ci95_wilson_high_pct": 47.1941,
        "rule_of_three_upper_pct": null
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        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.587,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
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      "n_colluders": 3,
      "attack": "mean",
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      "eta": 0.01,
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        "innocent_mean": -0.4129416282018615,
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      },
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      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
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        "trials": 1000,
        "rate_pct": 63.5,
        "ci95_wilson_low_pct": 60.4697,
        "ci95_wilson_high_pct": 66.427,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
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        "trials": 1000,
        "rate_pct": 36.5,
        "ci95_wilson_low_pct": 33.573,
        "ci95_wilson_high_pct": 39.5303,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
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        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
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        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
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      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
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      "n_colluders": 3,
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      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.871747,
      "z_cal": {
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        "innocent_mean": -0.4129416282018615,
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      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
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        "rate_pct": 27.6,
        "ci95_wilson_low_pct": 24.9191,
        "ci95_wilson_high_pct": 30.4524,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 724,
        "trials": 1000,
        "rate_pct": 72.4,
        "ci95_wilson_low_pct": 69.5476,
        "ci95_wilson_high_pct": 75.0809,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 999,
        "trials": 1000,
        "rate_pct": 99.9,
        "ci95_wilson_low_pct": 99.4357,
        "ci95_wilson_high_pct": 99.9823,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.807,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": false,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": false
    },
    {
      "cover_id": "tardos-p-draw-2",
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      "n_colluders": 3,
      "attack": "max",
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      "eta": 0.01,
      "z": 33.871747,
      "z_cal": {
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      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
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        "trials": 1000,
        "rate_pct": 48.1,
        "ci95_wilson_low_pct": 45.0164,
        "ci95_wilson_high_pct": 51.1981,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 519,
        "trials": 1000,
        "rate_pct": 51.9,
        "ci95_wilson_low_pct": 48.8019,
        "ci95_wilson_high_pct": 54.9836,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
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        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.318,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": false,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 3,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.871747,
      "z_cal": {
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        "innocent_mean": -0.4129416282018615,
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      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 637,
        "trials": 1000,
        "rate_pct": 63.7,
        "ci95_wilson_low_pct": 60.6724,
        "ci95_wilson_high_pct": 66.6228,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 363,
        "trials": 1000,
        "rate_pct": 36.3,
        "ci95_wilson_low_pct": 33.3772,
        "ci95_wilson_high_pct": 39.3276,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
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        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 1000,
        "trials": 1000,
        "rate_pct": 100.0,
        "ci95_wilson_low_pct": 99.6173,
        "ci95_wilson_high_pct": 100.0,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.315,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "mean",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.871747,
      "z_cal": {
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        "innocent_mean": -0.4129416282018615,
        "innocent_std": 14.64444113548097
      },
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      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 653,
        "trials": 1000,
        "rate_pct": 65.3,
        "ci95_wilson_low_pct": 62.2961,
        "ci95_wilson_high_pct": 68.1868,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 338,
        "trials": 1000,
        "rate_pct": 33.8,
        "ci95_wilson_low_pct": 30.9351,
        "ci95_wilson_high_pct": 36.7889,
        "rule_of_three_upper_pct": null
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      "no_accusation": {
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        "rate_pct": 0.9,
        "ci95_wilson_low_pct": 0.4742,
        "ci95_wilson_high_pct": 1.7016,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 990,
        "trials": 1000,
        "rate_pct": 99.0,
        "ci95_wilson_low_pct": 98.169,
        "ci95_wilson_high_pct": 99.4559,
        "rule_of_three_upper_pct": null
      },
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      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "min",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.871747,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": -0.4129416282018615,
        "innocent_std": 14.64444113548097
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 123,
        "trials": 1000,
        "rate_pct": 12.3,
        "ci95_wilson_low_pct": 10.4074,
        "ci95_wilson_high_pct": 14.4812,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 874,
        "trials": 1000,
        "rate_pct": 87.4,
        "ci95_wilson_low_pct": 85.199,
        "ci95_wilson_high_pct": 89.3147,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 3,
        "trials": 1000,
        "rate_pct": 0.3,
        "ci95_wilson_low_pct": 0.1021,
        "ci95_wilson_high_pct": 0.8783,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 972,
        "trials": 1000,
        "rate_pct": 97.2,
        "ci95_wilson_low_pct": 95.983,
        "ci95_wilson_high_pct": 98.0558,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.666,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": false,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": false
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "max",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.871747,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": -0.4129416282018615,
        "innocent_std": 14.64444113548097
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 446,
        "trials": 1000,
        "rate_pct": 44.6,
        "ci95_wilson_low_pct": 41.5456,
        "ci95_wilson_high_pct": 47.6957,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 553,
        "trials": 1000,
        "rate_pct": 55.3,
        "ci95_wilson_low_pct": 52.204,
        "ci95_wilson_high_pct": 58.3555,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
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        "rate_pct": 0.1,
        "ci95_wilson_low_pct": 0.0177,
        "ci95_wilson_high_pct": 0.5643,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 992,
        "trials": 1000,
        "rate_pct": 99.2,
        "ci95_wilson_low_pct": 98.4293,
        "ci95_wilson_high_pct": 99.5941,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.166,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": false,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 5,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.871747,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": -0.4129416282018615,
        "innocent_std": 14.64444113548097
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 696,
        "trials": 1000,
        "rate_pct": 69.6,
        "ci95_wilson_low_pct": 66.6785,
        "ci95_wilson_high_pct": 72.3715,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 298,
        "trials": 1000,
        "rate_pct": 29.8,
        "ci95_wilson_low_pct": 27.0468,
        "ci95_wilson_high_pct": 32.7078,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 6,
        "trials": 1000,
        "rate_pct": 0.6,
        "ci95_wilson_low_pct": 0.2753,
        "ci95_wilson_high_pct": 1.3028,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 988,
        "trials": 1000,
        "rate_pct": 98.8,
        "ci95_wilson_low_pct": 97.9143,
        "ci95_wilson_high_pct": 99.3122,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.107,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "monotonicity_note_ko": "같은 표지·공격에서 공모자 수 N이 늘수록 정지지목률이 올랐습니다. 임계 지목에서도 이 역전이 관측됩니다. 공모자 증가가 항상 추적을 어렵게 하지는 않습니다.",
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 10,
      "attack": "mean",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.871747,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": -0.4129416282018615,
        "innocent_std": 14.64444113548097
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 620,
        "trials": 1000,
        "rate_pct": 62.0,
        "ci95_wilson_low_pct": 58.951,
        "ci95_wilson_high_pct": 64.9571,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 202,
        "trials": 1000,
        "rate_pct": 20.2,
        "ci95_wilson_low_pct": 17.8277,
        "ci95_wilson_high_pct": 22.8004,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 178,
        "trials": 1000,
        "rate_pct": 17.8,
        "ci95_wilson_low_pct": 15.5537,
        "ci95_wilson_high_pct": 20.2927,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 782,
        "trials": 1000,
        "rate_pct": 78.2,
        "ci95_wilson_low_pct": 75.5356,
        "ci95_wilson_high_pct": 80.6486,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 1.51,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 10,
      "attack": "min",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.871747,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": -0.4129416282018615,
        "innocent_std": 14.64444113548097
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 58,
        "trials": 1000,
        "rate_pct": 5.8,
        "ci95_wilson_low_pct": 4.5133,
        "ci95_wilson_high_pct": 7.425,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 942,
        "trials": 1000,
        "rate_pct": 94.2,
        "ci95_wilson_low_pct": 92.575,
        "ci95_wilson_high_pct": 95.4867,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 0,
        "trials": 1000,
        "rate_pct": 0.0,
        "ci95_wilson_low_pct": 0.0,
        "ci95_wilson_high_pct": 0.3827,
        "rule_of_three_upper_pct": 0.3
      },
      "colluder_caught_any": {
        "count": 857,
        "trials": 1000,
        "rate_pct": 85.7,
        "ci95_wilson_low_pct": 83.3935,
        "ci95_wilson_high_pct": 87.7333,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 3.38,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": false,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": false
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 10,
      "attack": "max",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.871747,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": -0.4129416282018615,
        "innocent_std": 14.64444113548097
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 344,
        "trials": 1000,
        "rate_pct": 34.4,
        "ci95_wilson_low_pct": 31.5204,
        "ci95_wilson_high_pct": 37.399,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 600,
        "trials": 1000,
        "rate_pct": 60.0,
        "ci95_wilson_low_pct": 56.9309,
        "ci95_wilson_high_pct": 62.9926,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 56,
        "trials": 1000,
        "rate_pct": 5.6,
        "ci95_wilson_low_pct": 4.3375,
        "ci95_wilson_high_pct": 7.2024,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 837,
        "trials": 1000,
        "rate_pct": 83.7,
        "ci95_wilson_low_pct": 81.2824,
        "ci95_wilson_high_pct": 85.8596,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 2.245,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": false,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    },
    {
      "cover_id": "tardos-p-draw-2",
      "n_users": 64,
      "n_colluders": 10,
      "attack": "median",
      "m_bits_used": 256,
      "eta": 0.01,
      "z": 33.871747,
      "z_cal": {
        "innocent_n": 12600,
        "innocent_mean": -0.4129416282018615,
        "innocent_std": 14.64444113548097
      },
      "trials": 1000,
      "accusation_rule": "score_gt_z_only",
      "argmax_forced_accusations": 0,
      "correct_accusation": {
        "count": 583,
        "trials": 1000,
        "rate_pct": 58.3,
        "ci95_wilson_low_pct": 55.2179,
        "ci95_wilson_high_pct": 61.3186,
        "rule_of_three_upper_pct": null
      },
      "false_accusation": {
        "count": 246,
        "trials": 1000,
        "rate_pct": 24.6,
        "ci95_wilson_low_pct": 22.0312,
        "ci95_wilson_high_pct": 27.3632,
        "rule_of_three_upper_pct": null
      },
      "no_accusation": {
        "count": 171,
        "trials": 1000,
        "rate_pct": 17.1,
        "ci95_wilson_low_pct": 14.8933,
        "ci95_wilson_high_pct": 19.5585,
        "rule_of_three_upper_pct": null
      },
      "colluder_caught_any": {
        "count": 770,
        "trials": 1000,
        "rate_pct": 77.0,
        "ci95_wilson_low_pct": 74.2913,
        "ci95_wilson_high_pct": 79.5021,
        "rule_of_three_upper_pct": null
      },
      "mean_accused_count": 1.623,
      "false_accusation_familywise_bound_pct": 50.8,
      "within_bound": true,
      "z_scope": "per_innocent_per_cover",
      "pixel_fixtures_used": false,
      "c0_max_for_this_n": 1.72,
      "within_guaranteed_c0": false,
      "familywise_bound_independent_pct": 50.8,
      "familywise_bound_independent_validity": "assumes_independence",
      "familywise_bound_union_pct": 63.0,
      "familywise_bound_union_validity": "dependence_free_union_bound",
      "within_union_bound": true
    }
  ],
  "bias": {
    "v1": {
      "published_n10_sample_identified_as": [
        8,
        8,
        8
      ],
      "published_n10_sample_all_8": true,
      "full_40_trial_ids_serialized": false,
      "pixel_fixture_present": false,
      "verdict_ko": "미확인 — 공개 sample_trials 3건은 모두 identified_as=8. 나머지 37건은 JSON에 없음. 픽셀 픽스처가 없어 v1 전체 히스토그램을 재현하지 못함."
    },
    "v2_per_codebook": [
      {
        "cover_id": "tardos-p-draw-0",
        "n_users": 32,
        "per_user_innocent_mean_min": -24.4448,
        "per_user_innocent_mean_max": 24.3877,
        "per_user_innocent_mean_std": 10.6716,
        "users_outside_3sd": [],
        "note_ko": "Tardos 무고자 점수 사용자별 평균. 3σ 이탈자를 기록. v1 identified_as=8 쏠림은 픽셀 MSE 점수 문제이며 픽스처 부재로 미확인."
      },
      {
        "cover_id": "tardos-p-draw-0",
        "n_users": 64,
        "per_user_innocent_mean_min": -32.5709,
        "per_user_innocent_mean_max": 20.6172,
        "per_user_innocent_mean_std": 10.0642,
        "users_outside_3sd": [
          2
        ],
        "note_ko": "Tardos 무고자 점수 사용자별 평균. 3σ 이탈자를 기록. v1 identified_as=8 쏠림은 픽셀 MSE 점수 문제이며 픽스처 부재로 미확인."
      },
      {
        "cover_id": "tardos-p-draw-1",
        "n_users": 32,
        "per_user_innocent_mean_min": -39.9913,
        "per_user_innocent_mean_max": 25.1385,
        "per_user_innocent_mean_std": 13.642,
        "users_outside_3sd": [],
        "note_ko": "Tardos 무고자 점수 사용자별 평균. 3σ 이탈자를 기록. v1 identified_as=8 쏠림은 픽셀 MSE 점수 문제이며 픽스처 부재로 미확인."
      },
      {
        "cover_id": "tardos-p-draw-1",
        "n_users": 64,
        "per_user_innocent_mean_min": -24.3744,
        "per_user_innocent_mean_max": 16.8982,
        "per_user_innocent_mean_std": 9.7274,
        "users_outside_3sd": [],
        "note_ko": "Tardos 무고자 점수 사용자별 평균. 3σ 이탈자를 기록. v1 identified_as=8 쏠림은 픽셀 MSE 점수 문제이며 픽스처 부재로 미확인."
      },
      {
        "cover_id": "tardos-p-draw-2",
        "n_users": 32,
        "per_user_innocent_mean_min": -52.444,
        "per_user_innocent_mean_max": 15.6631,
        "per_user_innocent_mean_std": 13.8315,
        "users_outside_3sd": [
          14
        ],
        "note_ko": "Tardos 무고자 점수 사용자별 평균. 3σ 이탈자를 기록. v1 identified_as=8 쏠림은 픽셀 MSE 점수 문제이며 픽스처 부재로 미확인."
      },
      {
        "cover_id": "tardos-p-draw-2",
        "n_users": 64,
        "per_user_innocent_mean_min": -24.3328,
        "per_user_innocent_mean_max": 19.2991,
        "per_user_innocent_mean_std": 9.1002,
        "users_outside_3sd": [],
        "note_ko": "Tardos 무고자 점수 사용자별 평균. 3σ 이탈자를 기록. v1 identified_as=8 쏠림은 픽셀 MSE 점수 문제이며 픽스처 부재로 미확인."
      }
    ]
  },
  "note_ko": "여러 명이 담합해 파일을 섞으면 추적이 어려워집니다. 저희는 확실하지 않으면 아무도 지목하지 않습니다. 가용 비트로 감당하는 c0를 넘으면 보증하지 않습니다.",
  "familywise_bound_independent_formula": "100*(1-(1-0.0112)^(n_users-1))",
  "familywise_bound_independent_pct_by_n_users": {
    "32": 29.5,
    "64": 50.8
  },
  "familywise_bound_independent_validity": "assumes_independence",
  "familywise_bound_independent_warning_ko": "곱 상한 1-(1-η)^(n-1)은 무고자 점수 독립을 가정한다. 실측 상관로 이 상한은 깨질 수 있어 단독 보증으로 쓰지 않는다.",
  "familywise_bound_union_formula": "100*(n_users-1)*eta",
  "familywise_bound_union_pct_by_n_users": {
    "32": 31.0,
    "64": 63.0
  },
  "familywise_bound_union_validity": "dependence_free_union_bound",
  "correlation_evidence_ko": "Z 스윕 η=0.05·c=1에서 88.0%(CI 83.4–91.5)가 독립 가정 상한 79.6%를 초과 → 무고자 점수 간 양의 상관 존재. 그래서 union 상한을 주 기준으로 쓴다.",
  "bound_summary": {
    "cells_total": 120,
    "cells_c1": 24,
    "cells_c1_exceeding": 0,
    "cells_c_ge2": 96,
    "cells_c_ge2_exceeding_product_bound": 33,
    "cells_exceeding_union_bound": 24,
    "c0_max_by_n_users": {
      "32": 1.79,
      "64": 1.72
    }
  },
  "reproduce": {
    "script": "scripts/ops/measure-forensic-collusion-roc-v2.py",
    "seed": 20260821,
    "command": "python3 scripts/ops/measure-forensic-collusion-roc-v2.py",
    "eta": 0.01,
    "eta_locked_a_priori": true,
    "eta_reselection_forbidden": true,
    "python": "3.12.3",
    "numpy": "1.26.4",
    "ledger_sentences_ko": [
      "이 기록은 우리가 직접 관리하고, 외부에서 지켜보는 사람은 없습니다.",
      "젠룩이 운영하는 폐쇄 원장에 기록을 고정합니다.",
      "크리스탈은 내부 가상화폐이며 현금으로 바꾸지 않습니다. 비트코인 같은 공개 체인에는 올리지 않습니다."
    ],
    "public_chain_used": false,
    "phrasing_ko": "폐쇄형(허가형) 원장 기반",
    "evidence_href": "/benchmarks/forensic-collusion-roc-v2.json",
    "file": "apps/c2pa/public/benchmarks/forensic-collusion-roc-v2.json"
  }
}