{
 "generator": "gen_forward_info.py",
 "tolerance": {
  "abs": 1e-12,
  "note": "预期值由有理数精确算出；与浮点实现比较用绝对误差 1e-12。"
 },
 "scenarios": [
  {
   "name": "cdf_method_example_2.44_2.52_2.62",
   "section": "6.2；约定 1–4",
   "params": {},
   "input": {
    "range": {
     "q1": 2.44,
     "q5": 2.52,
     "q9": 2.62
    },
    "x": [
     2.3,
     2.36,
     2.4,
     2.44,
     2.48,
     2.52,
     2.57,
     2.62,
     2.67,
     2.72,
     2.8
    ],
    "densityAt": [
     2.3,
     2.36,
     2.4,
     2.44,
     2.48,
     2.52,
     2.57,
     2.62,
     2.67,
     2.72,
     2.8
    ]
   },
   "expected": {
    "points": [
     [
      2.36,
      0.0
     ],
     [
      2.44,
      0.1
     ],
     [
      2.52,
      0.5
     ],
     [
      2.62,
      0.9
     ],
     [
      2.72,
      1.0
     ]
    ],
    "cdf": [
     0.0,
     0.0,
     0.05,
     0.1,
     0.3,
     0.5,
     0.6999999999999991,
     0.9,
     0.9499999999999997,
     1.0,
     1.0
    ],
    "density": [
     0.0,
     1.249999999999999,
     1.249999999999999,
     4.999999999999996,
     4.999999999999996,
     3.9999999999999964,
     3.9999999999999964,
     0.9999999999999991,
     0.9999999999999991,
     0.0,
     0.0
    ],
    "mean": 2.527
   },
   "note": "方法 6.2 示例：低于 2.57 的把握 0.70；尾巴 2.36–2.44、2.62–2.72。"
  },
  {
   "name": "cdf_asymmetric_narrow",
   "section": "6.2；约定 1–4",
   "params": {},
   "input": {
    "range": {
     "q1": 1.2999,
     "q5": 1.3,
     "q9": 1.3005
    },
    "x": [
     1.2997,
     1.2998,
     1.29995,
     1.3,
     1.3002,
     1.3005,
     1.30075,
     1.301
    ],
    "densityAt": [
     1.2997,
     1.2998,
     1.29995,
     1.3,
     1.3002,
     1.3005,
     1.30075,
     1.301
    ]
   },
   "expected": {
    "points": [
     [
      1.2998,
      0.0
     ],
     [
      1.2999,
      0.1
     ],
     [
      1.3,
      0.5
     ],
     [
      1.3005,
      0.9
     ],
     [
      1.301,
      1.0
     ]
    ],
    "cdf": [
     0.0,
     0.0,
     0.2999999999995559,
     0.5,
     0.66,
     0.9,
     0.9500000000000222,
     1.0
    ],
    "density": [
     0.0,
     1000.0000000001102,
     4000.0000000004407,
     800.0000000000881,
     800.0000000000881,
     200.00000000002203,
     200.00000000002203,
     0.0
    ],
    "mean": 1.30014
   },
   "note": "方法第五部分的窄范围写法（不对称）：低端尾巴 1.2998–1.2999，高端尾巴 1.3005–1.3010。折点上密度取右边那段。"
  },
  {
   "name": "minimize_to_improvement",
   "section": "6.1；约定 5",
   "params": {
    "direction": "minimize"
   },
   "input": {
    "b": 0.4,
    "range": {
     "q1": 0.3,
     "q5": 0.35,
     "q9": 0.45
    },
    "y": [
     -0.2,
     -0.05,
     0.0,
     0.05,
     0.08,
     0.1,
     0.25
    ]
   },
   "expected": {
    "Yrange": {
     "q1": -0.04999999999999999,
     "q5": 0.050000000000000044,
     "q9": 0.10000000000000003
    },
    "Ypoints": [
     [
      -0.15000000000000002,
      0.0
     ],
     [
      -0.04999999999999999,
      0.1
     ],
     [
      0.050000000000000044,
      0.5
     ],
     [
      0.10000000000000003,
      0.9
     ],
     [
      0.15000000000000002,
      1.0
     ]
    ],
    "Ycdf": [
     0.0,
     0.09999999999999999,
     0.2999999999999999,
     0.49999999999999983,
     0.7399999999999997,
     0.8999999999999998,
     1.0
    ]
   },
   "note": "Y = b − 分数，一成九成对调：Y 的三个数 = (b−q9, b−q5, b−q1) = (−0.05, 0.05, 0.10)；低端尾巴宽 = 原 q9−q5 = 0.10，高端尾巴宽 = 原 q5−q1 = 0.05。"
  },
  {
   "name": "forward_merge_r1_real",
   "section": "6.3、6.1；约定 6–8",
   "params": {
    "lambda": 0.1,
    "direction": "maximize",
    "eps": 0.01
   },
   "input": {
    "b": 0.9597642169962064,
    "candidates": {
     "r1-v1-c1": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 2.0,
        "q5": 2.45,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 2.2,
        "q5": 2.5,
        "q9": 2.62
       }
      },
      {
       "researcher": "researcher-3",
       "range": {
        "q1": 2.2,
        "q5": 2.5,
        "q9": 2.63
       }
      }
     ],
     "r1-v1-c2": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 1.85,
        "q5": 2.35,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 1.6,
        "q5": 2.35,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-3",
       "range": {
        "q1": 1.8,
        "q5": 2.4,
        "q9": 2.62
       }
      }
     ],
     "r1-v1-c3": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 2.3,
        "q5": 2.5,
        "q9": 2.62
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 2.42,
        "q5": 2.52,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-3",
       "range": {
        "q1": 2.1,
        "q5": 2.5,
        "q9": 2.6
       }
      }
     ]
    },
    "Yprobe": [
     -1.0,
     -0.01,
     0.0,
     0.5,
     1.0,
     1.4,
     1.5,
     1.6,
     1.7,
     2.0
    ]
   },
   "expected": {
    "reserveY": [
     -1.1097642169962063,
     2.890235783003794
    ],
    "reserveRaw": [
     -0.1499999999999999,
     3.85
    ],
    "candidates": {
     "r1-v1-c1": {
      "Ycdf": [
       0.002744105424905158,
       0.02749410542490516,
       0.027744105424905158,
       0.04024410542490516,
       0.09201456329056014,
       0.3764926035541918,
       0.4908668526188352,
       0.7204866655530365,
       0.909006668533861,
       0.9777441054249052
      ],
      "Yquantiles": {
       "q1": 1.027378640146651,
       "q5": 1.505620398388409,
       "q9": 1.6872385077994339
      },
      "rawQuantiles": {
       "q1": 1.9871428571428573,
       "q5": 2.4653846153846155,
       "q9": 2.6470027247956405
      },
      "Ymean": 1.3919857830037936
     },
     "r1-v1-c2": {
      "Ycdf": [
       0.002744105424905158,
       0.03148467410475341,
       0.03213467410475341,
       0.0842087379743361,
       0.258602635622629,
       0.5140705971405044,
       0.6532164175573758,
       0.8062618721028304,
       0.9000099107307501,
       0.9777441054249052
      ],
      "Yquantiles": {
       "q1": 0.5902357830037936,
       "q5": 1.3862357830037937,
       "q9": 1.6999753073526045
      },
      "rawQuantiles": {
       "q1": 1.55,
       "q5": 2.346,
       "q9": 2.659739524348811
      },
      "Ymean": 1.2365857830037936
     },
     "r1-v1-c3": {
      "Ycdf": [
       0.002744105424905158,
       0.02749410542490516,
       0.027744105424905158,
       0.04024410542490516,
       0.07222642169962064,
       0.24846116582035283,
       0.40674896111693865,
       0.708871708310869,
       0.9305260061463959,
       0.9777441054249052
      ],
      "Yquantiles": {
       "q1": 1.169183151424846,
       "q5": 1.5424985567264213,
       "q9": 1.6678673619511621
      },
      "rawQuantiles": {
       "q1": 2.1289473684210525,
       "q5": 2.5022627737226277,
       "q9": 2.6276315789473683
      },
      "Ymean": 1.4392357830037936
     }
    }
   },
   "note": "真实第 1 轮三候选×三人（每人一份，等权）。开放预留取三候选九条折线（含尾巴）的最低首点和最高末点。合并分位数在改进量上用广义逆 inf{y: P(Y≤y) ≥ p} 求，再加回 b。"
  },
  {
   "name": "forward_merge_minimize",
   "section": "6.3、6.1；约定 6–8",
   "params": {
    "lambda": 0.1,
    "direction": "minimize",
    "eps": 0.01
   },
   "input": {
    "b": 0.4,
    "candidates": {
     "c1": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.36,
        "q5": 0.38,
        "q9": 0.4
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.35,
        "q5": 0.37,
        "q9": 0.39
       }
      }
     ],
     "c2": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.33,
        "q5": 0.36,
        "q9": 0.41
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.37,
        "q5": 0.39,
        "q9": 0.42
       }
      }
     ],
     "c3": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.41,
        "q5": 0.43,
        "q9": 0.46
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.4,
        "q5": 0.42,
        "q9": 0.45
       }
      }
     ],
     "c4": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.37,
        "q5": 0.39,
        "q9": 0.4
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.38,
        "q5": 0.395,
        "q9": 0.41
       }
      }
     ]
    },
    "Yprobe": [
     -0.1,
     -0.02,
     -0.01,
     0.0,
     0.01,
     0.02,
     0.05
    ]
   },
   "expected": {
    "reserveY": [
     -0.18500000000000003,
     0.19499999999999998
    ],
    "reserveRaw": [
     0.20500000000000004,
     0.5850000000000001
    ],
    "candidates": {
     "c1": {
      "Ycdf": [
       0.022368421052631586,
       0.04342105263157899,
       0.06855263157894742,
       0.11618421052631579,
       0.2313157894736841,
       0.41394736842105234,
       0.8943421052631574
      ],
      "Yquantiles": {
       "q1": -0.0033977900552486233,
       "q5": 0.024711815561959675,
       "q9": 0.05118784530386745
      },
      "rawQuantiles": {
       "q1": 0.3488121546961326,
       "q5": 0.37528818443804035,
       "q9": 0.4033977900552487
      },
      "Ymean": 0.023000000000000017
     },
     "c2": {
      "Ycdf": [
       0.022368421052631586,
       0.12442105263157885,
       0.19605263157894717,
       0.29468421052631555,
       0.393315789473684,
       0.5219473684210524,
       0.7968421052631577
      ],
      "Yquantiles": {
       "q1": -0.02916996047430826,
       "q5": 0.01829378068739773,
       "q9": 0.06647058823529413
      },
      "rawQuantiles": {
       "q1": 0.3335294117647059,
       "q5": 0.3817062193126023,
       "q9": 0.4291699604743083
      },
      "Ymean": 0.01827500000000002
     },
     "c3": {
      "Ycdf": [
       0.022368421052631586,
       0.5834210526315784,
       0.7660526315789468,
       0.8811842105263157,
       0.9288157894736842,
       0.9539473684210527,
       0.9618421052631579
      ],
      "Yquantiles": {
       "q1": -0.06241935483870968,
       "q5": -0.025465517241379278,
       "q9": 0.003950276243093946
      },
      "rawQuantiles": {
       "q1": 0.39604972375690606,
       "q5": 0.4254655172413793,
       "q9": 0.4624193548387097
      },
      "Ymean": -0.025149999999999985
     },
     "c4": {
      "Ycdf": [
       0.022368421052631586,
       0.05842105263157873,
       0.09105263157894727,
       0.25868421052631557,
       0.561315789473684,
       0.7739473684210523,
       0.9618421052631578
      ],
      "Yquantiles": {
       "q1": -0.009466248037676579,
       "q5": 0.007973913043478267,
       "q9": 0.030620525059665896
      },
      "rawQuantiles": {
       "q1": 0.36937947494033413,
       "q5": 0.39202608695652175,
       "q9": 0.4094662480376766
      },
      "Ymean": 0.008825000000000013
     }
    }
   },
   "note": "越小越好：逐人换成 Y = b − 分数再合并；原值分位数 = b − Y 的分位数，一成九成对调。"
  },
  {
   "name": "ablation_cell_merge_r1_p1",
   "section": "6.3、6.7 成分与权重；约定 6–8、24",
   "params": {
    "lambda": 0.1
   },
   "input": {
    "explanations": [
     {
      "id": "r1-e1-1",
      "author": "researcher-1",
      "range": {
       "q1": 1.2,
       "q5": 2,
       "q9": 2.44
      }
     },
     {
      "id": "r1-e1-2",
      "author": "researcher-1",
      "range": {
       "q1": 1.22,
       "q5": 1.4,
       "q9": 1.52
      }
     },
     {
      "id": "r1-e2-1",
      "author": "researcher-2",
      "range": {
       "q1": 1.05,
       "q5": 1.35,
       "q9": 1.95
      }
     },
     {
      "id": "r1-e2-2",
      "author": "researcher-2",
      "range": {
       "q1": 0.95,
       "q5": 1.3,
       "q9": 2.1
      }
     },
     {
      "id": "r1-e3-1",
      "author": "researcher-3",
      "range": {
       "q1": 1.15,
       "q5": 1.36,
       "q9": 1.55
      }
     },
     {
      "id": "r1-e3-2",
      "author": "researcher-3",
      "range": {
       "q1": 1.2,
       "q5": 1.42,
       "q9": 2.46
      }
     }
    ],
    "x": [
     0.5,
     1.0,
     1.3,
     1.5,
     2.0,
     2.5,
     3.0
    ]
   },
   "expected": {
    "reserve": [
     -1.1500000000000001,
     5.05
    ],
    "weights": [
     0.15,
     0.15,
     0.15,
     0.15,
     0.15,
     0.15,
     0.1
    ],
    "cdf": [
     0.028487903225806455,
     0.08764819857561795,
     0.34381266582879494,
     0.584067846415045,
     0.7980179900744416,
     0.9227433453643131,
     0.9597239454094293
    ],
    "quantiles": {
     "q1": 1.031197878433162,
     "q5": 1.4262310909924365,
     "q9": 2.3794554469188443
    }
   },
   "note": "真实第 1 轮消融 p1 格（关掉 p1）。三人各两条解释：每条 0.9/3/2 = 0.15，预留 0.1（权重最后一项）。开放预留只看这一格六条折线。分位数在原值上求。"
  },
  {
   "name": "quantile_flat_left_end",
   "section": "约定 8",
   "params": {},
   "input": {
    "mixture": [
     {
      "weight": 0.5,
      "range": {
       "q1": 0.99,
       "q5": 1.0,
       "q9": 1.01
      }
     },
     {
      "weight": 0.5,
      "range": {
       "q1": 1.99,
       "q5": 2.0,
       "q9": 2.01
      }
     }
    ],
    "p": [
     0.1,
     0.5,
     0.9
    ]
   },
   "expected": {
    "quantiles": [
     0.9924999999999999,
     1.02,
     2.0075
    ]
   },
   "note": "两条窄折线各占一半，中间 [1.02, 1.98] 把握走平在 0.5：一半取平段左端 1.02；一成落在第一条的[0.99, 1.0] 段里（第一条自己的 0.2 分位），九成落在第二条的 [2.0, 2.01] 段里。"
  },
  {
   "name": "pool_r1_real",
   "section": "6.4 入池；约定 9",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "direction": "maximize"
   },
   "input": {
    "b": 0.9597642169962064,
    "candidates": {
     "r1-v1-c1": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 2.0,
        "q5": 2.45,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 2.2,
        "q5": 2.5,
        "q9": 2.62
       }
      },
      {
       "researcher": "researcher-3",
       "range": {
        "q1": 2.2,
        "q5": 2.5,
        "q9": 2.63
       }
      }
     ],
     "r1-v1-c2": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 1.85,
        "q5": 2.35,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 1.6,
        "q5": 2.35,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-3",
       "range": {
        "q1": 1.8,
        "q5": 2.4,
        "q9": 2.62
       }
      }
     ],
     "r1-v1-c3": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 2.3,
        "q5": 2.5,
        "q9": 2.62
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 2.42,
        "q5": 2.52,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-3",
       "range": {
        "q1": 2.1,
        "q5": 2.5,
        "q9": 2.6
       }
      }
     ]
    }
   },
   "expected": {
    "r1-v1-c1": {
     "probBelowMinusEps": 0.02749410542490516,
     "inPool": true
    },
    "r1-v1-c2": {
     "probBelowMinusEps": 0.03148467410475341,
     "inPool": true
    },
    "r1-v1-c3": {
     "probBelowMinusEps": 0.02749410542490516,
     "inPool": true
    }
   },
   "note": "真实第 1 轮：三个候选都远高于 b，都入池。"
  },
  {
   "name": "pool_minimize",
   "section": "6.4 入池；约定 9",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "direction": "minimize"
   },
   "input": {
    "b": 0.4,
    "candidates": {
     "c1": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.36,
        "q5": 0.38,
        "q9": 0.4
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.35,
        "q5": 0.37,
        "q9": 0.39
       }
      }
     ],
     "c2": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.33,
        "q5": 0.36,
        "q9": 0.41
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.37,
        "q5": 0.39,
        "q9": 0.42
       }
      }
     ],
     "c3": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.41,
        "q5": 0.43,
        "q9": 0.46
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.4,
        "q5": 0.42,
        "q9": 0.45
       }
      }
     ],
     "c4": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.37,
        "q5": 0.39,
        "q9": 0.4
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.38,
        "q5": 0.395,
        "q9": 0.41
       }
      }
     ]
    }
   },
   "expected": {
    "c1": {
     "probBelowMinusEps": 0.06855263157894742,
     "inPool": true
    },
    "c2": {
     "probBelowMinusEps": 0.19605263157894717,
     "inPool": true
    },
    "c3": {
     "probBelowMinusEps": 0.7660526315789468,
     "inPool": false
    },
    "c4": {
     "probBelowMinusEps": 0.09105263157894727,
     "inPool": true
    }
   },
   "note": "越小越好：P(Y < −ε) = P(分数 > b+ε)。c3 的大部分把握在 0.41 以上，不入池。"
  },
  {
   "name": "pool_exactly_half",
   "section": "6.4 入池；约定 9",
   "params": {
    "eps": 0.25,
    "lambda": 0.1,
    "direction": "maximize"
   },
   "input": {
    "b": 1.0,
    "cases": [
     {
      "candidates": {
       "c1": [
        {
         "researcher": "researcher-1",
         "range": {
          "q1": 0.5,
          "q5": 0.75,
          "q9": 1.0
         }
        }
       ]
      }
     },
     {
      "candidates": {
       "c1": [
        {
         "researcher": "researcher-1",
         "range": {
          "q1": 0.5,
          "q5": 0.7509765625,
          "q9": 1.0
         }
        }
       ]
      }
     }
    ]
   },
   "expected": {
    "cases": [
     {
      "probBelowMinusEps": 0.5,
      "inPool": false
     },
     {
      "probBelowMinusEps": 0.49864804991488326,
      "inPool": true
     }
    ]
   },
   "note": "第一例：Y 三个数 (−0.5,−0.25,0)，预留 [−1.25,0.75]，都以 −ε=−0.25 为中点，P(Y<−ε) = 0.9×0.5+0.1×0.5 = 0.5（浮点下也正好 0.5），不严格小于一半，不入池。第二例把 q5 往上挪 2⁻¹⁰，把握略小于 0.5，入池。ε 取 0.25 是为了全部是二进制精确数。"
  },
  {
   "name": "V_method_example_X_Y",
   "section": "6.4 批内最好期望",
   "params": {},
   "input": {
    "Ymixtures": {
     "X": [
      {
       "weight": 0.5,
       "range": {
        "q1": -0.001,
        "q5": 0.0,
        "q9": 0.001
       }
      },
      {
       "weight": 0.5,
       "range": {
        "q1": 0.019,
        "q5": 0.02,
        "q9": 0.021
       }
      }
     ],
     "Y": [
      {
       "weight": 1,
       "range": {
        "q1": 0.009,
        "q5": 0.01,
        "q9": 0.011
       }
      }
     ]
    }
   },
   "expected": {
    "V": {
     "X": 0.010175,
     "Y": 0.01,
     "X,Y": 0.015
    }
   },
   "note": "方法示例换成窄范围（三个数严格递增）：X 一半在 0 附近、一半在 0.02 附近；Y 在 0.01 附近。输入是改进量上的混合（每个成分一个三个数）。V(X) ≈ 0.010175（0 附近那一半有一点低于 0、被截成 0），V(Y) ≈ 0.01，V(X,Y) ≈ 0.015。"
  },
  {
   "name": "batch_r1_real_k2",
   "section": "6.4 选批、分数尺读数；约定 10–14",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "direction": "maximize",
    "batchCap": 2
   },
   "input": {
    "b": 0.9597642169962064,
    "balance": 100,
    "candidates": {
     "r1-v1-c1": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 2.0,
        "q5": 2.45,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 2.2,
        "q5": 2.5,
        "q9": 2.62
       }
      },
      {
       "researcher": "researcher-3",
       "range": {
        "q1": 2.2,
        "q5": 2.5,
        "q9": 2.63
       }
      }
     ],
     "r1-v1-c2": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 1.85,
        "q5": 2.35,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 1.6,
        "q5": 2.35,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-3",
       "range": {
        "q1": 1.8,
        "q5": 2.4,
        "q9": 2.62
       }
      }
     ],
     "r1-v1-c3": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 2.3,
        "q5": 2.5,
        "q9": 2.62
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 2.42,
        "q5": 2.52,
        "q9": 2.6
       }
      },
      {
       "researcher": "researcher-3",
       "range": {
        "q1": 2.1,
        "q5": 2.5,
        "q9": 2.6
       }
      }
     ]
    }
   },
   "expected": {
    "pool": [
     "r1-v1-c1",
     "r1-v1-c2",
     "r1-v1-c3"
    ],
    "k": 2,
    "combos": [
     {
      "combo": [
       "r1-v1-c1",
       "r1-v1-c2"
      ],
      "V": 1.563610390779633
     },
     {
      "combo": [
       "r1-v1-c1",
       "r1-v1-c3"
      ],
      "V": 1.606671885433043
     },
     {
      "combo": [
       "r1-v1-c2",
       "r1-v1-c3"
      ],
      "V": 1.5843489675642095
     }
    ],
    "selected": [
     "r1-v1-c1",
     "r1-v1-c3"
    ],
    "selectedV": 1.606671885433043,
    "poolAllV": 1.6614292532574937,
    "rulerReading": 0.0547573678244507
   },
   "note": "真实第 1 轮，每批上限 2：三选二，列出三个组合的 V。分数尺读数 = E[max(0, max_池 Y)] − V(S*)。"
  },
  {
   "name": "batch_minimize_out_of_pool",
   "section": "6.4 选批、分数尺读数；约定 10–14",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "direction": "minimize",
    "batchCap": 2
   },
   "input": {
    "b": 0.4,
    "balance": 100,
    "candidates": {
     "c1": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.36,
        "q5": 0.38,
        "q9": 0.4
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.35,
        "q5": 0.37,
        "q9": 0.39
       }
      }
     ],
     "c2": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.33,
        "q5": 0.36,
        "q9": 0.41
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.37,
        "q5": 0.39,
        "q9": 0.42
       }
      }
     ],
     "c3": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.41,
        "q5": 0.43,
        "q9": 0.46
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.4,
        "q5": 0.42,
        "q9": 0.45
       }
      }
     ],
     "c4": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.37,
        "q5": 0.39,
        "q9": 0.4
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.38,
        "q5": 0.395,
        "q9": 0.41
       }
      }
     ]
    }
   },
   "expected": {
    "pool": [
     "c1",
     "c2",
     "c4"
    ],
    "k": 2,
    "combos": [
     {
      "combo": [
       "c1",
       "c2"
      ],
      "V": 0.042511208189058194
     },
     {
      "combo": [
       "c1",
       "c4"
      ],
      "V": 0.03455455687326872
     },
     {
      "combo": [
       "c2",
       "c4"
      ],
      "V": 0.03528487545879503
     }
    ],
    "selected": [
     "c1",
     "c2"
    ],
    "selectedV": 0.042511208189058194,
    "poolAllV": 0.04700708419008786,
    "rulerReading": 0.004495876001029669
   },
   "note": "越小越好，c3 在池外：只在池内 {c1,c2,c4} 里选二；分数尺读数只按池内候选算（约定 13），池外的 c3 不进。"
  },
  {
   "name": "batch_tie_by_id",
   "section": "6.4 选批、分数尺读数；约定 10–14",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "direction": "maximize",
    "batchCap": 1
   },
   "input": {
    "b": 2.45,
    "balance": 100,
    "candidates": {
     "c2": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 2.4,
        "q5": 2.5,
        "q9": 2.6
       }
      }
     ],
     "c10": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 2.4,
        "q5": 2.5,
        "q9": 2.6
       }
      }
     ]
    }
   },
   "expected": {
    "pool": [
     "c2",
     "c10"
    ],
    "k": 1,
    "combos": [
     {
      "combo": [
       "c2"
      ],
      "V": 0.07115624999999991
     },
     {
      "combo": [
       "c10"
      ],
      "V": 0.07115624999999991
     }
    ],
    "selected": [
     "c2"
    ],
    "selectedV": 0.07115624999999991,
    "poolAllV": 0.11286726562499991,
    "rulerReading": 0.041711015624999986
   },
   "note": "两个候选的范围完全相同，V 完全相等；按编号的自然序，c2 排在 c10 前面，选 c2。"
  },
  {
   "name": "batch_uniform_random_minimize",
   "section": "第十一部分 均匀随机；约定 12–14",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "direction": "minimize",
    "batchCap": 2
   },
   "input": {
    "b": 0.4,
    "balance": 100,
    "seed": "b05ff00c97f5436a04ba877196edf1e1dc5a25ede85acd190ec55eb4647a45e3",
    "seedFrom": {
     "studyId": "uniform-batch",
     "round": 1,
     "version": 1
    },
    "candidates": {
     "c1": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.36,
        "q5": 0.38,
        "q9": 0.4
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.35,
        "q5": 0.37,
        "q9": 0.39
       }
      }
     ],
     "c2": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.33,
        "q5": 0.36,
        "q9": 0.41
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.37,
        "q5": 0.39,
        "q9": 0.42
       }
      }
     ],
     "c3": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.41,
        "q5": 0.43,
        "q9": 0.46
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.4,
        "q5": 0.42,
        "q9": 0.45
       }
      }
     ],
     "c4": [
      {
       "researcher": "researcher-1",
       "range": {
        "q1": 0.37,
        "q5": 0.39,
        "q9": 0.4
       }
      },
      {
       "researcher": "researcher-2",
       "range": {
        "q1": 0.38,
        "q5": 0.395,
        "q9": 0.41
       }
      }
     ]
    }
   },
   "expected": {
    "pool": [
     "c1",
     "c2",
     "c4"
    ],
    "k": 2,
    "selected": [
     "c1",
     "c3"
    ],
    "selectedV": 0.03193200753116345,
    "poolAllV": 0.04700708419008786,
    "rulerReading": 0.015075076658924408
   },
   "note": "越小越好四候选，c3 在池外。均匀随机从全部四个候选里抽两个（编号按 JS 字符串序排好再做部分 Fisher–Yates），这个种子抽中了池外的 c3。selectedV = V(S*)；分数尺读数 = V(候选池 c1,c2,c4) − V(S*)。不列组合。"
  },
  {
   "name": "adoption_line_cases",
   "section": "6.5；约定 15",
   "params": {
    "eps": 0.01
   },
   "input": {
    "cases": [
     {
      "B": 2.6,
      "knownBest": null,
      "direction": "maximize",
      "note": "没有已知最好：ε"
     },
     {
      "B": 2.6,
      "knownBest": 2.635983,
      "direction": "maximize",
      "note": "正常：min(0.01, 0.035983/4=0.00899575)"
     },
     {
      "B": 2.6359,
      "knownBest": 2.635983,
      "direction": "maximize",
      "note": "下限：(K*−B)/4 < ε/100，取 ε/100 = 0.0001"
     },
     {
      "B": 2.64,
      "knownBest": 2.635983,
      "direction": "maximize",
      "note": "B 超过 K*：取 ε/100"
     },
     {
      "B": 2.5,
      "knownBest": 2.635983,
      "direction": "maximize",
      "note": "差距大：取上限 ε"
     },
     {
      "B": 0.4,
      "knownBest": 0.38,
      "direction": "minimize",
      "note": "越小越好：(B−K*)/4 = 0.005"
     },
     {
      "B": 0.37,
      "knownBest": 0.38,
      "direction": "minimize",
      "note": "越小越好、B 已比 K* 好：ε/100"
     }
    ]
   },
   "expected": {
    "lines": [
     0.01,
     0.008995749999999969,
     0.0001,
     0.0001,
     0.01,
     0.0050000000000000044,
     0.0001
    ]
   },
   "note": "逐例对应 input.cases。"
  },
  {
   "name": "adoption_decision_cases",
   "section": "6.5；约定 16",
   "params": {
    "eps": 0.01
   },
   "input": {
    "cases": [
     {
      "B": 2.6,
      "knownBest": 2.635983,
      "direction": "maximize",
      "results": {
       "c1": 2.605,
       "c2": 2.6185,
       "c3": null
      }
     },
     {
      "B": 2.6,
      "knownBest": null,
      "direction": "maximize",
      "results": {
       "c1": 2.61,
       "c2": 2.605
      }
     },
     {
      "B": 2.6,
      "knownBest": null,
      "direction": "maximize",
      "results": {
       "c1": 2.6125,
       "c2": 2.6125
      }
     },
     {
      "B": 0.4,
      "knownBest": null,
      "direction": "minimize",
      "results": {
       "c1": 0.385,
       "c2": 0.395
      }
     }
    ]
   },
   "expected": {
    "cases": [
     {
      "line": 0.008995749999999969,
      "best": "c2",
      "gain": 0.01849999999999996,
      "adopt": true
     },
     {
      "line": 0.01,
      "best": "c1",
      "gain": 0.009999999999999787,
      "adopt": false
     },
     {
      "line": 0.01,
      "best": "c1",
      "gain": 0.012499999999999734,
      "adopt": true
     },
     {
      "line": 0.01,
      "best": "c1",
      "gain": 0.015000000000000013,
      "adopt": true
     }
    ]
   },
   "note": "改进量 > 采纳线（严格）才采纳；同分取编号小的。第二例是'正好高 ε'：浮点输入 2.61、2.60 的精确差 = 0.009999999999999787（浮点减法 2.61-2.6 也是这个数），不大于 0.01，不采纳。"
  }
 ]
}