{
 "generator": "gen_ablation.py",
 "tolerance": {
  "exact": "有理数精确算出的量（G、撑、i、h、权重、成分期望收益、ĝ₀、voiFullExact、exactK1VOI、成本、m′）：绝对误差 1e-12",
  "grid": "网格 VOI 及由它得到的价值、净值：|差| ≤ 1e-12 + 1e-9·|值|（逐项浮点累加顺序不同，约 1e-13 量级）",
  "discrete": "标签、选中组合、原因、押的因子、状态：必须完全相同",
  "gridVsExact": "同一输入全测时 gridFullVOI 与 voiFullExact 的对照（两种算法之间，不是实现与本脚本之间）：k ≤ 3 时 |差| ≤ 5e-4·|精确值|，k = 4 时 ≤ 3e-3·|精确值|；本脚本实测相对差 7.3e-6（calc15，k=2）、4.7e-5（minimize，k=2）、1.05e-4（r1real，k=3，s=5–7）、1.0e-3（fourCells，k=4，s=1 和 0）。理由：网格用小段中点代表整段，误差随小段宽度平方缩小、随格数增多（m 变小）变大；s ≥ 1 时各成分在小段内是均匀分布，max 是凸函数，按 Jensen 不等式网格值不会超过精确值，所以还可以断言 gridFullVOI ≤ voiFullExact + 1e-12（fourCells 有 s = 0 的格，不适用）。"
 },
 "models": {
  "calc15": {
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "B": 0.9597642169962064,
    "full": 2.6276819772628,
    "knownBest": 2.635,
    "direction": "maximize",
    "cells": [
     "p1",
     "p2"
    ],
    "explanations": [
     {
      "id": "e1",
      "author": "researcher-1",
      "cells": {
       "p1": {
        "q1": 1.4,
        "q5": 1.75,
        "q9": 2.1
       },
       "p2": {
        "q1": 1.9,
        "q5": 2.05,
        "q9": 2.18
       }
      }
     },
     {
      "id": "e2",
      "author": "researcher-1",
      "cells": {
       "p1": {
        "q1": 1.9,
        "q5": 2.3,
        "q9": 2.55
       },
       "p2": {
        "q1": 1.8,
        "q5": 1.95,
        "q9": 2.1
       }
      }
     },
     {
      "id": "e3",
      "author": "researcher-1",
      "cells": {
       "p1": {
        "q1": 1.65,
        "q5": 2.05,
        "q9": 2.4
       },
       "p2": {
        "q1": 1.8,
        "q5": 1.98,
        "q9": 2.15
       }
      }
     },
     {
      "id": "e4",
      "author": "researcher-2",
      "cells": {
       "p1": {
        "q1": 2.3,
        "q5": 2.45,
        "q9": 2.58
       },
       "p2": {
        "q1": 1.85,
        "q5": 2.02,
        "q9": 2.18
       }
      }
     },
     {
      "id": "e5",
      "author": "researcher-2",
      "cells": {
       "p1": {
        "q1": 1.5,
        "q5": 1.95,
        "q9": 2.35
       },
       "p2": {
        "q1": 1.9,
        "q5": 2.06,
        "q9": 2.2
       }
      }
     },
     {
      "id": "e6",
      "author": "researcher-2",
      "cells": {
       "p1": {
        "q1": 1.8,
        "q5": 2.05,
        "q9": 2.3
       },
       "p2": {
        "q1": 1.85,
        "q5": 2,
        "q9": 2.15
       }
      }
     },
     {
      "id": "e7",
      "author": "researcher-3",
      "cells": {
       "p1": {
        "q1": 1.9,
        "q5": 2.15,
        "q9": 2.4
       },
       "p2": {
        "q1": 1.95,
        "q5": 2.1,
        "q9": 2.2
       }
      }
     },
     {
      "id": "e8",
      "author": "researcher-3",
      "cells": {
       "p1": {
        "q1": 2.25,
        "q5": 2.45,
        "q9": 2.55
       },
       "p2": {
        "q1": 1.7,
        "q5": 1.9,
        "q9": 2.05
       }
      }
     },
     {
      "id": "e9",
      "author": "researcher-3",
      "cells": {
       "p1": {
        "q1": 1.7,
        "q5": 1.95,
        "q9": 2.2
       },
       "p2": {
        "q1": 1.85,
        "q5": 2,
        "q9": 2.15
       }
      }
     }
    ]
   }
  },
  "r1real": {
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "B": 0.9597642169962064,
    "full": 1.552176048093269,
    "knownBest": 2.635983,
    "direction": "maximize",
    "cells": [
     "p1",
     "p2",
     "p3"
    ],
    "explanations": [
     {
      "id": "r1-e1-1",
      "author": "researcher-1",
      "cells": {
       "p1": {
        "q1": 1.2,
        "q5": 2,
        "q9": 2.44
       },
       "p2": {
        "q1": 1.49,
        "q5": 1.54,
        "q9": 1.58
       },
       "p3": {
        "q1": 2.3,
        "q5": 2.44,
        "q9": 2.45
       }
      }
     },
     {
      "id": "r1-e1-2",
      "author": "researcher-1",
      "cells": {
       "p1": {
        "q1": 1.22,
        "q5": 1.4,
        "q9": 1.52
       },
       "p2": {
        "q1": 1.49,
        "q5": 1.54,
        "q9": 1.58
       },
       "p3": {
        "q1": 1.2,
        "q5": 1.42,
        "q9": 1.55
       }
      }
     },
     {
      "id": "r1-e2-1",
      "author": "researcher-2",
      "cells": {
       "p1": {
        "q1": 1.05,
        "q5": 1.35,
        "q9": 1.95
       },
       "p2": {
        "q1": 1.44,
        "q5": 1.53,
        "q9": 1.59
       },
       "p3": {
        "q1": 0.85,
        "q5": 2.4,
        "q9": 2.45
       }
      }
     },
     {
      "id": "r1-e2-2",
      "author": "researcher-2",
      "cells": {
       "p1": {
        "q1": 0.95,
        "q5": 1.3,
        "q9": 2.1
       },
       "p2": {
        "q1": 1.4,
        "q5": 1.52,
        "q9": 1.62
       },
       "p3": {
        "q1": 0.6,
        "q5": 1.45,
        "q9": 2.45
       }
      }
     },
     {
      "id": "r1-e3-1",
      "author": "researcher-3",
      "cells": {
       "p1": {
        "q1": 1.15,
        "q5": 1.36,
        "q9": 1.55
       },
       "p2": {
        "q1": 1.49,
        "q5": 1.535,
        "q9": 1.58
       },
       "p3": {
        "q1": 1.8,
        "q5": 2.42,
        "q9": 2.58
       }
      }
     },
     {
      "id": "r1-e3-2",
      "author": "researcher-3",
      "cells": {
       "p1": {
        "q1": 1.2,
        "q5": 1.42,
        "q9": 2.46
       },
       "p2": {
        "q1": 1.5,
        "q5": 1.53,
        "q9": 1.58
       },
       "p3": {
        "q1": 1.9,
        "q5": 2.44,
        "q9": 2.57
       }
      }
     }
    ]
   }
  },
  "minimize": {
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "B": 0.4,
    "full": 0.35,
    "knownBest": 0.33,
    "direction": "minimize",
    "cells": [
     "p1",
     "p2"
    ],
    "explanations": [
     {
      "id": "e1",
      "author": "ra",
      "cells": {
       "p1": {
        "q1": 0.36,
        "q5": 0.37,
        "q9": 0.39
       },
       "p2": {
        "q1": 0.35,
        "q5": 0.36,
        "q9": 0.37
       }
      }
     },
     {
      "id": "e2",
      "author": "ra",
      "cells": {
       "p1": {
        "q1": 0.35,
        "q5": 0.355,
        "q9": 0.36
       },
       "p2": {
        "q1": 0.36,
        "q5": 0.38,
        "q9": 0.4
       }
      }
     },
     {
      "id": "e3",
      "author": "rb",
      "cells": {
       "p1": {
        "q1": 0.37,
        "q5": 0.38,
        "q9": 0.4
       },
       "p2": {
        "q1": 0.355,
        "q5": 0.365,
        "q9": 0.38
       }
      }
     }
    ]
   }
  },
  "fourCells": {
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "B": 0.9597642169962064,
    "full": 2.6276819772628,
    "knownBest": 2.635,
    "direction": "maximize",
    "cells": [
     "p1",
     "p2",
     "p3",
     "p4"
    ],
    "explanations": [
     {
      "id": "e1",
      "author": "researcher-1",
      "cells": {
       "p1": {
        "q1": 1.4,
        "q5": 1.75,
        "q9": 2.1
       },
       "p2": {
        "q1": 1.9,
        "q5": 2.05,
        "q9": 2.18
       },
       "p3": {
        "q1": 1.1,
        "q5": 1.45,
        "q9": 1.8
       },
       "p4": {
        "q1": 2.0,
        "q5": 2.15,
        "q9": 2.28
       }
      }
     },
     {
      "id": "e2",
      "author": "researcher-1",
      "cells": {
       "p1": {
        "q1": 1.9,
        "q5": 2.3,
        "q9": 2.55
       },
       "p2": {
        "q1": 1.8,
        "q5": 1.95,
        "q9": 2.1
       },
       "p3": {
        "q1": 1.6013,
        "q5": 2.0013,
        "q9": 2.2513
       },
       "p4": {
        "q1": 1.9007,
        "q5": 2.0507,
        "q9": 2.2007
       }
      }
     },
     {
      "id": "e3",
      "author": "researcher-1",
      "cells": {
       "p1": {
        "q1": 1.65,
        "q5": 2.05,
        "q9": 2.4
       },
       "p2": {
        "q1": 1.8,
        "q5": 1.98,
        "q9": 2.15
       },
       "p3": {
        "q1": 1.3526,
        "q5": 1.7526,
        "q9": 2.1026
       },
       "p4": {
        "q1": 1.9014,
        "q5": 2.0814,
        "q9": 2.2514
       }
      }
     },
     {
      "id": "e4",
      "author": "researcher-2",
      "cells": {
       "p1": {
        "q1": 2.3,
        "q5": 2.45,
        "q9": 2.58
       },
       "p2": {
        "q1": 1.85,
        "q5": 2.02,
        "q9": 2.18
       },
       "p3": {
        "q1": 2.0039,
        "q5": 2.1539,
        "q9": 2.2839
       },
       "p4": {
        "q1": 1.9521,
        "q5": 2.1221,
        "q9": 2.2821
       }
      }
     },
     {
      "id": "e5",
      "author": "researcher-2",
      "cells": {
       "p1": {
        "q1": 1.5,
        "q5": 1.95,
        "q9": 2.35
       },
       "p2": {
        "q1": 1.9,
        "q5": 2.06,
        "q9": 2.2
       },
       "p3": {
        "q1": 1.2052,
        "q5": 1.6552,
        "q9": 2.0552
       },
       "p4": {
        "q1": 2.0028,
        "q5": 2.1628,
        "q9": 2.3028
       }
      }
     },
     {
      "id": "e6",
      "author": "researcher-2",
      "cells": {
       "p1": {
        "q1": 1.8,
        "q5": 2.05,
        "q9": 2.3
       },
       "p2": {
        "q1": 1.85,
        "q5": 2,
        "q9": 2.15
       },
       "p3": {
        "q1": 1.5065,
        "q5": 1.7565,
        "q9": 2.0065
       },
       "p4": {
        "q1": 1.9535,
        "q5": 2.1035,
        "q9": 2.2535
       }
      }
     },
     {
      "id": "e7",
      "author": "researcher-3",
      "cells": {
       "p1": {
        "q1": 1.9,
        "q5": 2.15,
        "q9": 2.4
       },
       "p2": {
        "q1": 1.95,
        "q5": 2.1,
        "q9": 2.2
       },
       "p3": {
        "q1": 1.6078,
        "q5": 1.8578,
        "q9": 2.1078
       },
       "p4": {
        "q1": 2.0542,
        "q5": 2.2042,
        "q9": 2.3042
       }
      }
     },
     {
      "id": "e8",
      "author": "researcher-3",
      "cells": {
       "p1": {
        "q1": 2.25,
        "q5": 2.45,
        "q9": 2.55
       },
       "p2": {
        "q1": 1.7,
        "q5": 1.9,
        "q9": 2.05
       },
       "p3": {
        "q1": 1.9591,
        "q5": 2.1591,
        "q9": 2.2591
       },
       "p4": {
        "q1": 1.8049,
        "q5": 2.0049,
        "q9": 2.1549
       }
      }
     },
     {
      "id": "e9",
      "author": "researcher-3",
      "cells": {
       "p1": {
        "q1": 1.7,
        "q5": 1.95,
        "q9": 2.2
       },
       "p2": {
        "q1": 1.85,
        "q5": 2,
        "q9": 2.15
       },
       "p3": {
        "q1": 1.4104,
        "q5": 1.6604,
        "q9": 1.9104
       },
       "p4": {
        "q1": 1.9556,
        "q5": 2.1056,
        "q9": 2.2556
       }
      }
     }
    ]
   }
  },
  "gainNotPositive": {
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "B": 1.0,
    "full": 2.0,
    "knownBest": null,
    "direction": "maximize",
    "cells": [
     "p1",
     "p2"
    ],
    "explanations": [
     {
      "id": "e1",
      "author": "ra",
      "cells": {
       "p1": {
        "q1": 1.9,
        "q5": 2.0,
        "q9": 2.1
       },
       "p2": {
        "q1": 2.1,
        "q5": 2.2,
        "q9": 2.3
       }
      }
     },
     {
      "id": "e2",
      "author": "rb",
      "cells": {
       "p1": {
        "q1": 1.95,
        "q5": 2.0,
        "q9": 2.05
       },
       "p2": {
        "q1": 2.05,
        "q5": 2.15,
        "q9": 2.25
       }
      }
     }
    ]
   }
  },
  "negativeG0": {
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "B": 1.0,
    "full": 2.0,
    "knownBest": null,
    "direction": "maximize",
    "cells": [
     "p1",
     "p2"
    ],
    "explanations": [
     {
      "id": "e1",
      "author": "ra",
      "cells": {
       "p1": {
        "q1": 2.05,
        "q5": 2.15,
        "q9": 2.3
       },
       "p2": {
        "q1": 1.9,
        "q5": 2.1,
        "q9": 2.2
       }
      }
     },
     {
      "id": "e2",
      "author": "rb",
      "cells": {
       "p1": {
        "q1": 2.0,
        "q5": 2.1,
        "q9": 2.2
       },
       "p2": {
        "q1": 2.02,
        "q5": 2.08,
        "q9": 2.15
       }
      }
     },
     {
      "id": "e3",
      "author": "rb",
      "cells": {
       "p1": {
        "q1": 1.95,
        "q5": 2.05,
        "q9": 2.1
       },
       "p2": {
        "q1": 1.85,
        "q5": 2.0,
        "q9": 2.2
       }
      }
     }
    ]
   }
  }
 },
 "scenarios": [
  {
   "name": "label_method_example_independent",
   "section": "6.6；约定 17–19",
   "params": {},
   "input": {
    "B": 1.0,
    "full": 1.5,
    "direction": "maximize",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 1.45
     },
     {
      "factor": "p2",
      "kind": "valid",
      "value": 1.1
     }
    ]
   },
   "expected": {
    "G": 0.5,
    "supports": {
     "p1": 0.10000000000000009,
     "p2": 0.7999999999999998
    },
    "interaction": -0.10000000000000009,
    "label": "independent"
   },
   "note": "方法 6.6 示例：撑 0.10、0.80，i = −0.10，各管各（independent）。"
  },
  {
   "name": "label_calc15_substitute",
   "section": "6.6；约定 17–19",
   "params": {},
   "input": {
    "B": 0.9597642169962064,
    "full": 2.6276819772628,
    "direction": "maximize",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 2.5989997592071172
     },
     {
      "factor": "p2",
      "kind": "valid",
      "value": 1.7602769492805097
     }
    ]
   },
   "expected": {
    "G": 1.6679177602665936,
    "supports": {
     "p1": 0.017196422233131125,
     "p2": 0.5200526360746033
    },
    "interaction": -0.46275094169226555,
    "label": "substitute"
   },
   "note": "calc15 实测：撑 0.017、0.518，i ≈ −0.465 < −0.2，替代（substitute）。"
  },
  {
   "name": "label_r1_negative",
   "section": "6.6；约定 17–19",
   "params": {},
   "input": {
    "B": 0.9597642169962064,
    "full": 1.552176048093269,
    "direction": "maximize",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 2.250011787062861
     },
     {
      "factor": "p2",
      "kind": "valid",
      "value": 1.9535929459502979
     },
     {
      "factor": "p3",
      "kind": "valid",
      "value": 2.4389662413796342
     }
    ]
   },
   "expected": {
    "G": 0.5924118310970625,
    "supports": {
     "p1": -1.1779571276915577,
     "p2": -0.6775977061661005,
     "p3": -1.4969150626923773
    },
    "interaction": null,
    "label": "negative"
   },
   "note": "真实第 1 轮：三格关掉后分数都比完整高，撑全 < 0，negative（不贴标签，i 不给）。"
  },
  {
   "name": "label_incomplete_with_other_outcomes",
   "section": "6.6；约定 17–19",
   "params": {},
   "input": {
    "B": 1.0,
    "full": 1.5,
    "direction": "maximize",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 1.45
     },
     {
      "factor": "p2",
      "kind": "insufficient"
     },
     {
      "factor": "p3",
      "kind": "joint",
      "value": 1.2
     },
     {
      "factor": "p4",
      "kind": "untested"
     },
     {
      "factor": "p5",
      "kind": "cannotRun"
     }
    ]
   },
   "expected": {
    "G": 0.5,
    "supports": {
     "p1": 0.10000000000000009,
     "p2": null,
     "p3": null,
     "p4": null,
     "p5": null
    },
    "interaction": null,
    "label": "incomplete"
   },
   "note": "只有有效分数进标签：p2–p5 都不是 valid（joint 有分数也不算），有因子没有有效格 → incomplete。"
  },
  {
   "name": "label_negative_beats_incomplete",
   "section": "6.6；约定 17–19",
   "params": {},
   "input": {
    "B": 1.0,
    "full": 1.5,
    "direction": "maximize",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 1.6
     },
     {
      "factor": "p2",
      "kind": "insufficient"
     }
    ]
   },
   "expected": {
    "G": 0.5,
    "supports": {
     "p1": -0.20000000000000018,
     "p2": null
    },
    "interaction": null,
    "label": "negative"
   },
   "note": "表从上往下判：任一有效格撑 < 0 先命中 negative，即使另一格没有有效分数。"
  },
  {
   "name": "label_indispensable",
   "section": "6.6；约定 17–19",
   "params": {},
   "input": {
    "B": 1.0,
    "full": 2.0,
    "direction": "maximize",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 1.05
     },
     {
      "factor": "p2",
      "kind": "valid",
      "value": 1.0
     }
    ]
   },
   "expected": {
    "G": 1.0,
    "supports": {
     "p1": 0.95,
     "p2": 1.0
    },
    "interaction": 0.95,
    "label": "indispensable"
   },
   "note": "撑 0.95、1.0，都 > 0.9：缺一不可（indispensable），虽然 i = 0.95 > 0.2 也先命中这一条。"
  },
  {
   "name": "label_complementary",
   "section": "6.6；约定 17–19",
   "params": {},
   "input": {
    "B": 1.0,
    "full": 2.0,
    "direction": "maximize",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 1.3
     },
     {
      "factor": "p2",
      "kind": "valid",
      "value": 1.4
     }
    ]
   },
   "expected": {
    "G": 1.0,
    "supports": {
     "p1": 0.7,
     "p2": 0.6000000000000001
    },
    "interaction": 0.30000000000000004,
    "label": "complementary"
   },
   "note": "撑 0.7、0.6，i = 0.3 > 0.2：互补（complementary）。"
  },
  {
   "name": "label_boundary_exact_0.9",
   "section": "6.6；约定 17–19",
   "params": {},
   "input": {
    "B": 1.0,
    "full": 2.0,
    "direction": "maximize",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 1.0
     },
     {
      "factor": "p2",
      "kind": "valid",
      "value": 1.125
     }
    ]
   },
   "expected": {
    "G": 1.0,
    "supports": {
     "p1": 1.0,
     "p2": 0.875
    },
    "interaction": 0.875,
    "label": "complementary"
   },
   "note": "撑 1.0、0.875；0.875 不 > 0.9，不是缺一不可；i = 0.875 > 0.2 → 互补。用二进制精确数避免舍入。"
  },
  {
   "name": "label_minimize_substitute",
   "section": "6.6；约定 17–19",
   "params": {},
   "input": {
    "B": 0.4,
    "full": 0.35,
    "direction": "minimize",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 0.372
     },
     {
      "factor": "p2",
      "kind": "valid",
      "value": 0.361
     }
    ]
   },
   "expected": {
    "G": 0.050000000000000044,
    "supports": {
     "p1": 0.44,
     "p2": 0.22
    },
    "interaction": -0.34,
    "label": "substitute"
   },
   "note": "越小越好：G = 0.40−0.35；撑(p) = (x − 0.35)/G = 0.44、0.22；i = −0.34 → 替代。"
  },
  {
   "name": "label_G_not_positive",
   "section": "6.6；约定 17–19",
   "params": {},
   "input": {
    "B": 1.5,
    "full": 1.5,
    "direction": "maximize",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 1.45
     }
    ]
   },
   "expected": {
    "error": "totalGainNotPositive"
   },
   "note": "G = 0 时报错。"
  },
  {
   "name": "label_G_negative_minimize",
   "section": "6.6；约定 17–19",
   "params": {},
   "input": {
    "B": 0.4,
    "full": 0.41,
    "direction": "minimize",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 0.405
     }
    ]
   },
   "expected": {
    "error": "totalGainNotPositive"
   },
   "note": "越小越好时完整比基线还大，G < 0，报错。"
  },
  {
   "name": "confirm_r1_real",
   "section": "6.6 确认与否定、现有测法分不开；约定 21–22",
   "params": {},
   "input": {
    "model": "r1real",
    "valid": {
     "p1": 2.250011787062861,
     "p2": 1.9535929459502979,
     "p3": 2.4389662413796342
    }
   },
   "expected": {
    "verdicts": {
     "r1-e1-1": {
      "p1": "confirmed",
      "p2": "refuted",
      "p3": "confirmed"
     },
     "r1-e1-2": {
      "p1": "refuted",
      "p2": "refuted",
      "p3": "refuted"
     },
     "r1-e2-1": {
      "p1": "refuted",
      "p2": "refuted",
      "p3": "confirmed"
     },
     "r1-e2-2": {
      "p1": "refuted",
      "p2": "refuted",
      "p3": "confirmed"
     },
     "r1-e3-1": {
      "p1": "refuted",
      "p2": "refuted",
      "p3": "confirmed"
     },
     "r1-e3-2": {
      "p1": "confirmed",
      "p2": "refuted",
      "p3": "confirmed"
     }
    },
    "inseparableGroups": [
     [
      "r1-e1-1",
      "r1-e3-2"
     ],
     [
      "r1-e2-1",
      "r1-e2-2",
      "r1-e3-1"
     ]
    ]
   },
   "note": "落在 [q1,q9]（含两端）记确认。分不开：在全部 valid 格上确认/否定序列相同的两条以上解释为一组（组内按解释顺序）。"
  },
  {
   "name": "confirm_calc15",
   "section": "6.6 确认与否定、现有测法分不开；约定 21–22",
   "params": {},
   "input": {
    "model": "calc15",
    "valid": {
     "p1": 2.5989997592071172,
     "p2": 1.7602769492805097
    }
   },
   "expected": {
    "verdicts": {
     "e1": {
      "p1": "refuted",
      "p2": "refuted"
     },
     "e2": {
      "p1": "refuted",
      "p2": "refuted"
     },
     "e3": {
      "p1": "refuted",
      "p2": "refuted"
     },
     "e4": {
      "p1": "refuted",
      "p2": "refuted"
     },
     "e5": {
      "p1": "refuted",
      "p2": "refuted"
     },
     "e6": {
      "p1": "refuted",
      "p2": "refuted"
     },
     "e7": {
      "p1": "refuted",
      "p2": "refuted"
     },
     "e8": {
      "p1": "refuted",
      "p2": "confirmed"
     },
     "e9": {
      "p1": "refuted",
      "p2": "refuted"
     }
    },
    "inseparableGroups": [
     [
      "e1",
      "e2",
      "e3",
      "e4",
      "e5",
      "e6",
      "e7",
      "e9"
     ]
    ]
   },
   "note": "calc15 两格都有效。"
  },
  {
   "name": "confirm_endpoint_inclusive",
   "section": "6.6 确认与否定、现有测法分不开；约定 21–22",
   "params": {},
   "input": {
    "model": "gainNotPositive",
    "valid": {
     "p1": 2.1,
     "p2": 2.05
    }
   },
   "expected": {
    "verdicts": {
     "e1": {
      "p1": "confirmed",
      "p2": "refuted"
     },
     "e2": {
      "p1": "refuted",
      "p2": "confirmed"
     }
    },
    "inseparableGroups": []
   },
   "note": "端点：e1 的 p1 上沿正好 2.1、e2 的 p2 下沿正好 2.05，都算确认；e2 在 p1（上沿 2.05）否定，e1 在 p2（下沿 2.1）否定。"
  },
  {
   "name": "discovery_r1real",
   "section": "4.3 ⑰、6.5；约定 23",
   "params": {
    "eps": 0.01
   },
   "input": {
    "model": "r1real",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 2.250011787062861
     },
     {
      "factor": "p2",
      "kind": "valid",
      "value": 1.9535929459502979
     },
     {
      "factor": "p3",
      "kind": "valid",
      "value": 2.4389662413796342
     }
    ]
   },
   "expected": {
    "line": 0.01,
    "overLine": [
     "p1",
     "p2",
     "p3"
    ],
    "newBaseline": "p3"
   },
   "note": "B 取 f(完整)=1.5522，采纳线 min(0.01,(2.635983−1.5522)/4)=0.01。三格都过线，取分数最好的 p3。"
  },
  {
   "name": "discovery_calc15",
   "section": "4.3 ⑰、6.5；约定 23",
   "params": {
    "eps": 0.01
   },
   "input": {
    "model": "calc15",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 2.5989997592071172
     },
     {
      "factor": "p2",
      "kind": "joint",
      "value": 2.64
     }
    ]
   },
   "expected": {
    "line": 0.001829505684299959,
    "overLine": [
     "p2"
    ],
    "newBaseline": "p2"
   },
   "note": "采纳线 = (2.635−2.62768)/4 ≈ 0.00183；p1 低于完整不过线；p2 是构造的一起关格、分数 2.64（不是真实数据），参与并过线。"
  },
  {
   "name": "discovery_gainNotPositive",
   "section": "4.3 ⑰、6.5；约定 23",
   "params": {
    "eps": 0.01
   },
   "input": {
    "model": "gainNotPositive",
    "cells": [
     {
      "factor": "p1",
      "kind": "valid",
      "value": 2.5
     },
     {
      "factor": "p2",
      "kind": "valid",
      "value": 2.5
     }
    ]
   },
   "expected": {
    "line": 0.01,
    "overLine": [
     "p1",
     "p2"
    ],
    "newBaseline": "p1"
   },
   "note": "无已知最好，采纳线 ε；两格同分 2.5 都过线，取因子编号小的 p1。"
  },
  {
   "name": "voi_calc15",
   "section": "6.7 方向收益、成分与权重、信息价值；约定 24–27",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "calc15"
   },
   "expected": {
    "G": 1.6679177602665936,
    "h": 0.007318022737199836,
    "componentNames": [
     "e1",
     "e2",
     "e3",
     "e4",
     "e5",
     "e6",
     "e7",
     "e8",
     "e9",
     "reserve"
    ],
    "weights": [
     0.1,
     0.1,
     0.1,
     0.1,
     0.1,
     0.1,
     0.1,
     0.1,
     0.1,
     0.1
    ],
    "reserve": {
     "p1": [
      0.17499999999999982,
      3.675
     ],
     "p2": [
      1.0799999999999998,
      2.7600000000000007
     ]
    },
    "componentExpectedPayoff": {
     "e1": {
      "p1": 0.0038508473371091563,
      "p2": 0.0025653039409786215
     },
     "e2": {
      "p1": 0.001668056075761235,
      "p2": 0.002973343312446675
     },
     "e3": {
      "p1": 0.002611372902273402,
      "p2": 0.0028570740291788965
     },
     "e4": {
      "p1": 0.0008102958916536589,
      "p2": 0.0026815732242463997
     },
     "e5": {
      "p1": 0.003050124914604642,
      "p2": 0.002521428739745497
     },
     "e6": {
      "p1": 0.0025345913001154348,
      "p2": 0.0027539673062810547
     },
     "e7": {
      "p1": 0.0020958392877841944,
      "p2": 0.002391996896107781
     },
     "e8": {
      "p1": 0.0009331464551064064,
      "p2": 0.003269500920770263
     },
     "e9": {
      "p1": 0.002973343312446675,
      "p2": 0.0027539673062810547
     },
     "reserve": {
      "p1": 0.003083031315529486,
      "p2": 0.0031049689161460467
     }
    },
    "priorExpectedPayoff": {
     "p1": 0.002361064879238429,
     "p2": 0.002787312459218229
    },
    "g0": 0.002787312459218229,
    "voiFullExact": 0.0006313506372333815,
    "partial": [
     {
      "cells": [
       "p1"
      ],
      "voiGrid": 0.0005820672232162904,
      "grid": {
       "k": 1,
       "m": 4000000,
       "cells": {
        "p1": {
         "breakpoints": 32,
         "segments": 31,
         "s": 20,
         "subsegments": 620
        }
       },
       "method": "grid"
      },
      "exactK1VOI": 0.0005820672330401876,
      "gridMinusExact": -9.823897229553624e-12
     },
     {
      "cells": [
       "p2"
      ],
      "voiGrid": 0.00020536458175531578,
      "grid": {
       "k": 1,
       "m": 4000000,
       "cells": {
        "p2": {
         "breakpoints": 31,
         "segments": 30,
         "s": 20,
         "subsegments": 600
        }
       },
       "method": "grid"
      },
      "exactK1VOI": 0.00020536666249124859,
      "gridMinusExact": -2.0807359328090577e-09
     }
    ],
    "gridFullVOI": 0.0006313460547053657,
    "gridFullInfo": {
     "k": 2,
     "m": 2000,
     "cells": {
      "p1": {
       "breakpoints": 32,
       "segments": 31,
       "s": 20,
       "subsegments": 620
      },
      "p2": {
       "breakpoints": 31,
       "segments": 30,
       "s": 20,
       "subsegments": 600
      }
     }
    },
    "gridFullMinusExact": -4.582528015796387e-09
   },
   "note": "weights/componentExpectedPayoff 的成分顺序 = explanations 顺序 + reserve。voiFullExact：全部格都测，一维精确（有理数 Stieltjes 积分）。partial[].voiGrid：照约定 27 的网格。partial[].exactK1VOI：只测一格时的精确值，只用来看网格误差，实现不需要算。gridFullVOI：全测时也用网格算一份，与 voiFullExact 对照（gridFullMinusExact）。grid.cells 给出每格折点数、段数、s、小段数：网格折点在浮点上按 q1-(q5-q1)、q9+(q9-q5)、L-W/2、U+W/2 计算后去重，实现应先核对这几个数一致（差一个 ulp 就会多出一段宽约 2e-16 的段，例如 calc15 p1 里 1.0499999999999998 与 1.05 并存）。"
  },
  {
   "name": "voi_r1real",
   "section": "6.7 方向收益、成分与权重、信息价值；约定 24–27",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "r1real"
   },
   "expected": {
    "G": 0.5924118310970625,
    "h": 1.083806951906731,
    "componentNames": [
     "r1-e1-1",
     "r1-e1-2",
     "r1-e2-1",
     "r1-e2-2",
     "r1-e3-1",
     "r1-e3-2",
     "reserve"
    ],
    "weights": [
     0.15,
     0.15,
     0.15,
     0.15,
     0.15,
     0.15,
     0.1
    ],
    "reserve": {
     "p1": [
      -1.1500000000000001,
      5.05
     ],
     "p2": [
      1.0599999999999996,
      1.9400000000000004
     ],
     "p3": [
      -2.7750000000000004,
      5.525
     ]
    },
    "componentExpectedPayoff": {
     "r1-e1-1": {
      "p1": -0.5887712197116215,
      "p2": 0.028679052324877385,
      "p3": -1.5410167503634666
     },
     "r1-e1-2": {
      "p1": 0.316822512608577,
      "p2": 0.028679052324877385,
      "p3": 0.29944243087717926
     },
     "r1-e2-1": {
      "p1": 0.1777818587573949,
      "p2": 0.059780251212641806,
      "p3": -0.5906007019991372
     },
     "r1-e2-2": {
      "p1": 0.17320815303860604,
      "p2": 0.0716718860814929,
      "p3": 0.09088145010040616
     },
     "r1-e3-1": {
      "p1": 0.3643890520839813,
      "p2": 0.031423275756150774,
      "p3": -1.2931219004051093
     },
     "r1-e3-2": {
      "p1": -0.28324767769652415,
      "p2": 0.02776431118111961,
      "p3": -1.3617274861869422
     },
     "reserve": {
      "p1": -0.7278118735628034,
      "p2": 0.09545515581919511,
      "p3": 0.32414044175863876
     }
    },
    "priorExpectedPayoff": {
     "p1": -0.0487537854942183,
     "p2": 0.04674518991409349,
     "p3": -0.6270073995206966
    },
    "g0": 0.04674518991409349,
    "voiFullExact": 0.6768856765570694,
    "partial": [
     {
      "cells": [
       "p1"
      ],
      "voiGrid": 0.3932819565009106,
      "grid": {
       "k": 1,
       "m": 4000000,
       "cells": {
        "p1": {
         "breakpoints": 31,
         "segments": 30,
         "s": 20,
         "subsegments": 600
        }
       },
       "method": "grid"
      },
      "exactK1VOI": 0.39328196654270475,
      "gridMinusExact": -1.0041794173965002e-08
     },
     {
      "cells": [
       "p2"
      ],
      "voiGrid": 0.04469391965086199,
      "grid": {
       "k": 1,
       "m": 4000000,
       "cells": {
        "p2": {
         "breakpoints": 21,
         "segments": 20,
         "s": 20,
         "subsegments": 400
        }
       },
       "method": "grid"
      },
      "exactK1VOI": 0.04469959609954742,
      "gridMinusExact": -5.676448685432156e-06
     },
     {
      "cells": [
       "p3"
      ],
      "voiGrid": 0.41273577238295406,
      "grid": {
       "k": 1,
       "m": 4000000,
       "cells": {
        "p3": {
         "breakpoints": 29,
         "segments": 28,
         "s": 20,
         "subsegments": 560
        }
       },
       "method": "grid"
      },
      "exactK1VOI": 0.41273577238295456,
      "gridMinusExact": -4.996003610813204e-16
     },
     {
      "cells": [
       "p1",
       "p2"
      ],
      "voiGrid": 0.40801451007605366,
      "grid": {
       "k": 2,
       "m": 2000,
       "cells": {
        "p1": {
         "breakpoints": 31,
         "segments": 30,
         "s": 20,
         "subsegments": 600
        },
        "p2": {
         "breakpoints": 21,
         "segments": 20,
         "s": 20,
         "subsegments": 400
        }
       },
       "method": "grid"
      }
     },
     {
      "cells": [
       "p1",
       "p3"
      ],
      "voiGrid": 0.6745232756112371,
      "grid": {
       "k": 2,
       "m": 2000,
       "cells": {
        "p1": {
         "breakpoints": 31,
         "segments": 30,
         "s": 20,
         "subsegments": 600
        },
        "p3": {
         "breakpoints": 29,
         "segments": 28,
         "s": 20,
         "subsegments": 560
        }
       },
       "method": "grid"
      }
     },
     {
      "cells": [
       "p2",
       "p3"
      ],
      "voiGrid": 0.43115260873837397,
      "grid": {
       "k": 2,
       "m": 2000,
       "cells": {
        "p2": {
         "breakpoints": 21,
         "segments": 20,
         "s": 20,
         "subsegments": 400
        },
        "p3": {
         "breakpoints": 29,
         "segments": 28,
         "s": 20,
         "subsegments": 560
        }
       },
       "method": "grid"
      }
     }
    ],
    "gridFullVOI": 0.6768144593327583,
    "gridFullInfo": {
     "k": 3,
     "m": 158,
     "cells": {
      "p1": {
       "breakpoints": 31,
       "segments": 30,
       "s": 5,
       "subsegments": 150
      },
      "p2": {
       "breakpoints": 21,
       "segments": 20,
       "s": 7,
       "subsegments": 140
      },
      "p3": {
       "breakpoints": 29,
       "segments": 28,
       "s": 5,
       "subsegments": 140
      }
     }
    },
    "gridFullMinusExact": -7.121722431113753e-05
   },
   "note": "weights/componentExpectedPayoff 的成分顺序 = explanations 顺序 + reserve。voiFullExact：全部格都测，一维精确（有理数 Stieltjes 积分）。partial[].voiGrid：照约定 27 的网格。partial[].exactK1VOI：只测一格时的精确值，只用来看网格误差，实现不需要算。gridFullVOI：全测时也用网格算一份，与 voiFullExact 对照（gridFullMinusExact）。grid.cells 给出每格折点数、段数、s、小段数：网格折点在浮点上按 q1-(q5-q1)、q9+(q9-q5)、L-W/2、U+W/2 计算后去重，实现应先核对这几个数一致（差一个 ulp 就会多出一段宽约 2e-16 的段，例如 calc15 p1 里 1.0499999999999998 与 1.05 并存）。"
  },
  {
   "name": "voi_minimize",
   "section": "6.7 方向收益、成分与权重、信息价值；约定 24–27",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "minimize"
   },
   "expected": {
    "G": 0.050000000000000044,
    "h": 0.019999999999999962,
    "componentNames": [
     "e1",
     "e2",
     "e3",
     "reserve"
    ],
    "weights": [
     0.225,
     0.225,
     0.45,
     0.1
    ],
    "reserve": {
     "p1": [
      0.30749999999999994,
      0.4575000000000001
     ],
     "p2": [
      0.29999999999999993,
      0.4600000000000001
     ]
    },
    "componentExpectedPayoff": {
     "e1": {
      "p1": 0.009399999999999983,
      "p2": 0.003999999999999992
     },
     "e2": {
      "p1": 0.001999999999999996,
      "p2": 0.011999999999999978
     },
     "e3": {
      "p1": 0.013399999999999974,
      "p2": 0.006699999999999987
     },
     "reserve": {
      "p1": 0.012999999999999975,
      "p2": 0.011999999999999978
     }
    },
    "priorExpectedPayoff": {
     "p1": 0.009894999999999982,
     "p2": 0.007814999999999985
    },
    "g0": 0.009894999999999982,
    "voiFullExact": 0.003645968749999993,
    "partial": [
     {
      "cells": [
       "p1"
      ],
      "voiGrid": 0.0029590833333333205,
      "grid": {
       "k": 1,
       "m": 4000000,
       "cells": {
        "p1": {
         "breakpoints": 13,
         "segments": 12,
         "s": 20,
         "subsegments": 240
        }
       },
       "method": "grid"
      },
      "exactK1VOI": 0.002959083333333328,
      "gridMinusExact": -7.37257477290143e-18
     },
     {
      "cells": [
       "p2"
      ],
      "voiGrid": 0.0026489437499999935,
      "grid": {
       "k": 1,
       "m": 4000000,
       "cells": {
        "p2": {
         "breakpoints": 13,
         "segments": 12,
         "s": 20,
         "subsegments": 240
        }
       },
       "method": "grid"
      },
      "exactK1VOI": 0.0026490793951612856,
      "gridMinusExact": -1.3564516129207713e-07
     }
    ],
    "gridFullVOI": 0.0036457966536462376,
    "gridFullInfo": {
     "k": 2,
     "m": 2000,
     "cells": {
      "p1": {
       "breakpoints": 13,
       "segments": 12,
       "s": 20,
       "subsegments": 240
      },
      "p2": {
       "breakpoints": 13,
       "segments": 12,
       "s": 20,
       "subsegments": 240
      }
     }
    },
    "gridFullMinusExact": -1.7209635375537574e-07
   },
   "note": "weights/componentExpectedPayoff 的成分顺序 = explanations 顺序 + reserve。voiFullExact：全部格都测，一维精确（有理数 Stieltjes 积分）。partial[].voiGrid：照约定 27 的网格。partial[].exactK1VOI：只测一格时的精确值，只用来看网格误差，实现不需要算。gridFullVOI：全测时也用网格算一份，与 voiFullExact 对照（gridFullMinusExact）。grid.cells 给出每格折点数、段数、s、小段数：网格折点在浮点上按 q1-(q5-q1)、q9+(q9-q5)、L-W/2、U+W/2 计算后去重，实现应先核对这几个数一致（差一个 ulp 就会多出一段宽约 2e-16 的段，例如 calc15 p1 里 1.0499999999999998 与 1.05 并存）。"
  },
  {
   "name": "voi_fourCells",
   "section": "6.7 方向收益、成分与权重、信息价值；约定 24–27",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "fourCells"
   },
   "expected": {
    "G": 1.6679177602665936,
    "h": 0.007318022737199836,
    "componentNames": [
     "e1",
     "e2",
     "e3",
     "e4",
     "e5",
     "e6",
     "e7",
     "e8",
     "e9",
     "reserve"
    ],
    "weights": [
     0.1,
     0.1,
     0.1,
     0.1,
     0.1,
     0.1,
     0.1,
     0.1,
     0.1,
     0.1
    ],
    "reserve": {
     "p1": [
      0.17499999999999982,
      3.675
     ],
     "p2": [
      1.0799999999999998,
      2.7600000000000007
     ],
     "p3": [
      -0.1256499999999997,
      3.37695
     ],
     "p4": [
      1.1859499999999996,
      2.8617500000000002
     ]
    },
    "componentExpectedPayoff": {
     "e1": {
      "p1": 0.0038508473371091563,
      "p2": 0.0025653039409786215,
      "p3": 0.005167103374102878,
      "p4": 0.002126551928647381
     },
     "e2": {
      "p1": 0.001668056075761235,
      "p2": 0.002973343312446675,
      "p3": 0.00297860833659465,
      "p4": 0.002531520036029116
     },
     "e3": {
      "p1": 0.002611372902273402,
      "p2": 0.0028570740291788965,
      "p3": 0.003916221386946511,
      "p4": 0.002412179488675019
     },
     "e4": {
      "p1": 0.0008102958916536589,
      "p2": 0.0026815732242463997,
      "p3": 0.0021094406001664623,
      "p4": 0.0022336074196562038
     },
     "e5": {
      "p1": 0.003050124914604642,
      "p2": 0.002521428739745497,
      "p3": 0.004343565846957139,
      "p4": 0.002070391671068982
     },
     "e6": {
      "p1": 0.0025345913001154348,
      "p2": 0.0027539673062810547,
      "p3": 0.0038223284563076256,
      "p4": 0.002299858973518221
     },
     "e7": {
      "p1": 0.0020958392877841944,
      "p2": 0.002391996896107781,
      "p3": 0.003377872667816079,
      "p4": 0.001934817299258629
     },
     "e8": {
      "p1": 0.0009331464551064064,
      "p2": 0.003269500920770263,
      "p3": 0.002209476058977985,
      "p4": 0.002809250059834791
     },
     "e9": {
      "p1": 0.002973343312446675,
      "p2": 0.0027539673062810547,
      "p3": 0.004243969140157947,
      "p4": 0.002290645181259265
     },
     "reserve": {
      "p1": 0.003083031315529486,
      "p2": 0.0031049689161460467,
      "p3": 0.004396435464443053,
      "p4": 0.0026493249513400543
     }
    },
    "priorExpectedPayoff": {
     "p1": 0.002361064879238429,
     "p2": 0.002787312459218229,
     "p3": 0.003656502133247033,
     "p4": 0.0023358147009287663
    },
    "g0": 0.003656502133247033,
    "voiFullExact": 0.0007241714702604439,
    "partial": [
     {
      "cells": [
       "p1",
       "p2",
       "p3"
      ],
      "voiGrid": 0.0006802215037563838,
      "grid": {
       "k": 3,
       "m": 158,
       "cells": {
        "p1": {
         "breakpoints": 32,
         "segments": 31,
         "s": 5,
         "subsegments": 155
        },
        "p2": {
         "breakpoints": 31,
         "segments": 30,
         "s": 5,
         "subsegments": 150
        },
        "p3": {
         "breakpoints": 47,
         "segments": 46,
         "s": 3,
         "subsegments": 138
        }
       },
       "method": "grid"
      }
     }
    ],
    "gridFullVOI": 0.0007234478512161647,
    "gridFullInfo": {
     "k": 4,
     "m": 44,
     "cells": {
      "p1": {
       "breakpoints": 32,
       "segments": 31,
       "s": 1,
       "subsegments": 31
      },
      "p2": {
       "breakpoints": 31,
       "segments": 30,
       "s": 1,
       "subsegments": 30
      },
      "p3": {
       "breakpoints": 47,
       "segments": 46,
       "s": 0,
       "subsegments": 44
      },
      "p4": {
       "breakpoints": 47,
       "segments": 46,
       "s": 0,
       "subsegments": 44
      }
     }
    },
    "gridFullMinusExact": -7.236190442791619e-07
   },
   "note": "weights/componentExpectedPayoff 的成分顺序 = explanations 顺序 + reserve。voiFullExact：全部格都测，一维精确（有理数 Stieltjes 积分）。partial[].voiGrid：照约定 27 的网格。partial[].exactK1VOI：只测一格时的精确值，只用来看网格误差，实现不需要算。gridFullVOI：全测时也用网格算一份，与 voiFullExact 对照（gridFullMinusExact）。grid.cells 给出每格折点数、段数、s、小段数：网格折点在浮点上按 q1-(q5-q1)、q9+(q9-q5)、L-W/2、U+W/2 计算后去重，实现应先核对这几个数一致（差一个 ulp 就会多出一段宽约 2e-16 的段，例如 calc15 p1 里 1.0499999999999998 与 1.05 并存）。"
  },
  {
   "name": "voi_negativeG0",
   "section": "6.7 方向收益、成分与权重、信息价值；约定 24–27",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "negativeG0"
   },
   "expected": {
    "G": 1.0,
    "h": 1.0,
    "componentNames": [
     "e1",
     "e2",
     "e3",
     "reserve"
    ],
    "weights": [
     0.45,
     0.225,
     0.225,
     0.1
    ],
    "reserve": {
     "p1": [
      1.5500000000000003,
      2.7499999999999996
     ],
     "p2": [
      1.3499999999999994,
      2.750000000000001
     ]
    },
    "componentExpectedPayoff": {
     "e1": {
      "p1": -0.16749999999999984,
      "p2": -0.06500000000000006
     },
     "e2": {
      "p1": -0.10000000000000009,
      "p2": -0.08349999999999999
     },
     "e3": {
      "p1": -0.03249999999999996,
      "p2": -0.017500000000000092
     },
     "reserve": {
      "p1": -0.1499999999999999,
      "p2": -0.050000000000000044
     }
    },
    "priorExpectedPayoff": {
     "p1": -0.12018749999999993,
     "p2": -0.05697500000000005
    },
    "g0": -0.05697500000000005,
    "voiFullExact": 0.049642821428571494,
    "partial": [
     {
      "cells": [
       "p1"
      ],
      "voiGrid": 0.023196666666666692,
      "grid": {
       "k": 1,
       "m": 4000000,
       "cells": {
        "p1": {
         "breakpoints": 15,
         "segments": 14,
         "s": 20,
         "subsegments": 280
        }
       },
       "method": "grid"
      },
      "exactK1VOI": 0.02319666666666669,
      "gridMinusExact": 3.469446951953614e-18
     },
     {
      "cells": [
       "p2"
      ],
      "voiGrid": 0.029396450892857223,
      "grid": {
       "k": 1,
       "m": 4000000,
       "cells": {
        "p2": {
         "breakpoints": 16,
         "segments": 15,
         "s": 20,
         "subsegments": 300
        }
       },
       "method": "grid"
      },
      "exactK1VOI": 0.02939925782355029,
      "gridMinusExact": -2.8069306930653126e-06
     }
    ],
    "gridFullVOI": 0.04964022946875037,
    "gridFullInfo": {
     "k": 2,
     "m": 2000,
     "cells": {
      "p1": {
       "breakpoints": 15,
       "segments": 14,
       "s": 20,
       "subsegments": 280
      },
      "p2": {
       "breakpoints": 16,
       "segments": 15,
       "s": 20,
       "subsegments": 300
      }
     }
    },
    "gridFullMinusExact": -2.591959821121592e-06
   },
   "note": "weights/componentExpectedPayoff 的成分顺序 = explanations 顺序 + reserve。voiFullExact：全部格都测，一维精确（有理数 Stieltjes 积分）。partial[].voiGrid：照约定 27 的网格。partial[].exactK1VOI：只测一格时的精确值，只用来看网格误差，实现不需要算。gridFullVOI：全测时也用网格算一份，与 voiFullExact 对照（gridFullMinusExact）。grid.cells 给出每格折点数、段数、s、小段数：网格折点在浮点上按 q1-(q5-q1)、q9+(q9-q5)、L-W/2、U+W/2 计算后去重，实现应先核对这几个数一致（差一个 ulp 就会多出一段宽约 2e-16 的段，例如 calc15 p1 里 1.0499999999999998 与 1.05 并存）。"
  },
  {
   "name": "select_calc15",
   "section": "6.7 价值减成本、选格；约定 28–29、文末",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "calc15",
    "balances": [
     0,
     1,
     2,
     3,
     10
    ]
   },
   "expected": {
    "g0": 0.002787312459218229,
    "byBalance": [
     {
      "balance": 0,
      "combos": [],
      "selected": [],
      "selectedNet": 0.0,
      "unselected": {
       "p1": {
        "reason": "insufficientBudget",
        "bestCombo": null,
        "bestNet": null
       },
       "p2": {
        "reason": "insufficientBudget",
        "bestCombo": null,
        "bestNet": null
       }
      },
      "fullRule": {
       "selected": [],
       "insufficientBudget": [
        "p1",
        "p2"
       ]
      }
     },
     {
      "balance": 1,
      "combos": [],
      "selected": [],
      "selectedNet": 0.0,
      "unselected": {
       "p1": {
        "reason": "insufficientBudget",
        "bestCombo": null,
        "bestNet": null
       },
       "p2": {
        "reason": "insufficientBudget",
        "bestCombo": null,
        "bestNet": null
       }
      },
      "fullRule": {
       "selected": [],
       "insufficientBudget": [
        "p1",
        "p2"
       ]
      }
     },
     {
      "balance": 2,
      "combos": [
       {
        "combo": [
         "p1"
        ],
        "voi": 0.0005820672232162904,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.0002910336116081452,
        "cost": 0.0004645520765363715,
        "net": -0.0001735184649282263
       },
       {
        "combo": [
         "p2"
        ],
        "voi": 0.00020536458175531578,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.00010268229087765789,
        "cost": 0.0004645520765363715,
        "net": -0.0003618697856587136
       }
      ],
      "selected": [],
      "selectedNet": 0.0,
      "unselected": {
       "p1": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p1"
        ],
        "bestNet": -0.0001735184649282263
       },
       "p2": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p2"
        ],
        "bestNet": -0.0003618697856587136
       }
      },
      "fullRule": {
       "selected": [
        "p1"
       ],
       "insufficientBudget": [
        "p2"
       ]
      }
     },
     {
      "balance": 3,
      "combos": [
       {
        "combo": [
         "p1"
        ],
        "voi": 0.0005820672232162904,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.0002910336116081452,
        "cost": 0.0004645520765363715,
        "net": -0.0001735184649282263
       },
       {
        "combo": [
         "p2"
        ],
        "voi": 0.00020536458175531578,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.00010268229087765789,
        "cost": 0.0004645520765363715,
        "net": -0.0003618697856587136
       },
       {
        "combo": [
         "p1",
         "p2"
        ],
        "voi": 0.0006313506372333815,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.00031567531861669077,
        "cost": 0.0007432833224581943,
        "net": -0.00042760800384150356
       }
      ],
      "selected": [],
      "selectedNet": 0.0,
      "unselected": {
       "p1": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p1"
        ],
        "bestNet": -0.0001735184649282263
       },
       "p2": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p2"
        ],
        "bestNet": -0.0003618697856587136
       }
      },
      "fullRule": {
       "selected": [
        "p1",
        "p2"
       ],
       "insufficientBudget": []
      }
     },
     {
      "balance": 10,
      "combos": [
       {
        "combo": [
         "p1"
        ],
        "voi": 0.0005820672232162904,
        "Rhat": 5,
        "mPrime": 1.9375,
        "value": 0.0005638776224907813,
        "cost": 0.0004645520765363715,
        "net": 9.932554595440982e-05
       },
       {
        "combo": [
         "p2"
        ],
        "voi": 0.00020536458175531578,
        "Rhat": 5,
        "mPrime": 1.9375,
        "value": 0.00019894693857546217,
        "cost": 0.0004645520765363715,
        "net": -0.00026560513796090933
       },
       {
        "combo": [
         "p1",
         "p2"
        ],
        "voi": 0.0006313506372333815,
        "Rhat": 4,
        "mPrime": 1.875,
        "value": 0.0005918912224062952,
        "cost": 0.0007432833224581943,
        "net": -0.00015139210005189914
       }
      ],
      "selected": [
       "p1"
      ],
      "selectedNet": 9.932554595440982e-05,
      "unselected": {
       "p2": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p1",
         "p2"
        ],
        "bestNet": -0.00015139210005189914
       }
      },
      "fullRule": {
       "selected": [
        "p1",
        "p2"
       ],
       "insufficientBudget": []
      }
     }
    ]
   },
   "note": "余额 0、1 不做消融，各格 reason=insufficientBudget、bestCombo=null；余额 2 只能选单格；余额 3 起可以两格全测（VOI 用一维精确值），部分格用网格。R̂ = ⌈(余额−|S|)/每批上限⌉，m′ = Σ_{j<R̂} 0.5^j，成本 = 2·max(0,ĝ₀)·[(K+|S|)/(K+|S|+1) − K/(K+1)]。unselected 里附“含这一格的可选组合中净值最大的那个”。fullRule = 全测规则（格数超过余额−1 时按编号取前余额−1 格）。"
  },
  {
   "name": "select_r1real",
   "section": "6.7 价值减成本、选格；约定 28–29、文末",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "r1real",
    "balances": [
     0,
     1,
     2,
     4,
     12
    ]
   },
   "expected": {
    "g0": 0.04674518991409349,
    "byBalance": [
     {
      "balance": 0,
      "combos": [],
      "selected": [],
      "selectedNet": 0.0,
      "unselected": {
       "p1": {
        "reason": "insufficientBudget",
        "bestCombo": null,
        "bestNet": null
       },
       "p2": {
        "reason": "insufficientBudget",
        "bestCombo": null,
        "bestNet": null
       },
       "p3": {
        "reason": "insufficientBudget",
        "bestCombo": null,
        "bestNet": null
       }
      },
      "fullRule": {
       "selected": [],
       "insufficientBudget": [
        "p1",
        "p2",
        "p3"
       ]
      }
     },
     {
      "balance": 1,
      "combos": [],
      "selected": [],
      "selectedNet": 0.0,
      "unselected": {
       "p1": {
        "reason": "insufficientBudget",
        "bestCombo": null,
        "bestNet": null
       },
       "p2": {
        "reason": "insufficientBudget",
        "bestCombo": null,
        "bestNet": null
       },
       "p3": {
        "reason": "insufficientBudget",
        "bestCombo": null,
        "bestNet": null
       }
      },
      "fullRule": {
       "selected": [],
       "insufficientBudget": [
        "p1",
        "p2",
        "p3"
       ]
      }
     },
     {
      "balance": 2,
      "combos": [
       {
        "combo": [
         "p1"
        ],
        "voi": 0.3932819565009106,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.1966409782504553,
        "cost": 0.007790864985682248,
        "net": 0.18885011326477305
       },
       {
        "combo": [
         "p2"
        ],
        "voi": 0.04469391965086199,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.022346959825430994,
        "cost": 0.007790864985682248,
        "net": 0.014556094839748745
       },
       {
        "combo": [
         "p3"
        ],
        "voi": 0.41273577238295406,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.20636788619147703,
        "cost": 0.007790864985682248,
        "net": 0.1985770212057948
       }
      ],
      "selected": [
       "p3"
      ],
      "selectedNet": 0.1985770212057948,
      "unselected": {
       "p1": {
        "reason": "insufficientBudget",
        "bestCombo": [
         "p1"
        ],
        "bestNet": 0.18885011326477305
       },
       "p2": {
        "reason": "insufficientBudget",
        "bestCombo": [
         "p2"
        ],
        "bestNet": 0.014556094839748745
       }
      },
      "fullRule": {
       "selected": [
        "p1"
       ],
       "insufficientBudget": [
        "p2",
        "p3"
       ]
      }
     },
     {
      "balance": 4,
      "combos": [
       {
        "combo": [
         "p1"
        ],
        "voi": 0.3932819565009106,
        "Rhat": 2,
        "mPrime": 1.5,
        "value": 0.29496146737568296,
        "cost": 0.007790864985682248,
        "net": 0.2871706023900007
       },
       {
        "combo": [
         "p2"
        ],
        "voi": 0.04469391965086199,
        "Rhat": 2,
        "mPrime": 1.5,
        "value": 0.03352043973814649,
        "cost": 0.007790864985682248,
        "net": 0.02572957475246424
       },
       {
        "combo": [
         "p3"
        ],
        "voi": 0.41273577238295406,
        "Rhat": 2,
        "mPrime": 1.5,
        "value": 0.30955182928721553,
        "cost": 0.007790864985682248,
        "net": 0.30176096430153326
       },
       {
        "combo": [
         "p1",
         "p2"
        ],
        "voi": 0.40801451007605366,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.20400725503802683,
        "cost": 0.012465383977091597,
        "net": 0.19154187106093523
       },
       {
        "combo": [
         "p1",
         "p3"
        ],
        "voi": 0.6745232756112371,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.3372616378056186,
        "cost": 0.012465383977091597,
        "net": 0.324796253828527
       },
       {
        "combo": [
         "p2",
         "p3"
        ],
        "voi": 0.43115260873837397,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.21557630436918698,
        "cost": 0.012465383977091597,
        "net": 0.20311092039209538
       },
       {
        "combo": [
         "p1",
         "p2",
         "p3"
        ],
        "voi": 0.6768856765570694,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.3384428382785347,
        "cost": 0.015581729971364497,
        "net": 0.32286110830717024
       }
      ],
      "selected": [
       "p1",
       "p3"
      ],
      "selectedNet": 0.324796253828527,
      "unselected": {
       "p2": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p1",
         "p2",
         "p3"
        ],
        "bestNet": 0.32286110830717024
       }
      },
      "fullRule": {
       "selected": [
        "p1",
        "p2",
        "p3"
       ],
       "insufficientBudget": []
      }
     },
     {
      "balance": 12,
      "combos": [
       {
        "combo": [
         "p1"
        ],
        "voi": 0.3932819565009106,
        "Rhat": 6,
        "mPrime": 1.96875,
        "value": 0.38713692593058385,
        "cost": 0.007790864985682248,
        "net": 0.3793460609449016
       },
       {
        "combo": [
         "p2"
        ],
        "voi": 0.04469391965086199,
        "Rhat": 6,
        "mPrime": 1.96875,
        "value": 0.04399557715631727,
        "cost": 0.007790864985682248,
        "net": 0.03620471217063503
       },
       {
        "combo": [
         "p3"
        ],
        "voi": 0.41273577238295406,
        "Rhat": 6,
        "mPrime": 1.96875,
        "value": 0.4062867759394704,
        "cost": 0.007790864985682248,
        "net": 0.3984959109537881
       },
       {
        "combo": [
         "p1",
         "p2"
        ],
        "voi": 0.40801451007605366,
        "Rhat": 5,
        "mPrime": 1.9375,
        "value": 0.395264056636177,
        "cost": 0.012465383977091597,
        "net": 0.3827986726590854
       },
       {
        "combo": [
         "p1",
         "p3"
        ],
        "voi": 0.6745232756112371,
        "Rhat": 5,
        "mPrime": 1.9375,
        "value": 0.653444423248386,
        "cost": 0.012465383977091597,
        "net": 0.6409790392712944
       },
       {
        "combo": [
         "p2",
         "p3"
        ],
        "voi": 0.43115260873837397,
        "Rhat": 5,
        "mPrime": 1.9375,
        "value": 0.41767908971529977,
        "cost": 0.012465383977091597,
        "net": 0.4052137057382082
       },
       {
        "combo": [
         "p1",
         "p2",
         "p3"
        ],
        "voi": 0.6768856765570694,
        "Rhat": 5,
        "mPrime": 1.9375,
        "value": 0.655732999164661,
        "cost": 0.015581729971364497,
        "net": 0.6401512691932965
       }
      ],
      "selected": [
       "p1",
       "p3"
      ],
      "selectedNet": 0.6409790392712944,
      "unselected": {
       "p2": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p1",
         "p2",
         "p3"
        ],
        "bestNet": 0.6401512691932965
       }
      },
      "fullRule": {
       "selected": [
        "p1",
        "p2",
        "p3"
       ],
       "insufficientBudget": []
      }
     }
    ]
   },
   "note": "真实第 1 轮三格。余额 4 时可选到三格全测；12 时 R̂ 更大、价值更高。"
  },
  {
   "name": "select_minimize",
   "section": "6.7 价值减成本、选格；约定 28–29、文末",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "minimize",
    "balances": [
     2,
     3,
     6
    ]
   },
   "expected": {
    "g0": 0.009894999999999982,
    "byBalance": [
     {
      "balance": 2,
      "combos": [
       {
        "combo": [
         "p1"
        ],
        "voi": 0.0029590833333333205,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.0014795416666666603,
        "cost": 0.0016491666666666636,
        "net": -0.00016962500000000332
       },
       {
        "combo": [
         "p2"
        ],
        "voi": 0.0026489437499999935,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.0013244718749999967,
        "cost": 0.0016491666666666636,
        "net": -0.00032469479166666684
       }
      ],
      "selected": [],
      "selectedNet": 0.0,
      "unselected": {
       "p1": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p1"
        ],
        "bestNet": -0.00016962500000000332
       },
       "p2": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p2"
        ],
        "bestNet": -0.00032469479166666684
       }
      },
      "fullRule": {
       "selected": [
        "p1"
       ],
       "insufficientBudget": [
        "p2"
       ]
      }
     },
     {
      "balance": 3,
      "combos": [
       {
        "combo": [
         "p1"
        ],
        "voi": 0.0029590833333333205,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.0014795416666666603,
        "cost": 0.0016491666666666636,
        "net": -0.00016962500000000332
       },
       {
        "combo": [
         "p2"
        ],
        "voi": 0.0026489437499999935,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.0013244718749999967,
        "cost": 0.0016491666666666636,
        "net": -0.00032469479166666684
       },
       {
        "combo": [
         "p1",
         "p2"
        ],
        "voi": 0.003645968749999993,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.0018229843749999965,
        "cost": 0.0026386666666666616,
        "net": -0.0008156822916666651
       }
      ],
      "selected": [],
      "selectedNet": 0.0,
      "unselected": {
       "p1": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p1"
        ],
        "bestNet": -0.00016962500000000332
       },
       "p2": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p2"
        ],
        "bestNet": -0.00032469479166666684
       }
      },
      "fullRule": {
       "selected": [
        "p1",
        "p2"
       ],
       "insufficientBudget": []
      }
     },
     {
      "balance": 6,
      "combos": [
       {
        "combo": [
         "p1"
        ],
        "voi": 0.0029590833333333205,
        "Rhat": 3,
        "mPrime": 1.75,
        "value": 0.0025891979166666555,
        "cost": 0.0016491666666666636,
        "net": 0.0009400312499999919
       },
       {
        "combo": [
         "p2"
        ],
        "voi": 0.0026489437499999935,
        "Rhat": 3,
        "mPrime": 1.75,
        "value": 0.0023178257812499943,
        "cost": 0.0016491666666666636,
        "net": 0.0006686591145833307
       },
       {
        "combo": [
         "p1",
         "p2"
        ],
        "voi": 0.003645968749999993,
        "Rhat": 2,
        "mPrime": 1.5,
        "value": 0.002734476562499995,
        "cost": 0.0026386666666666616,
        "net": 9.580989583333338e-05
       }
      ],
      "selected": [
       "p1"
      ],
      "selectedNet": 0.0009400312499999919,
      "unselected": {
       "p2": {
        "reason": "notWorthCost",
        "bestCombo": [
         "p2"
        ],
        "bestNet": 0.0006686591145833307
       }
      },
      "fullRule": {
       "selected": [
        "p1",
        "p2"
       ],
       "insufficientBudget": []
      }
     }
    ]
   },
   "note": "越小越好的合成例。"
  },
  {
   "name": "select_negativeG0",
   "section": "6.7 价值减成本、选格；约定 28–29、文末",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "negativeG0",
    "balances": [
     3,
     5
    ]
   },
   "expected": {
    "g0": -0.05697500000000005,
    "byBalance": [
     {
      "balance": 3,
      "combos": [
       {
        "combo": [
         "p1"
        ],
        "voi": 0.023196666666666692,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.011598333333333346,
        "cost": 0.0,
        "net": 0.011598333333333346
       },
       {
        "combo": [
         "p2"
        ],
        "voi": 0.029396450892857223,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.014698225446428612,
        "cost": 0.0,
        "net": 0.014698225446428612
       },
       {
        "combo": [
         "p1",
         "p2"
        ],
        "voi": 0.049642821428571494,
        "Rhat": 1,
        "mPrime": 1.0,
        "value": 0.024821410714285747,
        "cost": 0.0,
        "net": 0.024821410714285747
       }
      ],
      "selected": [
       "p1",
       "p2"
      ],
      "selectedNet": 0.024821410714285747,
      "unselected": {},
      "fullRule": {
       "selected": [
        "p1",
        "p2"
       ],
       "insufficientBudget": []
      }
     },
     {
      "balance": 5,
      "combos": [
       {
        "combo": [
         "p1"
        ],
        "voi": 0.023196666666666692,
        "Rhat": 2,
        "mPrime": 1.5,
        "value": 0.017397500000000017,
        "cost": 0.0,
        "net": 0.017397500000000017
       },
       {
        "combo": [
         "p2"
        ],
        "voi": 0.029396450892857223,
        "Rhat": 2,
        "mPrime": 1.5,
        "value": 0.022047338169642917,
        "cost": 0.0,
        "net": 0.022047338169642917
       },
       {
        "combo": [
         "p1",
         "p2"
        ],
        "voi": 0.049642821428571494,
        "Rhat": 2,
        "mPrime": 1.5,
        "value": 0.03723211607142862,
        "cost": 0.0,
        "net": 0.03723211607142862
       }
      ],
      "selected": [
       "p1",
       "p2"
      ],
      "selectedNet": 0.03723211607142862,
      "unselected": {},
      "fullRule": {
       "selected": [
        "p1",
        "p2"
       ],
       "insufficientBudget": []
      }
     }
    ]
   },
   "note": "ĝ₀ < 0（各因子事前期望收益都为负）：g0 照记原始负值，成本 = 2·max(0, ĝ₀)·[…] = 0，净值 = 价值。"
  },
  {
   "name": "value_cost_pure",
   "section": "6.7 价值减成本；约定 28",
   "params": {
    "u": 0.5,
    "r": 0.5
   },
   "input": {
    "cases": [
     {
      "balance": 5,
      "size": 1,
      "batchCap": 2,
      "g0": 0.01,
      "voi": 0.004
     },
     {
      "balance": 13,
      "size": 2,
      "batchCap": 2,
      "g0": 0.01,
      "voi": 0.004
     },
     {
      "balance": 3,
      "size": 3,
      "batchCap": 2,
      "g0": 0.01,
      "voi": 0.004
     },
     {
      "balance": 4,
      "size": 1,
      "batchCap": 3,
      "g0": 0.02,
      "voi": 0.01
     },
     {
      "balance": 6,
      "size": 2,
      "batchCap": 2,
      "g0": -0.005,
      "voi": 0.003
     }
    ]
   },
   "expected": {
    "cases": [
     {
      "Rhat": 2,
      "mPrime": 1.5,
      "value": 0.003,
      "cost": 0.0016666666666666668,
      "net": 0.0013333333333333333
     },
     {
      "Rhat": 6,
      "mPrime": 1.96875,
      "value": 0.0039375,
      "cost": 0.0026666666666666666,
      "net": 0.0012708333333333335
     },
     {
      "Rhat": 0,
      "mPrime": 0.0,
      "value": 0.0,
      "cost": 0.0033333333333333335,
      "net": -0.0033333333333333335
     },
     {
      "Rhat": 1,
      "mPrime": 1.0,
      "value": 0.005,
      "cost": 0.002,
      "net": 0.003
     },
     {
      "Rhat": 2,
      "mPrime": 1.5,
      "value": 0.0022500000000000003,
      "cost": 0.0,
      "net": 0.0022500000000000003
     }
    ]
   },
   "note": "R̂ = ⌈(余额−|S|)/每批上限⌉，余额−|S| = 0 时 R̂ = 0、m′ = 0；m′ = Σ_{j<R̂} r^j；成本 = 2·max(0,ĝ₀)·[(K+|S|)/(K+|S|+1) − K/(K+1)]，ĝ₀ < 0 时成本 0。例：余额 13、|S| 2、K 2 → R̂ 6、m′ 1.96875。"
  },
  {
   "name": "select_pure_net_at_tolerance",
   "section": "6.7 选格第 2–3 条；约定 29",
   "params": {
    "tolerance": 1e-12
   },
   "input": {
    "cells": [
     "p1",
     "p2"
    ],
    "balance": 3,
    "nets": {
     "p1": 1e-12,
     "p2": 9e-13,
     "p1,p2": 1e-12
    }
   },
   "expected": {
    "selected": [],
    "selectedNet": 0.0,
    "unselected": {
     "p1": {
      "reason": "notWorthCost",
      "bestCombo": [
       "p1"
      ],
      "bestNet": 1e-12
     },
     "p2": {
      "reason": "notWorthCost",
      "bestCombo": [
       "p2"
      ],
      "bestNet": 9e-13
     }
    }
   },
   "note": "净值都不大于 1e-12：一格都不测；各格 notWorthCost，附各自含它的最大净值组合（同一条规则：差不到 1e-12 视为相同，先取格数少的）。p2 的附带组合曾是 {p1,p2}（1e-12，按“严格更大才替换”）；改后 {p2}（0.9e-12）与它差不到 1e-12，格数少，取 {p2}。"
  },
  {
   "name": "select_pure_just_above_tolerance",
   "section": "6.7 选格第 2–3 条；约定 29",
   "params": {
    "tolerance": 1e-12
   },
   "input": {
    "cells": [
     "p1",
     "p2"
    ],
    "balance": 3,
    "nets": {
     "p1": 2.5e-12,
     "p2": 1e-12,
     "p1,p2": 3e-12
    }
   },
   "expected": {
    "selected": [
     "p1"
    ],
    "selectedNet": 2.5e-12,
    "unselected": {
     "p2": {
      "reason": "notWorthCost",
      "bestCombo": [
       "p1",
       "p2"
      ],
      "bestNet": 3e-12
     }
    }
   },
   "note": "p1 = 2.5e-12 > 1e-12，入选；{p1,p2} = 3.0e-12 只比当前最好多 0.5e-12（不超过 1e-12），视为相同，保留格数少的 p1。"
  },
  {
   "name": "select_pure_tie_chain",
   "section": "6.7 选格第 2–3 条；约定 29",
   "params": {
    "tolerance": 1e-12
   },
   "input": {
    "cells": [
     "p1",
     "p2",
     "p3"
    ],
    "balance": 4,
    "nets": {
     "p1": 0.01,
     "p2": 0.010000000000800001,
     "p3": 0.0100000000016,
     "p1,p2": 0.0,
     "p1,p3": 0.0,
     "p2,p3": 0.0,
     "p1,p2,p3": -1.0
    }
   },
   "expected": {
    "selected": [
     "p2"
    ],
    "selectedNet": 0.010000000000800001,
    "unselected": {
     "p1": {
      "reason": "notWorthCost",
      "bestCombo": [
       "p1"
      ],
      "bestNet": 0.01
     },
     "p3": {
      "reason": "notWorthCost",
      "bestCombo": [
       "p3"
      ],
      "bestNet": 0.0100000000016
     }
    }
   },
   "note": "最大净值 M = p3 = 0.01+1.6e-12；净值 ≥ M − 1e-12 的 p2、p3 视为相同，同格数按编号取小的 p2。（预期值曾按“逐个扫描、比当前最好多 1e-12 才替换”的接力写法选 p3；审阅指出方法 6.7 是先求最大净值、再在差不到 1e-12 的组合里按格数和编号挑，改后选 p2。）"
  },
  {
   "name": "select_pure_filter_before_max",
   "section": "6.7 选格第 2–3 条；约定 29",
   "params": {
    "tolerance": 1e-12
   },
   "input": {
    "cells": [
     "p1",
     "p2"
    ],
    "balance": 3,
    "nets": {
     "p1": 6e-13,
     "p2": -1.0,
     "p1,p2": 1.5e-12
    }
   },
   "expected": {
    "selected": [
     "p1",
     "p2"
    ],
    "selectedNet": 1.5e-12,
    "unselected": {}
   },
   "note": "第二轮审阅的反例：先只留净值 > 1e-12 的组合（只剩 {p1,p2}），再在其中求最大值和容差窗口，选 {p1,p2}。若先在全部组合里求 M = 1.5e-12、窗口 ≥ 0.5e-12，{p1}（0.6e-12）会因格数少被选中，而它的净值并不 > 1e-12。p1、p2 都被选中，没有没测的格。"
  },
  {
   "name": "select_pure_tolerance_relay",
   "section": "6.7 选格第 2–3 条；约定 29",
   "params": {
    "tolerance": 1e-12
   },
   "input": {
    "cells": [
     "p1",
     "p2"
    ],
    "balance": 3,
    "nets": {
     "p1": 1.0,
     "p2": 1.0000000000009,
     "p1,p2": 1.0000000000018
    }
   },
   "expected": {
    "selected": [
     "p2"
    ],
    "selectedNet": 1.0000000000009,
    "unselected": {
     "p1": {
      "reason": "notWorthCost",
      "bestCombo": [
       "p1",
       "p2"
      ],
      "bestNet": 1.0000000000018
     }
    }
   },
   "note": "审阅给的接力反例：M = {p1,p2} = 1+1.8e-12，窗口 ≥ 1+0.8e-12 内有 {p2} 和 {p1,p2}，先取格数少的 {p2}。接力写法会因 {p2} 比 {p1} 只多 0.9e-12 不替换、{p1,p2} 比 {p1} 多 1.8e-12 替换而选 {p1,p2}。p1 没选中，含它的组合 {p1}、{p1,p2} 里同样按这条挑：M = 1+1.8e-12，窗口内只有 {p1,p2}。"
  },
  {
   "name": "select_pure_budget_reason",
   "section": "6.7 选格第 2–3 条；约定 29",
   "params": {
    "tolerance": 1e-12
   },
   "input": {
    "cells": [
     "p1",
     "p2",
     "p3"
    ],
    "balance": 2,
    "nets": {
     "p1": 0.002,
     "p2": 0.003,
     "p3": -0.001
    }
   },
   "expected": {
    "selected": [
     "p2"
    ],
    "selectedNet": 0.003,
    "unselected": {
     "p1": {
      "reason": "insufficientBudget",
      "bestCombo": [
       "p1"
      ],
      "bestNet": 0.002
     },
     "p3": {
      "reason": "insufficientBudget",
      "bestCombo": [
       "p3"
      ],
      "bestNet": -0.001
     }
    }
   },
   "note": "余额 2 只能测 1 格：选 p2；p1、p3 再加进来就超过余额−1，reason = insufficientBudget。"
  },
  {
   "name": "bet_calc15_all_valid",
   "section": "6.8；约定 30",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "calc15",
    "outcomes": {
     "p1": {
      "kind": "valid",
      "value": 2.5989997592071172
     },
     "p2": {
      "kind": "valid",
      "value": 1.7602769492805097
     }
    }
   },
   "expected": {
    "weightsUpdated": true,
    "weights": {
     "e1": 0.0,
     "e2": 0.08322400974382729,
     "e3": 0.049538101037992416,
     "e4": 0.14121721110377944,
     "e5": 0.04876406820927372,
     "e6": 0.0,
     "e7": 0.0,
     "e8": 0.6241800730787067,
     "e9": 0.0,
     "reserve": 0.053076536826420426
    },
    "payoffs": {
     "p1": 0.00012584380890054235,
     "p2": 0.0038057570153346588
    },
    "picked": "p2",
    "predictedGain": 0.0038057570153346588,
    "status": "bet",
    "negativeFactors": []
   },
   "note": "两格都有效：收益用实测换算，押 p2。weights 是按两格密度更新后的成分权重（只用于没有有效分数的格，这里只是记录）。"
  },
  {
   "name": "bet_calc15_p2_insufficient",
   "section": "6.8；约定 30",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "calc15",
    "outcomes": {
     "p1": {
      "kind": "valid",
      "value": 2.5989997592071172
     },
     "p2": {
      "kind": "insufficient"
     }
    }
   },
   "expected": {
    "weightsUpdated": true,
    "weights": {
     "e1": 0.0,
     "e2": 0.11797115540431034,
     "e3": 0.08426511100307879,
     "e4": 0.22686760654675084,
     "e5": 0.07373197212769395,
     "e6": 0.0,
     "e7": 0.11797115540431034,
     "e8": 0.2949278885107769,
     "e9": 0.0,
     "reserve": 0.08426511100307882
    },
    "payoffs": {
     "p1": 0.00012584380890054235,
     "p2": 0.002893886609905632
    },
    "picked": "p2",
    "predictedGain": 0.002893886609905632,
    "status": "bet",
    "negativeFactors": []
   },
   "note": "p2 证据不足：权重 ∝ 起始权重 × 各成分在 p1 实测处的密度，再用新权重估 p2 的期望收益。"
  },
  {
   "name": "bet_calc15_joint_ignored",
   "section": "6.8；约定 30",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "calc15",
    "outcomes": {
     "p1": {
      "kind": "valid",
      "value": 2.5989997592071172
     },
     "p2": {
      "kind": "joint",
      "value": 1.76
     }
    }
   },
   "expected": {
    "weightsUpdated": true,
    "weights": {
     "e1": 0.0,
     "e2": 0.11797115540431034,
     "e3": 0.08426511100307879,
     "e4": 0.22686760654675084,
     "e5": 0.07373197212769395,
     "e6": 0.0,
     "e7": 0.11797115540431034,
     "e8": 0.2949278885107769,
     "e9": 0.0,
     "reserve": 0.08426511100307882
    },
    "payoffs": {
     "p1": 0.00012584380890054235,
     "p2": 0.002893886609905632
    },
    "picked": "p2",
    "predictedGain": 0.002893886609905632,
    "status": "bet",
    "negativeFactors": []
   },
   "note": "p2 是一起关，它的分数不参与权重更新，也不当实测用；结果应与 p2 证据不足那一例完全相同。"
  },
  {
   "name": "bet_r1_negative_support",
   "section": "6.8；约定 30",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "r1real",
    "outcomes": {
     "p1": {
      "kind": "valid",
      "value": 2.250011787062861
     },
     "p2": {
      "kind": "valid",
      "value": 1.9535929459502979
     },
     "p3": {
      "kind": "valid",
      "value": 2.4389662413796342
     }
    }
   },
   "expected": {
    "weightsUpdated": false,
    "weights": {
     "r1-e1-1": 0.15,
     "r1-e1-2": 0.15,
     "r1-e2-1": 0.15,
     "r1-e2-2": 0.15,
     "r1-e3-1": 0.15,
     "r1-e3-2": 0.15,
     "reserve": 0.1
    },
    "payoffs": {
     "p1": -1.276678124040195,
     "p2": -0.7343851045388742,
     "p3": -1.6223669513598986
    },
    "picked": "p2",
    "predictedGain": -0.7343851045388742,
    "status": "noBetNegativeSupport",
    "negativeFactors": [
     {
      "factor": "p1",
      "offBetterBy": 0.697835738969592
     },
     {
      "factor": "p2",
      "offBetterBy": 0.40141689785702894
     },
     {
      "factor": "p3",
      "offBetterBy": 0.8867901932863653
     }
    ]
   },
   "note": "三格撑都 < 0：不押，negativeFactors 记“关掉反而更好”的分数（x − 完整，按方向，正数）。挑出的因子与预测收益照记。另外：p2 实测 1.9536 落在 p2 所有成分（含预留 [1.06,1.94]）之外，各成分在三格密度连乘全为 0，权重无从更新、保持起始权重（weightsUpdated=false）——真实数据里就出现了这种情况。"
  },
  {
   "name": "bet_gain_not_positive",
   "section": "6.8；约定 30",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "gainNotPositive",
    "outcomes": {
     "p1": {
      "kind": "valid",
      "value": 2.0
     },
     "p2": {
      "kind": "untested"
     }
    }
   },
   "expected": {
    "weightsUpdated": true,
    "weights": {
     "e1": 0.325791855203619,
     "e2": 0.6515837104072408,
     "reserve": 0.02262443438914021
    },
    "payoffs": {
     "p1": 0.0,
     "p2": -0.16685520361990938
    },
    "picked": "p1",
    "predictedGain": 0.0,
    "status": "noBetNonPositiveGain",
    "negativeFactors": []
   },
   "note": "p1 实测正好等于完整，收益 0（撑 0，不是负）；p2 各成分都预计关掉更好，估计收益为负。最大收益 0 ≤ 0，不押。"
  },
  {
   "name": "bet_weights_not_updatable",
   "section": "6.8；约定 30",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "gainNotPositive",
    "outcomes": {
     "p1": {
      "kind": "valid",
      "value": -5.0
     },
     "p2": {
      "kind": "untested"
     }
    }
   },
   "expected": {
    "weightsUpdated": false,
    "weights": {
     "e1": 0.45,
     "e2": 0.45,
     "reserve": 0.1
    },
    "payoffs": {
     "p1": 7.0,
     "p2": -0.17499999999999993
    },
    "picked": "p1",
    "predictedGain": 7.0,
    "status": "bet",
    "negativeFactors": []
   },
   "note": "p1 实测 −5 落在所有成分（含预留）之外，密度全为 0，权重无从更新：保持起始权重，weightsUpdated=false。"
  },
  {
   "name": "bet_minimize",
   "section": "6.8；约定 30",
   "params": {
    "eps": 0.01,
    "lambda": 0.1,
    "u": 0.5,
    "r": 0.5,
    "batchCap": 2
   },
   "input": {
    "model": "minimize",
    "outcomes": {
     "p1": {
      "kind": "valid",
      "value": 0.372
     },
     "p2": {
      "kind": "cannotRun"
     }
    }
   },
   "expected": {
    "weightsUpdated": true,
    "weights": {
     "e1": 0.19424460431654675,
     "e2": 0.0,
     "e3": 0.776978417266187,
     "reserve": 0.02877697841726619
    },
    "payoffs": {
     "p1": 0.008799999999999983,
     "p2": 0.006328057553956823
    },
    "picked": "p1",
    "predictedGain": 0.008799999999999983,
    "status": "bet",
    "negativeFactors": []
   },
   "note": "越小越好：收益 = h·(x − 完整)/G，h = max(完整 − K*, ε/100) = 0.02。"
  }
 ]
}