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              "y": 3.03125,
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              "y": 3.40625,
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              "y": 3.46875,
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              "y": 3.5,
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              "y": 3.53125,
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              "y": 3.6875,
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              "y": 3.71875,
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              "y": 3.75,
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              "y": 3.78125,
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              "y": 3.8125,
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              "y": 3.84375,
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              "y": 3.875,
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              "y": 3.90625,
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              "y": 3.9375,
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              "y": 3.96875,
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              "feasible": false
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            {
              "y": 4,
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          "strongDualityReason": "g(z)=(z−b)²/2在全空间连续，f(x)=λ|x|为真闭凸；本族满足有限维Fenchel约束品性。"
        },
        "scope": "一维解析共轭与闭凸包络；四次双阱共轭用单调根区间二分并给出浮点残差。有限图窗不替代上确界；独立l1二次问题给原始/对偶可行性及两项间隙。"
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              "y": 3,
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              "y": 3.03125,
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              "y": 3.0625,
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              "feasible": false
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              "y": 3.09375,
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              "feasible": false
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              "y": 3.15625,
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              "y": 3.1875,
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              "feasible": false
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              "y": 3.21875,
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              "feasible": false
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              "y": 3.25,
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              "feasible": false
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              "y": 3.28125,
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              "feasible": false
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            {
              "y": 3.3125,
              "value": "-Infinity",
              "feasible": false
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              "y": 3.34375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.40625,
              "value": "-Infinity",
              "feasible": false
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            {
              "y": 3.4375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.46875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.5,
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              "feasible": false
            },
            {
              "y": 3.53125,
              "value": "-Infinity",
              "feasible": false
            },
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              "y": 3.5625,
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              "feasible": false
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              "y": 3.59375,
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              "feasible": false
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              "y": 3.625,
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              "y": 3.65625,
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              "feasible": false
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              "y": 3.6875,
              "value": "-Infinity",
              "feasible": false
            },
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              "y": 3.71875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.75,
              "value": "-Infinity",
              "feasible": false
            },
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              "y": 3.78125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.8125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.84375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.90625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.9375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.96875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 4,
              "value": "-Infinity",
              "feasible": false
            }
          ],
          "strongDualityReason": "g(z)=(z−b)²/2在全空间连续，f(x)=λ|x|为真闭凸；本族满足有限维Fenchel约束品性。"
        },
        "scope": "一维解析共轭与闭凸包络；四次双阱共轭用单调根区间二分并给出浮点残差。有限图窗不替代上确界；独立l1二次问题给原始/对偶可行性及两项间隙。"
      }
    },
    {
      "key": "open",
      "data": {
        "version": 171,
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          "a": 1,
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        "infinityEncoding": "扩展实数以+Infinity/-Infinity字符串保存；不把它们改成null或大有限数。",
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          "star": 2,
          "pairing": 2,
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          "effectiveDomain": false,
          "dualDomain": true,
          "contactByExactModelConditions": false,
          "slopeResidual": null,
          "numericallySmallGap": false,
          "attained": false,
          "argmax": {
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          "supportAtX": 0,
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        "curves": [
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        "scope": "一维解析共轭与闭凸包络；四次双阱共轭用单调根区间二分并给出浮点残差。有限图窗不替代上确界；独立l1二次问题给原始/对偶可行性及两项间隙。"
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              "feasible": false
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              "y": 3.25,
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              "feasible": false
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              "y": 3.28125,
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              "feasible": false
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              "y": 3.3125,
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              "y": 3.34375,
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              "feasible": false
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              "y": 3.375,
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              "y": 3.40625,
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              "y": 3.4375,
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              "feasible": false
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            {
              "y": 3.46875,
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              "feasible": false
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            {
              "y": 3.5,
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              "feasible": false
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            {
              "y": 3.53125,
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              "y": 3.8125,
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          "strongDualityReason": "g(z)=(z−b)²/2在全空间连续，f(x)=λ|x|为真闭凸；本族满足有限维Fenchel约束品性。"
        },
        "scope": "一维解析共轭与闭凸包络；四次双阱共轭用单调根区间二分并给出浮点残差。有限图窗不替代上确界；独立l1二次问题给原始/对偶可行性及两项间隙。"
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            {
              "y": -2.28125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -2.25,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -2.21875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -2.1875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -2.15625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -2.125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -2.09375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -2.0625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -2.03125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -2,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.96875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.9375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.90625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.84375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.8125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.78125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.75,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.71875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.6875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.65625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.59375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.5625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.53125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.5,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.46875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.4375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.40625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.34375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.3125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.28125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.25,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.21875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.1875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.15625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.09375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.0625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1.03125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": -1,
              "value": -2.5,
              "feasible": true
            },
            {
              "y": -0.96875,
              "value": -2.40673828125,
              "feasible": true
            },
            {
              "y": -0.9375,
              "value": -2.314453125,
              "feasible": true
            },
            {
              "y": -0.90625,
              "value": -2.22314453125,
              "feasible": true
            },
            {
              "y": -0.875,
              "value": -2.1328125,
              "feasible": true
            },
            {
              "y": -0.84375,
              "value": -2.04345703125,
              "feasible": true
            },
            {
              "y": -0.8125,
              "value": -1.955078125,
              "feasible": true
            },
            {
              "y": -0.78125,
              "value": -1.86767578125,
              "feasible": true
            },
            {
              "y": -0.75,
              "value": -1.78125,
              "feasible": true
            },
            {
              "y": -0.71875,
              "value": -1.69580078125,
              "feasible": true
            },
            {
              "y": -0.6875,
              "value": -1.611328125,
              "feasible": true
            },
            {
              "y": -0.65625,
              "value": -1.52783203125,
              "feasible": true
            },
            {
              "y": -0.625,
              "value": -1.4453125,
              "feasible": true
            },
            {
              "y": -0.59375,
              "value": -1.36376953125,
              "feasible": true
            },
            {
              "y": -0.5625,
              "value": -1.283203125,
              "feasible": true
            },
            {
              "y": -0.53125,
              "value": -1.20361328125,
              "feasible": true
            },
            {
              "y": -0.5,
              "value": -1.125,
              "feasible": true
            },
            {
              "y": -0.46875,
              "value": -1.04736328125,
              "feasible": true
            },
            {
              "y": -0.4375,
              "value": -0.970703125,
              "feasible": true
            },
            {
              "y": -0.40625,
              "value": -0.89501953125,
              "feasible": true
            },
            {
              "y": -0.375,
              "value": -0.8203125,
              "feasible": true
            },
            {
              "y": -0.34375,
              "value": -0.74658203125,
              "feasible": true
            },
            {
              "y": -0.3125,
              "value": -0.673828125,
              "feasible": true
            },
            {
              "y": -0.28125,
              "value": -0.60205078125,
              "feasible": true
            },
            {
              "y": -0.25,
              "value": -0.53125,
              "feasible": true
            },
            {
              "y": -0.21875,
              "value": -0.46142578125,
              "feasible": true
            },
            {
              "y": -0.1875,
              "value": -0.392578125,
              "feasible": true
            },
            {
              "y": -0.15625,
              "value": -0.32470703125,
              "feasible": true
            },
            {
              "y": -0.125,
              "value": -0.2578125,
              "feasible": true
            },
            {
              "y": -0.09375,
              "value": -0.19189453125,
              "feasible": true
            },
            {
              "y": -0.0625,
              "value": -0.126953125,
              "feasible": true
            },
            {
              "y": -0.03125,
              "value": -0.06298828125,
              "feasible": true
            },
            {
              "y": 0,
              "value": 0,
              "feasible": true
            },
            {
              "y": 0.03125,
              "value": 0.06201171875,
              "feasible": true
            },
            {
              "y": 0.0625,
              "value": 0.123046875,
              "feasible": true
            },
            {
              "y": 0.09375,
              "value": 0.18310546875,
              "feasible": true
            },
            {
              "y": 0.125,
              "value": 0.2421875,
              "feasible": true
            },
            {
              "y": 0.15625,
              "value": 0.30029296875,
              "feasible": true
            },
            {
              "y": 0.1875,
              "value": 0.357421875,
              "feasible": true
            },
            {
              "y": 0.21875,
              "value": 0.41357421875,
              "feasible": true
            },
            {
              "y": 0.25,
              "value": 0.46875,
              "feasible": true
            },
            {
              "y": 0.28125,
              "value": 0.52294921875,
              "feasible": true
            },
            {
              "y": 0.3125,
              "value": 0.576171875,
              "feasible": true
            },
            {
              "y": 0.34375,
              "value": 0.62841796875,
              "feasible": true
            },
            {
              "y": 0.375,
              "value": 0.6796875,
              "feasible": true
            },
            {
              "y": 0.40625,
              "value": 0.72998046875,
              "feasible": true
            },
            {
              "y": 0.4375,
              "value": 0.779296875,
              "feasible": true
            },
            {
              "y": 0.46875,
              "value": 0.82763671875,
              "feasible": true
            },
            {
              "y": 0.5,
              "value": 0.875,
              "feasible": true
            },
            {
              "y": 0.53125,
              "value": 0.92138671875,
              "feasible": true
            },
            {
              "y": 0.5625,
              "value": 0.966796875,
              "feasible": true
            },
            {
              "y": 0.59375,
              "value": 1.01123046875,
              "feasible": true
            },
            {
              "y": 0.625,
              "value": 1.0546875,
              "feasible": true
            },
            {
              "y": 0.65625,
              "value": 1.09716796875,
              "feasible": true
            },
            {
              "y": 0.6875,
              "value": 1.138671875,
              "feasible": true
            },
            {
              "y": 0.71875,
              "value": 1.17919921875,
              "feasible": true
            },
            {
              "y": 0.75,
              "value": 1.21875,
              "feasible": true
            },
            {
              "y": 0.78125,
              "value": 1.25732421875,
              "feasible": true
            },
            {
              "y": 0.8125,
              "value": 1.294921875,
              "feasible": true
            },
            {
              "y": 0.84375,
              "value": 1.33154296875,
              "feasible": true
            },
            {
              "y": 0.875,
              "value": 1.3671875,
              "feasible": true
            },
            {
              "y": 0.90625,
              "value": 1.40185546875,
              "feasible": true
            },
            {
              "y": 0.9375,
              "value": 1.435546875,
              "feasible": true
            },
            {
              "y": 0.96875,
              "value": 1.46826171875,
              "feasible": true
            },
            {
              "y": 1,
              "value": 1.5,
              "feasible": true
            },
            {
              "y": 1.03125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.0625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.09375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.15625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.1875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.21875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.25,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.28125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.3125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.34375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.40625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.4375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.46875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.5,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.53125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.5625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.59375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.65625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.6875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.71875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.75,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.78125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.8125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.84375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.90625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.9375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.96875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.03125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.0625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.09375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.15625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.1875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.21875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.25,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.28125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.3125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.34375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.40625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.4375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.46875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.5,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.53125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.5625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.59375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.65625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.6875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.71875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.75,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.78125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.8125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.84375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.90625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.9375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.96875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.03125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.0625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.09375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.15625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.1875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.21875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.25,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.28125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.3125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.34375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.40625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.4375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.46875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.5,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.53125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.5625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.59375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.65625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.6875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.71875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.75,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.78125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.8125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.84375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.90625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.9375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.96875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 4,
              "value": "-Infinity",
              "feasible": false
            }
          ],
          "strongDualityReason": "g(z)=(z−b)²/2在全空间连续，f(x)=λ|x|为真闭凸；本族满足有限维Fenchel约束品性。"
        },
        "scope": "一维解析共轭与闭凸包络；四次双阱共轭用单调根区间二分并给出浮点残差。有限图窗不替代上确界；独立l1二次问题给原始/对偶可行性及两项间隙。"
      }
    },
    {
      "key": "dual-invalid",
      "data": {
        "version": 171,
        "parameters": {
          "model": "quadratic",
          "x": 1,
          "y": 2,
          "a": 1,
          "b": 2,
          "lambda": 1
        },
        "infinityEncoding": "扩展实数以+Infinity/-Infinity字符串保存；不把它们改成null或大有限数。",
        "current": {
          "f": 0.5,
          "star": 2,
          "pairing": 2,
          "gap": 0.5,
          "effectiveDomain": true,
          "dualDomain": true,
          "contactByExactModelConditions": false,
          "slopeResidual": 1,
          "numericallySmallGap": false,
          "attained": true,
          "argmax": {
            "kind": "point",
            "points": [
              2
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              "feasible": true
            },
            {
              "y": -0.96875,
              "value": -2.40673828125,
              "feasible": true
            },
            {
              "y": -0.9375,
              "value": -2.314453125,
              "feasible": true
            },
            {
              "y": -0.90625,
              "value": -2.22314453125,
              "feasible": true
            },
            {
              "y": -0.875,
              "value": -2.1328125,
              "feasible": true
            },
            {
              "y": -0.84375,
              "value": -2.04345703125,
              "feasible": true
            },
            {
              "y": -0.8125,
              "value": -1.955078125,
              "feasible": true
            },
            {
              "y": -0.78125,
              "value": -1.86767578125,
              "feasible": true
            },
            {
              "y": -0.75,
              "value": -1.78125,
              "feasible": true
            },
            {
              "y": -0.71875,
              "value": -1.69580078125,
              "feasible": true
            },
            {
              "y": -0.6875,
              "value": -1.611328125,
              "feasible": true
            },
            {
              "y": -0.65625,
              "value": -1.52783203125,
              "feasible": true
            },
            {
              "y": -0.625,
              "value": -1.4453125,
              "feasible": true
            },
            {
              "y": -0.59375,
              "value": -1.36376953125,
              "feasible": true
            },
            {
              "y": -0.5625,
              "value": -1.283203125,
              "feasible": true
            },
            {
              "y": -0.53125,
              "value": -1.20361328125,
              "feasible": true
            },
            {
              "y": -0.5,
              "value": -1.125,
              "feasible": true
            },
            {
              "y": -0.46875,
              "value": -1.04736328125,
              "feasible": true
            },
            {
              "y": -0.4375,
              "value": -0.970703125,
              "feasible": true
            },
            {
              "y": -0.40625,
              "value": -0.89501953125,
              "feasible": true
            },
            {
              "y": -0.375,
              "value": -0.8203125,
              "feasible": true
            },
            {
              "y": -0.34375,
              "value": -0.74658203125,
              "feasible": true
            },
            {
              "y": -0.3125,
              "value": -0.673828125,
              "feasible": true
            },
            {
              "y": -0.28125,
              "value": -0.60205078125,
              "feasible": true
            },
            {
              "y": -0.25,
              "value": -0.53125,
              "feasible": true
            },
            {
              "y": -0.21875,
              "value": -0.46142578125,
              "feasible": true
            },
            {
              "y": -0.1875,
              "value": -0.392578125,
              "feasible": true
            },
            {
              "y": -0.15625,
              "value": -0.32470703125,
              "feasible": true
            },
            {
              "y": -0.125,
              "value": -0.2578125,
              "feasible": true
            },
            {
              "y": -0.09375,
              "value": -0.19189453125,
              "feasible": true
            },
            {
              "y": -0.0625,
              "value": -0.126953125,
              "feasible": true
            },
            {
              "y": -0.03125,
              "value": -0.06298828125,
              "feasible": true
            },
            {
              "y": 0,
              "value": 0,
              "feasible": true
            },
            {
              "y": 0.03125,
              "value": 0.06201171875,
              "feasible": true
            },
            {
              "y": 0.0625,
              "value": 0.123046875,
              "feasible": true
            },
            {
              "y": 0.09375,
              "value": 0.18310546875,
              "feasible": true
            },
            {
              "y": 0.125,
              "value": 0.2421875,
              "feasible": true
            },
            {
              "y": 0.15625,
              "value": 0.30029296875,
              "feasible": true
            },
            {
              "y": 0.1875,
              "value": 0.357421875,
              "feasible": true
            },
            {
              "y": 0.21875,
              "value": 0.41357421875,
              "feasible": true
            },
            {
              "y": 0.25,
              "value": 0.46875,
              "feasible": true
            },
            {
              "y": 0.28125,
              "value": 0.52294921875,
              "feasible": true
            },
            {
              "y": 0.3125,
              "value": 0.576171875,
              "feasible": true
            },
            {
              "y": 0.34375,
              "value": 0.62841796875,
              "feasible": true
            },
            {
              "y": 0.375,
              "value": 0.6796875,
              "feasible": true
            },
            {
              "y": 0.40625,
              "value": 0.72998046875,
              "feasible": true
            },
            {
              "y": 0.4375,
              "value": 0.779296875,
              "feasible": true
            },
            {
              "y": 0.46875,
              "value": 0.82763671875,
              "feasible": true
            },
            {
              "y": 0.5,
              "value": 0.875,
              "feasible": true
            },
            {
              "y": 0.53125,
              "value": 0.92138671875,
              "feasible": true
            },
            {
              "y": 0.5625,
              "value": 0.966796875,
              "feasible": true
            },
            {
              "y": 0.59375,
              "value": 1.01123046875,
              "feasible": true
            },
            {
              "y": 0.625,
              "value": 1.0546875,
              "feasible": true
            },
            {
              "y": 0.65625,
              "value": 1.09716796875,
              "feasible": true
            },
            {
              "y": 0.6875,
              "value": 1.138671875,
              "feasible": true
            },
            {
              "y": 0.71875,
              "value": 1.17919921875,
              "feasible": true
            },
            {
              "y": 0.75,
              "value": 1.21875,
              "feasible": true
            },
            {
              "y": 0.78125,
              "value": 1.25732421875,
              "feasible": true
            },
            {
              "y": 0.8125,
              "value": 1.294921875,
              "feasible": true
            },
            {
              "y": 0.84375,
              "value": 1.33154296875,
              "feasible": true
            },
            {
              "y": 0.875,
              "value": 1.3671875,
              "feasible": true
            },
            {
              "y": 0.90625,
              "value": 1.40185546875,
              "feasible": true
            },
            {
              "y": 0.9375,
              "value": 1.435546875,
              "feasible": true
            },
            {
              "y": 0.96875,
              "value": 1.46826171875,
              "feasible": true
            },
            {
              "y": 1,
              "value": 1.5,
              "feasible": true
            },
            {
              "y": 1.03125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.0625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.09375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.15625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.1875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.21875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.25,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.28125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.3125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.34375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.40625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.4375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.46875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.5,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.53125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.5625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.59375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.65625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.6875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.71875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.75,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.78125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.8125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.84375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.90625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.9375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 1.96875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.03125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.0625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.09375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.15625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.1875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.21875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.25,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.28125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.3125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.34375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.40625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.4375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.46875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.5,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.53125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.5625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.59375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.65625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.6875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.71875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.75,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.78125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.8125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.84375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.90625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.9375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 2.96875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.03125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.0625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.09375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.15625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.1875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.21875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.25,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.28125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.3125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.34375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.40625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.4375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.46875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.5,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.53125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.5625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.59375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.65625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.6875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.71875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.75,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.78125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.8125,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.84375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.90625,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.9375,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 3.96875,
              "value": "-Infinity",
              "feasible": false
            },
            {
              "y": 4,
              "value": "-Infinity",
              "feasible": false
            }
          ],
          "strongDualityReason": "g(z)=(z−b)²/2在全空间连续，f(x)=λ|x|为真闭凸；本族满足有限维Fenchel约束品性。"
        },
        "scope": "一维解析共轭与闭凸包络；四次双阱共轭用单调根区间二分并给出浮点残差。有限图窗不替代上确界；独立l1二次问题给原始/对偶可行性及两项间隙。"
      }
    }
  ]
}
