{
  "status": "PASS_EXACT_ALGEBRAIC_SCALAR_ONLY_WITH_TWO_BACKGROUND_MOMENT_GRANTED",
  "theta_exact": "(777-sqrt(1081))/852",
  "b_exact": "-11/71+595*sqrt(1081)/76751",
  "sqrt_enclosure": [
    "1643928222277359651023/50000000000000000000",
    "3287856444554719302047/100000000000000000000"
  ],
  "contact_factorization_verified_symbolically": true,
  "boundary_derivative_identity_verified_symbolically": true,
  "certificates": [
    {
      "name": "left numerator gain>1e-8",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "2920530607413209591820370605225"
          ],
          [
            1,
            0,
            "-17595868919270487554382066319340"
          ],
          [
            1,
            1,
            "8933312612291732354023986838660"
          ],
          [
            2,
            0,
            "34527542564400000000000000000000"
          ],
          [
            2,
            1,
            "-47278729286000594062771769392156"
          ],
          [
            2,
            2,
            "18940690215300078490948272399392"
          ]
        ],
        "tree": {
          "axis": 0,
          "left": {
            "min": "5505367294010415748779054290221339/62500"
          },
          "right": {
            "min": "662606457513589700051266293196113/4000"
          }
        },
        "leaves": 2
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "right numerator gain>1e-8",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "73013265185330239795509265130625"
          ],
          [
            1,
            0,
            "-365932287840647154761924306947710"
          ],
          [
            1,
            1,
            "91276311670885144879415525966500"
          ],
          [
            2,
            0,
            "833602790053553986360949059585684"
          ],
          [
            2,
            1,
            "-1188317178808343613258841825290024"
          ],
          [
            2,
            2,
            "579162458291628493450654125984800"
          ]
        ],
        "tree": {
          "axis": 0,
          "left": {
            "min": "12220521925997063477743726521682501/2500"
          },
          "right": {
            "min": "31960753367519699316717444291510021/5000"
          }
        },
        "leaves": 2
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "main reference slope>1/5",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "258672030"
          ],
          [
            1,
            0,
            "-384634062"
          ],
          [
            1,
            1,
            "-285020249"
          ],
          [
            2,
            1,
            "481097450"
          ],
          [
            2,
            2,
            "-50000000"
          ]
        ],
        "tree": {
          "min": "5881606143/500"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "main reference slope<1",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "191192370"
          ],
          [
            1,
            0,
            "204688302"
          ],
          [
            1,
            1,
            "-74871271"
          ],
          [
            2,
            1,
            "-481097450"
          ],
          [
            2,
            2,
            "50000000"
          ]
        ],
        "tree": {
          "min": "16284481353/80"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "main reference exponent<1/250",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "10833249555235013435461111815675"
          ],
          [
            1,
            0,
            "-53616269851009616527146198958020"
          ],
          [
            1,
            1,
            "13241790137258220166970166515980"
          ],
          [
            2,
            0,
            "103582627693200000000000000000000"
          ],
          [
            2,
            1,
            "-137075859252713514521471774976468"
          ],
          [
            2,
            2,
            "66342727856476770806526252398176"
          ]
        ],
        "tree": {
          "axis": 0,
          "left": {
            "min": "640080745033439915088042814848339/4000"
          },
          "right": {
            "axis": 1,
            "left": {
              "min": "34083412794108276317845968809430581421/25000000"
            },
            "right": {
              "axis": 0,
              "left": {
                "min": "387075503226309157840878124874849/8000"
              },
              "right": {
                "min": "8534436300496431284032951660637259/16000"
              }
            }
          }
        },
        "leaves": 4
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "main reference stock",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "-20731785"
          ],
          [
            1,
            0,
            "258292714"
          ],
          [
            1,
            1,
            "-15914572"
          ],
          [
            2,
            1,
            "-387000000"
          ],
          [
            2,
            2,
            "126000000"
          ]
        ],
        "tree": {
          "min": "662530229/25"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "short-source saving>1e-5",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "-69691020703199757280699897361535"
          ],
          [
            1,
            0,
            "233958705339071754206164201256652"
          ],
          [
            1,
            1,
            "228123202141271604476136211599304"
          ],
          [
            2,
            0,
            "1035826276932000000000000000000000"
          ],
          [
            2,
            1,
            "-2470332383387951681531763530910960"
          ],
          [
            2,
            2,
            "980362887292147301596104471981760"
          ]
        ],
        "tree": {
          "min": "1135973221086407099159424606723243/125"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "short-source slope positive",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "1568902095"
          ],
          [
            1,
            0,
            "-2127108838"
          ],
          [
            1,
            1,
            "-1542395676"
          ],
          [
            2,
            1,
            "2514186400"
          ],
          [
            2,
            2,
            "-370000000"
          ]
        ],
        "tree": {
          "min": "885216913/5"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "short-source slope<2",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "2929741905"
          ],
          [
            1,
            0,
            "327651238"
          ],
          [
            1,
            1,
            "-2056519524"
          ],
          [
            2,
            1,
            "-2514186400"
          ],
          [
            2,
            2,
            "370000000"
          ]
        ],
        "tree": {
          "min": "9911528687/5"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "detector md>7/20",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "-5"
          ],
          [
            1,
            0,
            "42"
          ],
          [
            1,
            1,
            "-36"
          ]
        ],
        "tree": {
          "min": "7/25"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "detector md<49/100",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "235"
          ],
          [
            1,
            0,
            "-294"
          ],
          [
            1,
            1,
            "12"
          ]
        ],
        "tree": {
          "min": "11443/250"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "detector rd>3/5",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "18"
          ],
          [
            1,
            1,
            "-24"
          ]
        ],
        "tree": {
          "min": "158/25"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "detector rd<1",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-6"
          ]
        ],
        "tree": {
          "min": "11/10"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "detector td>1",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            1,
            0,
            "1"
          ],
          [
            1,
            1,
            "-1"
          ]
        ],
        "tree": {
          "min": "11/100"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "detector td<3/2",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-6"
          ]
        ],
        "tree": {
          "min": "11/10"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "detector upper m endpoint stronger",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "235"
          ],
          [
            0,
            1,
            "-235"
          ],
          [
            1,
            0,
            "-294"
          ],
          [
            1,
            1,
            "306"
          ],
          [
            1,
            2,
            "-12"
          ]
        ],
        "tree": {
          "min": "239/10"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "numerator saving bound",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "1124661"
          ],
          [
            1,
            1,
            "-3123305"
          ]
        ],
        "tree": {
          "min": "876695/8"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "1"
          ]
        ],
        "tree": {
          "min": "1"
        },
        "leaves": 1
      }
    },
    {
      "name": "old denominator positive",
      "box": [
        "1/8",
        "5/6",
        "0",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "16869915"
          ],
          [
            0,
            1,
            "-10623305"
          ],
          [
            1,
            0,
            "-6747966"
          ],
          [
            1,
            1,
            "-6747966"
          ],
          [
            1,
            2,
            "6000000"
          ]
        ],
        "tree": {
          "min": "4373305"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "1"
          ]
        ],
        "tree": {
          "min": "1"
        },
        "leaves": 1
      }
    },
    {
      "name": "old reference slope positive",
      "box": [
        "1/8",
        "5/6",
        "0",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "626106870635895"
          ],
          [
            0,
            1,
            "-394271355211965"
          ],
          [
            1,
            0,
            "-724766135099733"
          ],
          [
            1,
            1,
            "-39568810754358"
          ],
          [
            1,
            2,
            "261724190500000"
          ],
          [
            2,
            1,
            "653537639214450"
          ],
          [
            2,
            2,
            "-421747875000000"
          ],
          [
            2,
            3,
            "37500000000000"
          ]
        ],
        "tree": {
          "min": "239953978316705/12"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "16869915"
          ],
          [
            0,
            1,
            "-10623305"
          ],
          [
            1,
            0,
            "-6747966"
          ],
          [
            1,
            1,
            "-6747966"
          ],
          [
            1,
            2,
            "6000000"
          ]
        ],
        "tree": {
          "min": "4373305"
        },
        "leaves": 1
      }
    },
    {
      "name": "old reference slope<1",
      "box": [
        "1/8",
        "5/6",
        "0",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "322539903054855"
          ],
          [
            0,
            1,
            "-203109486018285"
          ],
          [
            1,
            0,
            "345307425623433"
          ],
          [
            1,
            1,
            "-339889898721942"
          ],
          [
            1,
            2,
            "75674109500000"
          ],
          [
            2,
            1,
            "-653537639214450"
          ],
          [
            2,
            2,
            "421747875000000"
          ],
          [
            2,
            3,
            "-37500000000000"
          ]
        ],
        "tree": {
          "min": "2711137366446295/12"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "16869915"
          ],
          [
            0,
            1,
            "-10623305"
          ],
          [
            1,
            0,
            "-6747966"
          ],
          [
            1,
            1,
            "-6747966"
          ],
          [
            1,
            2,
            "6000000"
          ]
        ],
        "tree": {
          "min": "4373305"
        },
        "leaves": 1
      }
    },
    {
      "name": "old reference stock",
      "box": [
        "1/8",
        "5/6",
        "0",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "-23316230049885"
          ],
          [
            0,
            1,
            "14682671683295"
          ],
          [
            1,
            0,
            "290491742019954"
          ],
          [
            1,
            1,
            "-230307615480046"
          ],
          [
            1,
            2,
            "40751988500000"
          ],
          [
            2,
            1,
            "-341544657000000"
          ],
          [
            2,
            2,
            "295853643000000"
          ],
          [
            2,
            3,
            "-63000000000000"
          ]
        ],
        "tree": {
          "min": "44641288020281/8"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "16869915"
          ],
          [
            0,
            1,
            "-10623305"
          ],
          [
            1,
            0,
            "-6747966"
          ],
          [
            1,
            1,
            "-6747966"
          ],
          [
            1,
            2,
            "6000000"
          ]
        ],
        "tree": {
          "min": "4373305"
        },
        "leaves": 1
      }
    },
    {
      "name": "complement reference saving>1e-5 0",
      "box": [
        "1/8",
        "5/6",
        "0",
        "6/25"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "9848001678076722241079129475728861175"
          ],
          [
            0,
            1,
            "-6201473182687691892206345274787377050"
          ],
          [
            1,
            0,
            "-59365835026920949051332771266325731220"
          ],
          [
            1,
            1,
            "33774358991558607976717297352777590590"
          ],
          [
            1,
            2,
            "9815753392919190970169895559966954980"
          ],
          [
            2,
            0,
            "116495341644062005200000000000000000000"
          ],
          [
            2,
            1,
            "-192074262495624504102268956505075536240"
          ],
          [
            2,
            2,
            "122430150917372460728367082816348509168"
          ],
          [
            2,
            3,
            "-33171363928238385403274662267416000000"
          ]
        ],
        "tree": {
          "axis": 0,
          "left": {
            "axis": 1,
            "left": {
              "axis": 0,
              "left": {
                "min": "18307600672524178449904974783487532755347/20000"
              },
              "right": {
                "min": "22409142014130501386976375768416596460019/20000"
              }
            },
            "right": {
              "axis": 0,
              "left": {
                "min": "1428216908473323613160713577520651627201/20000"
              },
              "right": {
                "axis": 1,
                "left": {
                  "min": "35614956550985239159370669338521882984219/80000"
                },
                "right": {
                  "axis": 0,
                  "left": {
                    "axis": 1,
                    "left": {
                      "min": "45665574998371064757479628368168723410341/256000"
                    },
                    "right": {
                      "axis": 0,
                      "left": {
                        "axis": 1,
                        "left": {
                          "min": "43423704821303475155821458326786348485839/409600"
                        },
                        "right": {
                          "axis": 0,
                          "left": {
                            "min": "21280347800267163661737533558727021756441/1280000"
                          },
                          "right": {
                            "min": "5180394070307287295990423175616765922757/640000"
                          }
                        }
                      },
                      "right": {
                        "min": "11931910875920588740814730032836936124289/320000"
                      }
                    }
                  },
                  "right": {
                    "min": "195170362523417477106255129601117702677/640"
                  }
                }
              }
            }
          },
          "right": {
            "min": "8728284565150113356624403129088264017849/5000"
          }
        },
        "leaves": 11
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "16869915"
          ],
          [
            0,
            1,
            "-10623305"
          ],
          [
            1,
            0,
            "-6747966"
          ],
          [
            1,
            1,
            "-6747966"
          ],
          [
            1,
            2,
            "6000000"
          ]
        ],
        "tree": {
          "min": "38177118/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "complement reference saving>1e-5 1",
      "box": [
        "1/8",
        "11/50",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "9848001678076722241079129475728861175"
          ],
          [
            0,
            1,
            "-6201473182687691892206345274787377050"
          ],
          [
            1,
            0,
            "-59365835026920949051332771266325731220"
          ],
          [
            1,
            1,
            "33774358991558607976717297352777590590"
          ],
          [
            1,
            2,
            "9815753392919190970169895559966954980"
          ],
          [
            2,
            0,
            "116495341644062005200000000000000000000"
          ],
          [
            2,
            1,
            "-192074262495624504102268956505075536240"
          ],
          [
            2,
            2,
            "122430150917372460728367082816348509168"
          ],
          [
            2,
            3,
            "-33171363928238385403274662267416000000"
          ]
        ],
        "tree": {
          "min": "132951727503201550005947107677719658953/625"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "16869915"
          ],
          [
            0,
            1,
            "-10623305"
          ],
          [
            1,
            0,
            "-6747966"
          ],
          [
            1,
            1,
            "-6747966"
          ],
          [
            1,
            2,
            "6000000"
          ]
        ],
        "tree": {
          "min": "241535843/25"
        },
        "leaves": 1
      }
    },
    {
      "name": "complement reference saving>1e-5 2",
      "box": [
        "13/20",
        "5/6",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "9848001678076722241079129475728861175"
          ],
          [
            0,
            1,
            "-6201473182687691892206345274787377050"
          ],
          [
            1,
            0,
            "-59365835026920949051332771266325731220"
          ],
          [
            1,
            1,
            "33774358991558607976717297352777590590"
          ],
          [
            1,
            2,
            "9815753392919190970169895559966954980"
          ],
          [
            2,
            0,
            "116495341644062005200000000000000000000"
          ],
          [
            2,
            1,
            "-192074262495624504102268956505075536240"
          ],
          [
            2,
            2,
            "122430150917372460728367082816348509168"
          ],
          [
            2,
            3,
            "-33171363928238385403274662267416000000"
          ]
        ],
        "tree": {
          "min": "55461484344307267741439814315249123317/100"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "16869915"
          ],
          [
            0,
            1,
            "-10623305"
          ],
          [
            1,
            0,
            "-6747966"
          ],
          [
            1,
            1,
            "-6747966"
          ],
          [
            1,
            2,
            "6000000"
          ]
        ],
        "tree": {
          "min": "4373305"
        },
        "leaves": 1
      }
    },
    {
      "name": "contact edge coefficient>.113",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "-1520932508782963755100471"
          ],
          [
            1,
            0,
            "6938290400000000000000000"
          ]
        ],
        "tree": {
          "min": "5491379217036244899529"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "transverse contact gain>.009",
      "box": [
        "2/5",
        "23/50",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "-5180692500000000000000000"
          ],
          [
            1,
            0,
            "-27495416941949475791209250"
          ],
          [
            1,
            1,
            "4144554000000000000000000"
          ],
          [
            2,
            0,
            "178621409192418603389520135"
          ],
          [
            2,
            1,
            "-69562200354493240993781490"
          ],
          [
            3,
            0,
            "-141290817052697782530602826"
          ],
          [
            3,
            1,
            "52997245723594592795000656"
          ]
        ],
        "tree": {
          "min": "39725067178761979227305316/125"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "25"
          ],
          [
            1,
            0,
            "-30"
          ],
          [
            1,
            1,
            "-20"
          ],
          [
            2,
            0,
            "8"
          ],
          [
            2,
            1,
            "16"
          ]
        ],
        "tree": {
          "min": "6241/625"
        },
        "leaves": 1
      }
    },
    {
      "name": "left noncontact gain>7e-5",
      "box": [
        "11/50",
        "2/5",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "7758198320808131015000175"
          ],
          [
            1,
            0,
            "-46923568312217609152576820"
          ],
          [
            1,
            1,
            "20763239696913075820940880"
          ],
          [
            2,
            0,
            "92101200000000000000000000"
          ],
          [
            2,
            1,
            "-124877856967192861458718248"
          ],
          [
            2,
            2,
            "52997245723594592795000656"
          ]
        ],
        "tree": {
          "min": "36361034360286566300947/5"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "17/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "right noncontact gain>7e-5",
      "box": [
        "23/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "7758198320808131015000175"
          ],
          [
            1,
            0,
            "-46923568312217609152576820"
          ],
          [
            1,
            1,
            "20763239696913075820940880"
          ],
          [
            2,
            0,
            "92101200000000000000000000"
          ],
          [
            2,
            1,
            "-124877856967192861458718248"
          ],
          [
            2,
            2,
            "52997245723594592795000656"
          ]
        ],
        "tree": {
          "min": "3624122390898432519298033/125"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    },
    {
      "name": "boundary derivative>2.37",
      "box": [
        "11/50",
        "13/20",
        "6/25",
        "1/2"
      ],
      "numerator": {
        "coefficients": [
          [
            0,
            0,
            "1315"
          ],
          [
            1,
            0,
            "-2026"
          ],
          [
            1,
            1,
            "1448"
          ],
          [
            2,
            1,
            "1400"
          ],
          [
            2,
            2,
            "-2600"
          ]
        ],
        "tree": {
          "min": "378343/1250"
        },
        "leaves": 1
      },
      "denominator": {
        "coefficients": [
          [
            0,
            0,
            "5"
          ],
          [
            1,
            0,
            "-2"
          ],
          [
            1,
            1,
            "-4"
          ]
        ],
        "tree": {
          "min": "12/5"
        },
        "leaves": 1
      }
    }
  ],
  "positive_constants": {
    "b": "3335541671782860803119/33370000000000000000000",
    "ell>1/6": "68928222277359651023/10650000000000000000000",
    "ell<1/5": "190714518481760232651/7100000000000000000000",
    "lx>ell": "730338149731572612442307/3837550000000000000000000",
    "Gram": "1642728291409527141905953/15350200000000000000000000",
    "p1 ell>3/4": "25639719464892527493059401/887500000000000000000000000",
    "T": "89899327845198602109831/767510000000000000000000",
    "ly<1/2": "8776297203299362559161/239846875000000000000000",
    "principal B>.87": "288143555445280697953/85200000000000000000000",
    "stock top buffered": "1092805872009550771429760918621/285000003459200003837550000000000",
    "shortened stock<2/9": "227853177201775548456821/144661297500000000000000000",
    "m0>.30": "1364460445050956161253/10687500000000000000000",
    "m0<.47": "100536567766454186387/2375000000000000000000",
    "ly/h>.57": "5536567766454186387/2375000000000000000000",
    "ly/h<.59": "188835445050956161253/10687500000000000000000",
    "small amplitude coefficient": "739642638605654282862613/171188100000000000000000000",
    "small amplitude margin": "62783149042844856224383/61400800000000000000000000",
    "floor margin": "277436709058283396410409/383755000000000000000000000",
    "small rows margin": "6147392624530826426253391/287816250000000000000000000",
    "principal h/600": "22516027900495850634473/16685000000000000000000000",
    "principal ly/20": "7248726541089172007011/312843750000000000000000",
    "reference theta0<.073": "850253/1124661000",
    "scale slope>.1": "499/40000"
  },
  "coefficient_enclosure_scope": "Each a+b sqrt1081 coefficient is lowered using the exact rational enclosure. All monomials delta^i x^j are nonnegative on the positive rectangles.",
  "complete_analytic_endpoint_proved_by_script": false,
  "Lean_endpoint": false,
  "tracker_admission": false
}