{
 "what": "The lambda(4) campaign record. Phase 0: Mercer arXiv:1709.06612 Section 5 executed mechanically — lambda(2) and lambda(3) re-derived end to end as calibration, the lambda(4) generic case derived with its exception list DISCOVERED, and the remaining reduction measured at NINE families (five of Mercer's fourteen carry strictly negative delta and are closed by the generic argument itself unless a positive-delta condition holds simultaneously). Phase 1, in progress: families closed so far are listed in lambda4families with their full derivations — second-level dot theorems, subfamily cones, derived thresholds, decided finite parts.",
 "provenance": "Statement and strategy: Idris Mercer, INTEGERS 19 (2019) #A4 (arXiv:1709.06612), read at source. Every threshold below is DERIVED by the engine, never transcribed.",
 "targets": {
  "L2": {
   "A": [
    1,
    2
   ],
   "lo": "-5066549580791809/4503599627370496",
   "hi": "-5066549580791807/4503599627370496"
  },
  "L3": {
   "A": [
    1,
    2,
    3
   ],
   "lo": "-5924778740580625/4503599627370496",
   "hi": "-370298671286289/281474976710656"
  },
  "L4": {
   "A": [
    1,
    2,
    3,
    4
   ],
   "lo": "-855435038691829/562949953421312",
   "hi": "-6843480309534631/4503599627370496"
  },
  "L2exact": "-9/8"
 },
 "lambda2": {
  "closure": {
   "ok": true,
   "tailMember": "b",
   "N0": 3,
   "validityFloor": 1,
   "expr": {
    "A": "-2",
    "B": "1/2",
    "C": "0",
    "D": "0"
   },
   "boundAtN0": {
    "lo": "-20038373596108193916090968595330243293666836312540805723172850846749975/13803492693581127574869511724554050904902217944340773110325048447598592",
    "hi": "-2885525797839579923917099477727555032200077975753987844723452293100217527/1987702947875682370781209688335783330305919383985071327886806976454197248"
   },
   "target": {
    "lo": "-9/8",
    "hi": "-9/8"
   },
   "pieces": [
    {
     "member": "a",
     "kind": "lemma3.2",
     "u": "0",
     "v": "1"
    },
    {
     "member": "b",
     "kind": "exact",
     "u": "1",
     "value": "-1"
    }
   ]
  },
  "finite": {
   "ok": true,
   "enumerated": 1,
   "closed": 0,
   "skipped": [
    "1,2"
   ],
   "undecided": []
  }
 },
 "lambda3": {
  "M0": {
   "ok": true,
   "base": "0",
   "posBase": "2",
   "dip": "-3/2",
   "dipQ": {
    "n": "-3",
    "d": "2"
   },
   "target": {
    "lo": "-5924778740580625/4503599627370496",
    "hi": "-370298671286289/281474976710656"
   },
   "anchoredVals": {
    "c": "-1"
   },
   "exceptions": [
    {
     "key": "1,-1,-1",
     "label": "2a = c",
     "cond": [
      "1",
      "-1",
      "-1"
     ],
     "delta": "1/2",
     "deltaSign": 1,
     "inhabited": true,
     "example": {
      "a": 2,
      "b": 3,
      "c": 4
     }
    },
    {
     "key": "1,1,-1",
     "label": "2b = c",
     "cond": [
      "1",
      "1",
      "-1"
     ],
     "delta": "1/2",
     "deltaSign": 1,
     "inhabited": true,
     "example": {
      "a": 1,
      "b": 2,
      "c": 4
     }
    },
    {
     "key": "1,0,-1",
     "label": "a+b = c",
     "cond": [
      "1",
      "0",
      "-1"
     ],
     "delta": "1",
     "deltaSign": 1,
     "inhabited": true,
     "example": {
      "a": 1,
      "b": 2,
      "c": 3
     }
    }
   ]
  },
  "families": [
   {
    "label": "c = 2a",
    "closure": {
     "ok": true,
     "tailMember": "a",
     "N0": 3,
     "validityFloor": 1,
     "expr": {
      "A": "-2",
      "B": "1/2",
      "C": "0",
      "D": "0"
     },
     "boundAtN0": {
      "lo": "-20038373596108193916090968595330243293666836312540805723172850846749975/13803492693581127574869511724554050904902217944340773110325048447598592",
      "hi": "-2885525797839579923917099477727555032200077975753987844723452293100217527/1987702947875682370781209688335783330305919383985071327886806976454197248"
     },
     "target": {
      "lo": "-5924778740580625/4503599627370496",
      "hi": "-370298671286289/281474976710656"
     },
     "pieces": [
      {
       "member": "a",
       "kind": "exact",
       "u": "1",
       "value": "-1/2"
      },
      {
       "member": "b",
       "kind": "lemma3.2",
       "u": "0",
       "v": "1"
      },
      {
       "member": "c",
       "kind": "exact",
       "u": "2",
       "value": "-1/2"
      }
     ]
    },
    "finite": {
     "ok": true,
     "enumerated": 1,
     "closed": 1,
     "skipped": [],
     "undecided": []
    }
   },
   {
    "label": "c = 2b",
    "closure": {
     "ok": true,
     "tailMember": "b",
     "N0": 3,
     "validityFloor": 1,
     "expr": {
      "A": "-2",
      "B": "1/2",
      "C": "0",
      "D": "0"
     },
     "boundAtN0": {
      "lo": "-20038373596108193916090968595330243293666836312540805723172850846749975/13803492693581127574869511724554050904902217944340773110325048447598592",
      "hi": "-2885525797839579923917099477727555032200077975753987844723452293100217527/1987702947875682370781209688335783330305919383985071327886806976454197248"
     },
     "target": {
      "lo": "-5924778740580625/4503599627370496",
      "hi": "-370298671286289/281474976710656"
     },
     "pieces": [
      {
       "member": "a",
       "kind": "lemma3.2",
       "u": "0",
       "v": "1"
      },
      {
       "member": "b",
       "kind": "exact",
       "u": "1",
       "value": "-1/2"
      },
      {
       "member": "c",
       "kind": "exact",
       "u": "2",
       "value": "-1/2"
      }
     ]
    },
    "finite": {
     "ok": true,
     "enumerated": 1,
     "closed": 1,
     "skipped": [],
     "undecided": []
    }
   },
   {
    "label": "c = a+b",
    "closure": {
     "ok": true,
     "tailMember": "b",
     "N0": 33,
     "validityFloor": 6,
     "expr": {
      "A": "-3/2",
      "B": "0",
      "C": "6",
      "D": "0"
     },
     "boundAtN0": {
      "lo": "-29/22",
      "hi": "-29/22"
     },
     "target": {
      "lo": "-5924778740580625/4503599627370496",
      "hi": "-370298671286289/281474976710656"
     },
     "pieces": [
      {
       "member": "a",
       "kind": "lemma3.3",
       "u": "0",
       "v": "1",
       "floor": 6
      },
      {
       "member": "b",
       "kind": "exact",
       "u": "1",
       "value": "-1/2"
      },
      {
       "member": "c",
       "kind": "lemma3.3",
       "u": "1",
       "v": "1",
       "floor": 6
      }
     ]
    },
    "finite": {
     "ok": true,
     "enumerated": 323,
     "closed": 322,
     "skipped": [
      "1,2,3"
     ],
     "undecided": []
    }
   }
  ]
 },
 "lambda4generic": {
  "base": "0",
  "posBase": "5",
  "dip": "-8/5",
  "exceptions": [
   {
    "label": "2a = d",
    "delta": "1/2",
    "example": {
     "a": 3,
     "b": 4,
     "c": 5,
     "d": 6
    }
   },
   {
    "label": "2b = d",
    "delta": "1/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 4
    }
   },
   {
    "label": "2c = a+d",
    "delta": "-1/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 5
    }
   },
   {
    "label": "2c = b+d",
    "delta": "-1/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 4
    }
   },
   {
    "label": "2c = d",
    "delta": "7/5",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 6
    }
   },
   {
    "label": "3c = 2d",
    "delta": "1/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 4,
     "d": 6
    }
   },
   {
    "label": "3c = d",
    "delta": "-1/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 9
    }
   },
   {
    "label": "a+2c = 2d",
    "delta": "1/2",
    "example": {
     "a": 2,
     "b": 3,
     "c": 4,
     "d": 5
    }
   },
   {
    "label": "a+2c = d",
    "delta": "-1/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 7
    }
   },
   {
    "label": "a+b = d",
    "delta": "1",
    "example": {
     "a": 2,
     "b": 3,
     "c": 4,
     "d": 5
    }
   },
   {
    "label": "a+c = d",
    "delta": "5/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 4
    }
   },
   {
    "label": "b+2c = 2d",
    "delta": "1/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 4
    }
   },
   {
    "label": "b+2c = d",
    "delta": "-1/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 8
    }
   },
   {
    "label": "b+c = d",
    "delta": "5/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 5
    }
   }
  ],
  "extremizerEscape": {
   "active": [
    "2b = d",
    "2c = b+d",
    "a+c = d",
    "b+2c = 2d"
   ],
   "deltaSum": "3",
   "note": "positive by inspection — the generic argument correctly fails on {1,2,3,4}"
  },
  "worklist": [
   {
    "family": "2a = d",
    "delta": "1/2",
    "example": {
     "a": 3,
     "b": 4,
     "c": 5,
     "d": 6
    }
   },
   {
    "family": "2b = d",
    "delta": "1/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 4
    }
   },
   {
    "family": "2c = d",
    "delta": "7/5",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 6
    }
   },
   {
    "family": "3c = 2d",
    "delta": "1/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 4,
     "d": 6
    }
   },
   {
    "family": "a+2c = 2d",
    "delta": "1/2",
    "example": {
     "a": 2,
     "b": 3,
     "c": 4,
     "d": 5
    }
   },
   {
    "family": "a+b = d",
    "delta": "1",
    "example": {
     "a": 2,
     "b": 3,
     "c": 4,
     "d": 5
    }
   },
   {
    "family": "a+c = d",
    "delta": "5/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 4
    }
   },
   {
    "family": "b+2c = 2d",
    "delta": "1/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 4
    }
   },
   {
    "family": "b+c = d",
    "delta": "5/2",
    "example": {
     "a": 1,
     "b": 2,
     "c": 3,
     "d": 5
    }
   }
  ],
  "closedFree": [
   {
    "family": "2c = a+d",
    "delta": "-1/2"
   },
   {
    "family": "2c = b+d",
    "delta": "-1/2"
   },
   {
    "family": "3c = d",
    "delta": "-1/2"
   },
   {
    "family": "a+2c = d",
    "delta": "-1/2"
   },
   {
    "family": "b+2c = d",
    "delta": "-1/2"
   }
  ]
 },
 "lambda4families": {
  "d = 2c": {
   "family": "d = 2c",
   "status": "CLOSED",
   "dot": {
    "base": "-2/5",
    "posBase": "6",
    "dip": "-8/5",
    "exceptions": [
     {
      "label": "2a = b",
      "delta": "1/2",
      "example": {
       "a": 1,
       "b": 2,
       "c": 3,
       "d": 6
      }
     },
     {
      "label": "2a = c",
      "delta": "7/10",
      "example": {
       "a": 2,
       "b": 3,
       "c": 4,
       "d": 8
      }
     },
     {
      "label": "2a+b = 2c",
      "delta": "-1/4",
      "example": {
       "a": 3,
       "b": 4,
       "c": 5,
       "d": 10
      }
     },
     {
      "label": "2a+b = c",
      "delta": "-1/4",
      "example": {
       "a": 1,
       "b": 2,
       "c": 4,
       "d": 8
      }
     },
     {
      "label": "2b = a+c",
      "delta": "-1/4",
      "example": {
       "a": 1,
       "b": 2,
       "c": 3,
       "d": 6
      }
     },
     {
      "label": "2b = c",
      "delta": "7/10",
      "example": {
       "a": 1,
       "b": 2,
       "c": 4,
       "d": 8
      }
     },
     {
      "label": "3a = 2c",
      "delta": "-1/4",
      "example": {
       "a": 4,
       "b": 5,
       "c": 6,
       "d": 12
      }
     },
     {
      "label": "3a = c",
      "delta": "-1/4",
      "example": {
       "a": 1,
       "b": 2,
       "c": 3,
       "d": 6
      }
     },
     {
      "label": "3b = 2c",
      "delta": "-1/4",
      "example": {
       "a": 1,
       "b": 2,
       "c": 3,
       "d": 6
      }
     },
     {
      "label": "3b = c",
      "delta": "-1/4",
      "example": {
       "a": 1,
       "b": 2,
       "c": 6,
       "d": 12
      }
     },
     {
      "label": "a+2b = 2c",
      "delta": "-1/4",
      "example": {
       "a": 2,
       "b": 3,
       "c": 4,
       "d": 8
      }
     },
     {
      "label": "a+2b = c",
      "delta": "-1/4",
      "example": {
       "a": 1,
       "b": 2,
       "c": 5,
       "d": 10
      }
     },
     {
      "label": "a+b = c",
      "delta": "2",
      "example": {
       "a": 1,
       "b": 2,
       "c": 3,
       "d": 6
      }
     }
    ]
   },
   "subfamilies": [
    {
     "label": "b = 2a",
     "closures": [
      {
       "ok": true,
       "tailMember": "a",
       "N0": 19,
       "validityFloor": 12,
       "expr": {
        "A": "-2",
        "B": "0",
        "C": "9",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-29/19",
        "hi": "-29/19"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "exact",
         "u": "1",
         "value": "-1/2"
        },
        {
         "member": "b",
         "kind": "exact",
         "u": "2",
         "value": "-1/2"
        },
        {
         "member": "c",
         "kind": "lemma3.3",
         "u": "0",
         "v": "1",
         "floor": 6
        },
        {
         "member": "d",
         "kind": "lemma3.3",
         "u": "0",
         "v": "2",
         "floor": 12
        }
       ]
      },
      {
       "ok": true,
       "tailMember": "c",
       "N0": 19,
       "validityFloor": 12,
       "expr": {
        "A": "-2",
        "B": "0",
        "C": "9",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-29/19",
        "hi": "-29/19"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "lemma3.3",
         "u": "0",
         "v": "1",
         "floor": 6
        },
        {
         "member": "b",
         "kind": "lemma3.3",
         "u": "0",
         "v": "2",
         "floor": 12
        },
        {
         "member": "c",
         "kind": "exact",
         "u": "1",
         "value": "-1/2"
        },
        {
         "member": "d",
         "kind": "exact",
         "u": "2",
         "value": "-1/2"
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 50,
      "closed": 50,
      "skipped": [],
      "undecided": []
     }
    },
    {
     "label": "c = 2a",
     "closures": [
      {
       "ok": true,
       "tailMember": "a",
       "N0": 3,
       "validityFloor": 1,
       "expr": {
        "A": "-5/2",
        "B": "1/2",
        "C": "0",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-26940119942898757703525724457607268746117945284711192278335375070549271/13803492693581127574869511724554050904902217944340773110325048447598592",
        "hi": "-3879377271777421109307704321895446697353037667746523508666855781327316151/1987702947875682370781209688335783330305919383985071327886806976454197248"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "exact",
         "u": "1",
         "value": "-1/2"
        },
        {
         "member": "b",
         "kind": "lemma3.2",
         "u": "0",
         "v": "1"
        },
        {
         "member": "c",
         "kind": "exact",
         "u": "2",
         "value": "-1/2"
        },
        {
         "member": "d",
         "kind": "exact",
         "u": "4",
         "value": "-1/2"
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 1,
      "closed": 1,
      "skipped": [],
      "undecided": []
     }
    },
    {
     "label": "c = 2b",
     "closures": [
      {
       "ok": true,
       "tailMember": "b",
       "N0": 3,
       "validityFloor": 1,
       "expr": {
        "A": "-5/2",
        "B": "1/2",
        "C": "0",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-26940119942898757703525724457607268746117945284711192278335375070549271/13803492693581127574869511724554050904902217944340773110325048447598592",
        "hi": "-3879377271777421109307704321895446697353037667746523508666855781327316151/1987702947875682370781209688335783330305919383985071327886806976454197248"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "lemma3.2",
         "u": "0",
         "v": "1"
        },
        {
         "member": "b",
         "kind": "exact",
         "u": "1",
         "value": "-1/2"
        },
        {
         "member": "c",
         "kind": "exact",
         "u": "2",
         "value": "-1/2"
        },
        {
         "member": "d",
         "kind": "exact",
         "u": "4",
         "value": "-1/2"
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 1,
      "closed": 1,
      "skipped": [],
      "undecided": []
     }
    },
    {
     "label": "c = a+b",
     "closures": [
      {
       "ok": true,
       "tailMember": "b",
       "N0": 25,
       "validityFloor": 12,
       "expr": {
        "A": "-2",
        "B": "0",
        "C": "12",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-38/25",
        "hi": "-38/25"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "lemma3.3",
         "u": "0",
         "v": "1",
         "floor": 6
        },
        {
         "member": "b",
         "kind": "exact",
         "u": "1",
         "value": "-1/2"
        },
        {
         "member": "c",
         "kind": "lemma3.3",
         "u": "1",
         "v": "1",
         "floor": 6
        },
        {
         "member": "d",
         "kind": "lemma3.3",
         "u": "2",
         "v": "2",
         "floor": 12
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 179,
      "closed": 179,
      "skipped": [],
      "undecided": []
     }
    }
   ],
   "coverage": [
    {
     "condition": "2a = b",
     "subfamily": "b = 2a",
     "pointsChecked": 380
    },
    {
     "condition": "2a = c",
     "subfamily": "c = 2a",
     "pointsChecked": 190
    },
    {
     "condition": "2b = c",
     "subfamily": "c = 2b",
     "pointsChecked": 190
    },
    {
     "condition": "a+b = c",
     "subfamily": "c = a+b",
     "pointsChecked": 380
    }
   ]
  },
  "d = 2a": {
   "family": "d = 2a",
   "status": "CLOSED",
   "dot": {
    "base": "-2/5",
    "posBase": "6",
    "dip": "-8/5",
    "exceptions": [
     {
      "label": "2u2 = 2r+u3",
      "delta": "-7/5",
      "example": {
       "a": 4,
       "b": 6,
       "c": 7,
       "d": 8
      }
     },
     {
      "label": "2u2 = 3r",
      "delta": "-1/4",
      "example": {
       "a": 4,
       "b": 5,
       "c": 6,
       "d": 8
      }
     },
     {
      "label": "2u2 = 3r+u3",
      "delta": "-1/4",
      "example": {
       "a": 5,
       "b": 8,
       "c": 9,
       "d": 10
      }
     },
     {
      "label": "2u2 = r+u3",
      "delta": "-1/4",
      "example": {
       "a": 3,
       "b": 4,
       "c": 5,
       "d": 6
      }
     },
     {
      "label": "2u3 = 3r",
      "delta": "-1/4",
      "example": {
       "a": 6,
       "b": 7,
       "c": 8,
       "d": 12
      }
     },
     {
      "label": "3u2 = 3r+2u3",
      "delta": "-1/4",
      "example": {
       "a": 6,
       "b": 10,
       "c": 11,
       "d": 12
      }
     },
     {
      "label": "3u2 = 3r+u3",
      "delta": "-1/4",
      "example": {
       "a": 3,
       "b": 4,
       "c": 5,
       "d": 6
      }
     },
     {
      "label": "u2 = 2r",
      "delta": "-4",
      "example": {
       "a": 3,
       "b": 4,
       "c": 5,
       "d": 6
      }
     },
     {
      "label": "u2 = 3r",
      "delta": "-1/4",
      "example": {
       "a": 4,
       "b": 6,
       "c": 7,
       "d": 8
      }
     },
     {
      "label": "u2+u3 = 3r",
      "delta": "-1/4",
      "example": {
       "a": 5,
       "b": 6,
       "c": 7,
       "d": 10
      }
     },
     {
      "label": "u3 = 2r",
      "delta": "-7/5",
      "example": {
       "a": 4,
       "b": 5,
       "c": 6,
       "d": 8
      }
     },
     {
      "label": "u3 = 3r",
      "delta": "-1/4",
      "example": {
       "a": 3,
       "b": 4,
       "c": 5,
       "d": 6
      }
     },
     {
      "label": "u3 = r+u2",
      "delta": "-1/4",
      "example": {
       "a": 3,
       "b": 4,
       "c": 5,
       "d": 6
      }
     }
    ]
   },
   "subfamilies": [],
   "coverage": [],
   "ontoChecked": 440
  },
  "d = b+c": {
   "family": "d = b+c",
   "status": "CLOSED",
   "dot": {
    "base": "-1/5",
    "posBase": "3",
    "dip": "-8/5",
    "exceptions": [
     {
      "label": "3a = b+c",
      "delta": "-1/2",
      "example": {
       "a": 3,
       "b": 4,
       "c": 5,
       "d": 9
      }
     }
    ]
   },
   "subfamilies": [],
   "coverage": [],
   "ontoChecked": 2024
  },
  "d = a+b": {
   "family": "d = a+b",
   "status": "CLOSED",
   "dot": {
    "base": "-1/5",
    "posBase": "3",
    "dip": "-8/5",
    "exceptions": [
     {
      "label": "2u3 = 2r+u2",
      "delta": "1/2",
      "example": {
       "a": 4,
       "b": 5,
       "c": 6,
       "d": 9
      }
     }
    ]
   },
   "subfamilies": [
    {
     "label": "E: 2d = 3c",
     "closures": [
      {
       "ok": true,
       "tailMember": null,
       "N0": 8,
       "validityFloor": 1,
       "expr": {
        "A": "-2",
        "B": "1/2",
        "C": "0",
        "D": "1"
       },
       "boundAtN0": {
        "lo": "-1351809948738618920028397686447221677151549320993329049914751943957020111/883423532389192164791648750371459257913741948437809479060803100646309888",
        "hi": "-21628959179817902720454362983155546827019930699501713127607364633359164599/14134776518227074636666380005943348126619871175004951664972849610340958208"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "lemma3.2",
         "u": "1",
         "v": "1"
        },
        {
         "member": "b",
         "kind": "lemma-halfpi",
         "u": "2",
         "v": "-1"
        },
        {
         "member": "c",
         "kind": "exact",
         "u": "2",
         "value": "-1"
        },
        {
         "member": "d",
         "kind": "exact",
         "u": "3",
         "value": "0"
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 8,
      "closed": 8,
      "skipped": [],
      "undecided": []
     }
    }
   ],
   "coverage": [
    {
     "condition": "2u3 = 2r+u2",
     "subfamilies": [
      "E: 2d = 3c"
     ],
     "pointsChecked": 30
    }
   ],
   "ontoChecked": 946
  },
  "d = a+c": {
   "family": "d = a+c",
   "status": "CLOSED",
   "dot": {
    "base": "-1/5",
    "posBase": "3",
    "dip": "-8/5",
    "exceptions": [
     {
      "label": "2b = a+c",
      "delta": "7/5",
      "example": {
       "a": 1,
       "b": 2,
       "c": 3,
       "d": 4
      }
     },
     {
      "label": "3b = 2a+2c",
      "delta": "1/2",
      "example": {
       "a": 1,
       "b": 4,
       "c": 5,
       "d": 6
      }
     },
     {
      "label": "3b = a+c",
      "delta": "-1/2",
      "example": {
       "a": 1,
       "b": 2,
       "c": 5,
       "d": 6
      }
     }
    ]
   },
   "subfamilies": [
    {
     "label": "AP: 2b = a+c",
     "closures": [
      {
       "ok": true,
       "tailMember": "b",
       "N0": 5,
       "validityFloor": 1,
       "expr": {
        "A": "-2",
        "B": "1",
        "C": "0",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-276969811220041638268905299429850545977317052423252663280830996753939919/172543658669764094685868896556925636311277724304259663879063105594982400",
        "hi": "-4431516979520666212302484790877608733549126385520154433079857719231259831/2760698538716225514973902344910810180980443588868154622065009689519718400"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "lemma3.2",
         "u": "1",
         "v": "-1"
        },
        {
         "member": "b",
         "kind": "exact",
         "u": "1",
         "value": "-1"
        },
        {
         "member": "c",
         "kind": "lemma3.2",
         "u": "1",
         "v": "1"
        },
        {
         "member": "d",
         "kind": "exact",
         "u": "2",
         "value": "1"
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 5,
      "closed": 4,
      "skipped": [
       "1,2,3,4"
      ],
      "undecided": []
     }
    },
    {
     "label": "3b = 2d",
     "closures": [
      {
       "ok": true,
       "tailMember": null,
       "N0": 8,
       "validityFloor": 1,
       "expr": {
        "A": "-2",
        "B": "1/2",
        "C": "0",
        "D": "1"
       },
       "boundAtN0": {
        "lo": "-1351809948738618920028397686447221677151549320993329049914751943957020111/883423532389192164791648750371459257913741948437809479060803100646309888",
        "hi": "-21628959179817902720454362983155546827019930699501713127607364633359164599/14134776518227074636666380005943348126619871175004951664972849610340958208"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "lemma-halfpi",
         "u": "0",
         "v": "1"
        },
        {
         "member": "b",
         "kind": "exact",
         "u": "2",
         "value": "-1"
        },
        {
         "member": "c",
         "kind": "lemma3.2",
         "u": "3",
         "v": "-1"
        },
        {
         "member": "d",
         "kind": "exact",
         "u": "3",
         "value": "0"
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 17,
      "closed": 17,
      "skipped": [],
      "undecided": []
     }
    }
   ],
   "coverage": [
    {
     "condition": "2b = a+c",
     "subfamilies": [
      "AP: 2b = a+c"
     ],
     "pointsChecked": 132
    },
    {
     "condition": "3b = 2a+2c",
     "subfamilies": [
      "3b = 2d"
     ],
     "pointsChecked": 40
    }
   ],
   "ontoChecked": 2024
  },
  "2d = 2c+a": {
   "family": "2d = 2c+a",
   "status": "CLOSED",
   "dot": {
    "base": "-1/5",
    "posBase": "3",
    "dip": "-8/5",
    "exceptions": [
     {
      "label": "2t = u3",
      "delta": "7/5",
      "example": {
       "a": 4,
       "b": 5,
       "c": 6,
       "d": 8
      }
     },
     {
      "label": "3t = u2",
      "delta": "1/2",
      "example": {
       "a": 2,
       "b": 4,
       "c": 5,
       "d": 6
      }
     },
     {
      "label": "3t = u3",
      "delta": "1/2",
      "example": {
       "a": 2,
       "b": 3,
       "c": 4,
       "d": 5
      }
     },
     {
      "label": "3t+u2 = u3",
      "delta": "-1/2",
      "example": {
       "a": 2,
       "b": 3,
       "c": 6,
       "d": 7
      }
     },
     {
      "label": "4t = u3",
      "delta": "-1/2",
      "example": {
       "a": 2,
       "b": 3,
       "c": 5,
       "d": 6
      }
     },
     {
      "label": "t+u2 = u3",
      "delta": "2",
      "example": {
       "a": 2,
       "b": 3,
       "c": 4,
       "d": 5
      }
     }
    ]
   },
   "subfamilies": [
    {
     "label": "2c = 3a",
     "closures": [
      {
       "ok": true,
       "tailMember": null,
       "N0": 6,
       "validityFloor": 6,
       "expr": {
        "A": "-5/2",
        "B": "0",
        "C": "3",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-2",
        "hi": "-2"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "exact",
         "u": "2",
         "value": "-1/2"
        },
        {
         "member": "b",
         "kind": "lemma3.3",
         "u": "2",
         "v": "1",
         "floor": 6
        },
        {
         "member": "c",
         "kind": "exact",
         "u": "3",
         "value": "-1"
        },
        {
         "member": "d",
         "kind": "exact",
         "u": "4",
         "value": "-1/2"
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 9,
      "closed": 9,
      "skipped": [],
      "undecided": []
     }
    },
    {
     "label": "b = 2a",
     "closures": [
      {
       "ok": true,
       "tailMember": null,
       "N0": 13,
       "validityFloor": 6,
       "expr": {
        "A": "-2",
        "B": "0",
        "C": "6",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-20/13",
        "hi": "-20/13"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "exact",
         "u": "2",
         "value": "-1/2"
        },
        {
         "member": "b",
         "kind": "exact",
         "u": "4",
         "value": "-1/2"
        },
        {
         "member": "c",
         "kind": "lemma3.3",
         "u": "0",
         "v": "1",
         "floor": 6
        },
        {
         "member": "d",
         "kind": "lemma3.3",
         "u": "1",
         "v": "1",
         "floor": 6
        }
       ]
      },
      {
       "ok": true,
       "tailMember": "c",
       "N0": 44,
       "validityFloor": 24,
       "expr": {
        "A": "-2",
        "B": "0",
        "C": "21",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-67/44",
        "hi": "-67/44"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "lemma3.3",
         "u": "0",
         "v": "2",
         "floor": 12
        },
        {
         "member": "b",
         "kind": "lemma3.3",
         "u": "0",
         "v": "4",
         "floor": 24
        },
        {
         "member": "c",
         "kind": "exact",
         "u": "1",
         "value": "-1/2"
        },
        {
         "member": "d",
         "kind": "lemma3.3",
         "u": "1",
         "v": "1",
         "floor": 6
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 144,
      "closed": 144,
      "skipped": [],
      "undecided": []
     }
    },
    {
     "label": "c = 2a, b < 3a/2·2",
     "closures": [
      {
       "ok": true,
       "tailMember": null,
       "N0": 7,
       "validityFloor": 6,
       "expr": {
        "A": "-2",
        "B": "0",
        "C": "3",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-11/7",
        "hi": "-11/7"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "exact",
         "u": "2",
         "value": "-1/2"
        },
        {
         "member": "b",
         "kind": "lemma3.3",
         "u": "2",
         "v": "1",
         "floor": 6
        },
        {
         "member": "c",
         "kind": "exact",
         "u": "4",
         "value": "-1/2"
        },
        {
         "member": "d",
         "kind": "exact",
         "u": "5",
         "value": "-1/2"
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 11,
      "closed": 11,
      "skipped": [],
      "undecided": []
     }
    },
    {
     "label": "c = 2a, b = 3al",
     "closures": [],
     "finite": {
      "ok": true,
      "enumerated": 1,
      "closed": 1,
      "skipped": [],
      "undecided": []
     }
    },
    {
     "label": "c = 2a, b > 3al",
     "closures": [
      {
       "ok": true,
       "tailMember": null,
       "N0": 7,
       "validityFloor": 6,
       "expr": {
        "A": "-2",
        "B": "0",
        "C": "3",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-11/7",
        "hi": "-11/7"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "exact",
         "u": "2",
         "value": "-1/2"
        },
        {
         "member": "b",
         "kind": "lemma3.3",
         "u": "3",
         "v": "1",
         "floor": 6
        },
        {
         "member": "c",
         "kind": "exact",
         "u": "4",
         "value": "-1/2"
        },
        {
         "member": "d",
         "kind": "exact",
         "u": "5",
         "value": "-1/2"
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 11,
      "closed": 11,
      "skipped": [],
      "undecided": []
     }
    },
    {
     "label": "2c = 2b+a",
     "closures": [
      {
       "ok": true,
       "tailMember": null,
       "N0": 14,
       "validityFloor": 1,
       "expr": {
        "A": "-2",
        "B": "1/2",
        "C": "0",
        "D": "2"
       },
       "boundAtN0": {
        "lo": "-84257816225374274564566948575515323183040702225647653912585043405594111/55213970774324510299478046898216203619608871777363092441300193790394368",
        "hi": "-66058127920693431258620487683204013354806772150667050267399936957229180087/43287753087070416074790788768201503637773355473452664473979351931669184512"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "exact",
         "u": "2",
         "value": "-1"
        },
        {
         "member": "b",
         "kind": "lemma-halfpi",
         "u": "0",
         "v": "1"
        },
        {
         "member": "c",
         "kind": "lemma3.2",
         "u": "1",
         "v": "1"
        },
        {
         "member": "d",
         "kind": "lemma-halfpi",
         "u": "2",
         "v": "1"
        }
       ]
      },
      {
       "ok": true,
       "tailMember": "b",
       "N0": 17,
       "validityFloor": 1,
       "expr": {
        "A": "-2",
        "B": "5/2",
        "C": "0",
        "D": "2"
       },
       "boundAtN0": {
        "lo": "-6163422904131273834339129195772529313676831227190284749530775998208668939/3989209388444945869137288888396120711516740985914483428883939001355993088",
        "hi": "-98614766466100381349426067132360468985792691440441545256060504802413950867/63827350215119133906196622214337931384267855774631734862143024021695889408"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "lemma3.2",
         "u": "0",
         "v": "2"
        },
        {
         "member": "b",
         "kind": "exact",
         "u": "1",
         "value": "0"
        },
        {
         "member": "c",
         "kind": "lemma3.2",
         "u": "1",
         "v": "1"
        },
        {
         "member": "d",
         "kind": "lemma-halfpi",
         "u": "1",
         "v": "2"
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 39,
      "closed": 39,
      "skipped": [],
      "undecided": []
     }
    }
   ],
   "coverage": [
    {
     "condition": "2t = u3",
     "subfamilies": [
      "2c = 3a"
     ],
     "pointsChecked": 28
    },
    {
     "condition": "3t = u2",
     "subfamilies": [
      "b = 2a"
     ],
     "pointsChecked": 60
    },
    {
     "condition": "3t = u3",
     "subfamilies": [
      "c = 2a, b < 3a/2·2",
      "c = 2a, b = 3al",
      "c = 2a, b > 3al"
     ],
     "pointsChecked": 36
    },
    {
     "condition": "t+u2 = u3",
     "subfamilies": [
      "2c = 2b+a"
     ],
     "pointsChecked": 84
    }
   ],
   "ontoChecked": 946
  },
  "d = 2b": {
   "family": "d = 2b",
   "status": "CLOSED",
   "cones": {
    "D1": {
     "base": "-2/5",
     "dip": "-8/5",
     "exceptions": [
      {
       "key": "1,-1,-1",
       "delta": "7/10"
      },
      {
       "key": "1,-1,-2",
       "delta": "1/2"
      },
      {
       "key": "2,0,-1",
       "delta": "-1/4"
      },
      {
       "key": "0,1,-1",
       "delta": "1/2"
      },
      {
       "key": "1,1,-1",
       "delta": "-7/5"
      },
      {
       "key": "1,-2,-2",
       "delta": "-1/4"
      },
      {
       "key": "2,-1,-1",
       "delta": "-1/4"
      },
      {
       "key": "1,1,-2",
       "delta": "-1/4"
      },
      {
       "key": "2,2,-1",
       "delta": "-1/4"
      },
      {
       "key": "1,0,-2",
       "delta": "-1/4"
      },
      {
       "key": "2,1,-1",
       "delta": "1/2"
      },
      {
       "key": "1,0,-1",
       "delta": "2"
      },
      {
       "key": "1,-1,0",
       "delta": "-1/4"
      }
     ]
    },
    "D2": {
     "closure": {
      "ok": true,
      "tailMember": "b",
      "N0": 13,
      "validityFloor": 6,
      "expr": {
       "A": "-2",
       "B": "0",
       "C": "6",
       "D": "0"
      },
      "boundAtN0": {
       "lo": "-20/13",
       "hi": "-20/13"
      },
      "target": {
       "lo": "-855435038691829/562949953421312",
       "hi": "-6843480309534631/4503599627370496"
      },
      "pieces": [
       {
        "member": "a",
        "kind": "lemma3.3",
        "u": "0",
        "v": "1",
        "floor": 6
       },
       {
        "member": "b",
        "kind": "exact",
        "u": "1",
        "value": "-1/2"
       },
       {
        "member": "c",
        "kind": "lemma3.3",
        "u": "1",
        "v": "1",
        "floor": 6
       },
       {
        "member": "d",
        "kind": "exact",
        "u": "2",
        "value": "-1/2"
       }
      ]
     },
     "finite": {
      "ok": true,
      "enumerated": 45,
      "closed": 44,
      "skipped": [
       "1,2,3,4"
      ],
      "undecided": []
     }
    },
    "D3": {
     "base": "-2/5",
     "dip": "-8/5",
     "exceptions": [
      {
       "key": "0,1,-1",
       "delta": "1/2"
      },
      {
       "key": "1,1,-1",
       "delta": "7/10"
      },
      {
       "key": "1,-1,0",
       "delta": "-1/4"
      },
      {
       "key": "1,-1,-1",
       "delta": "-7/5"
      },
      {
       "key": "1,-1,-2",
       "delta": "-1/4"
      },
      {
       "key": "2,0,-1",
       "delta": "1/2"
      },
      {
       "key": "1,1,-2",
       "delta": "-1/4"
      },
      {
       "key": "2,2,-1",
       "delta": "-1/4"
      },
      {
       "key": "1,-2,-2",
       "delta": "-1/4"
      },
      {
       "key": "2,-1,-1",
       "delta": "-1/4"
      },
      {
       "key": "1,0,-2",
       "delta": "1/2"
      },
      {
       "key": "2,1,-1",
       "delta": "-1/4"
      },
      {
       "key": "1,0,-1",
       "delta": "2"
      }
     ]
    }
   },
   "subfamilies": [
    {
     "label": "U1: b = 2a",
     "parts": [
      {
       "closures": [
        {
         "ok": true,
         "tailMember": null,
         "N0": 7,
         "validityFloor": 6,
         "expr": {
          "A": "-2",
          "B": "0",
          "C": "3",
          "D": "0"
         },
         "boundAtN0": {
          "lo": "-11/7",
          "hi": "-11/7"
         },
         "target": {
          "lo": "-855435038691829/562949953421312",
          "hi": "-6843480309534631/4503599627370496"
         },
         "pieces": [
          {
           "member": "a",
           "kind": "exact",
           "u": "1",
           "value": "-1/2"
          },
          {
           "member": "b",
           "kind": "exact",
           "u": "2",
           "value": "-1/2"
          },
          {
           "member": "c",
           "kind": "lemma3.3",
           "u": "0",
           "v": "1",
           "floor": 6
          },
          {
           "member": "d",
           "kind": "exact",
           "u": "4",
           "value": "-1/2"
          }
         ]
        }
       ],
       "finite": {
        "ok": true,
        "enumerated": 11,
        "closed": 11,
        "skipped": [],
        "undecided": []
       }
      },
      {
       "closures": [
        {
         "ok": true,
         "tailMember": null,
         "N0": 7,
         "validityFloor": 6,
         "expr": {
          "A": "-2",
          "B": "0",
          "C": "3",
          "D": "0"
         },
         "boundAtN0": {
          "lo": "-11/7",
          "hi": "-11/7"
         },
         "target": {
          "lo": "-855435038691829/562949953421312",
          "hi": "-6843480309534631/4503599627370496"
         },
         "pieces": [
          {
           "member": "a",
           "kind": "exact",
           "u": "1",
           "value": "-1/2"
          },
          {
           "member": "b",
           "kind": "exact",
           "u": "2",
           "value": "-1/2"
          },
          {
           "member": "c",
           "kind": "lemma3.3",
           "u": "0",
           "v": "1",
           "floor": 6
          },
          {
           "member": "d",
           "kind": "exact",
           "u": "4",
           "value": "-1/2"
          }
         ]
        }
       ],
       "finite": {
        "ok": true,
        "enumerated": 11,
        "closed": 11,
        "skipped": [],
        "undecided": []
       }
      },
      {
       "closures": [],
       "finite": {
        "ok": true,
        "enumerated": 1,
        "closed": 0,
        "skipped": [
         "1,2,3,4"
        ],
        "undecided": []
       }
      }
     ]
    },
    {
     "label": "U2: c = 2b-a (AP)",
     "parts": [
      {
       "closures": [
        {
         "ok": true,
         "tailMember": "b",
         "N0": 5,
         "validityFloor": 1,
         "expr": {
          "A": "-2",
          "B": "1",
          "C": "0",
          "D": "0"
         },
         "boundAtN0": {
          "lo": "-276969811220041638268905299429850545977317052423252663280830996753939919/172543658669764094685868896556925636311277724304259663879063105594982400",
          "hi": "-4431516979520666212302484790877608733549126385520154433079857719231259831/2760698538716225514973902344910810180980443588868154622065009689519718400"
         },
         "target": {
          "lo": "-855435038691829/562949953421312",
          "hi": "-6843480309534631/4503599627370496"
         },
         "pieces": [
          {
           "member": "a",
           "kind": "lemma3.2",
           "u": "1",
           "v": "-1"
          },
          {
           "member": "b",
           "kind": "exact",
           "u": "1",
           "value": "-1"
          },
          {
           "member": "c",
           "kind": "lemma3.2",
           "u": "1",
           "v": "1"
          },
          {
           "member": "d",
           "kind": "exact",
           "u": "2",
           "value": "1"
          }
         ]
        }
       ],
       "finite": {
        "ok": true,
        "enumerated": 5,
        "closed": 4,
        "skipped": [
         "1,2,3,4"
        ],
        "undecided": []
       }
      }
     ]
    },
    {
     "label": "U3: c = 3b-2a",
     "parts": [
      {
       "closures": [
        {
         "ok": true,
         "tailMember": "b",
         "N0": 19,
         "validityFloor": 12,
         "expr": {
          "A": "-2",
          "B": "0",
          "C": "9",
          "D": "0"
         },
         "boundAtN0": {
          "lo": "-29/19",
          "hi": "-29/19"
         },
         "target": {
          "lo": "-855435038691829/562949953421312",
          "hi": "-6843480309534631/4503599627370496"
         },
         "pieces": [
          {
           "member": "a",
           "kind": "lemma3.3",
           "u": "0",
           "v": "1",
           "floor": 6
          },
          {
           "member": "b",
           "kind": "exact",
           "u": "1",
           "value": "-1/2"
          },
          {
           "member": "c",
           "kind": "lemma3.3",
           "u": "3",
           "v": "-2",
           "floor": 12
          },
          {
           "member": "d",
           "kind": "exact",
           "u": "2",
           "value": "-1/2"
          }
         ]
        }
       ],
       "finite": {
        "ok": true,
        "enumerated": 50,
        "closed": 50,
        "skipped": [],
        "undecided": []
       }
      }
     ]
    },
    {
     "label": "U4: 2c = 3b+a",
     "parts": [
      {
       "closures": [
        {
         "ok": true,
         "tailMember": "b",
         "N0": 19,
         "validityFloor": 12,
         "expr": {
          "A": "-2",
          "B": "0",
          "C": "9",
          "D": "0"
         },
         "boundAtN0": {
          "lo": "-29/19",
          "hi": "-29/19"
         },
         "target": {
          "lo": "-855435038691829/562949953421312",
          "hi": "-6843480309534631/4503599627370496"
         },
         "pieces": [
          {
           "member": "a",
           "kind": "lemma3.3",
           "u": "1",
           "v": "-2",
           "floor": 12
          },
          {
           "member": "b",
           "kind": "exact",
           "u": "1",
           "value": "-1/2"
          },
          {
           "member": "c",
           "kind": "lemma3.3",
           "u": "2",
           "v": "-1",
           "floor": 6
          },
          {
           "member": "d",
           "kind": "exact",
           "u": "2",
           "value": "-1/2"
          }
         ]
        }
       ],
       "finite": {
        "ok": true,
        "enumerated": 50,
        "closed": 50,
        "skipped": [],
        "undecided": []
       }
      }
     ]
    },
    {
     "label": "U5: 2c = 3b-a",
     "parts": [
      {
       "closures": [
        {
         "ok": true,
         "tailMember": null,
         "N0": 32,
         "validityFloor": 12,
         "expr": {
          "A": "-2",
          "B": "0",
          "C": "15",
          "D": "0"
         },
         "boundAtN0": {
          "lo": "-49/32",
          "hi": "-49/32"
         },
         "target": {
          "lo": "-855435038691829/562949953421312",
          "hi": "-6843480309534631/4503599627370496"
         },
         "pieces": [
          {
           "member": "a",
           "kind": "lemma3.3",
           "u": "0",
           "v": "1",
           "floor": 6
          },
          {
           "member": "b",
           "kind": "lemma3.3",
           "u": "2",
           "v": "1",
           "floor": 6
          },
          {
           "member": "c",
           "kind": "lemma3.3",
           "u": "3",
           "v": "1",
           "floor": 6
          },
          {
           "member": "d",
           "kind": "lemma3.3",
           "u": "4",
           "v": "2",
           "floor": 12
          }
         ]
        },
        {
         "ok": true,
         "tailMember": null,
         "N0": 57,
         "validityFloor": 24,
         "expr": {
          "A": "-2",
          "B": "0",
          "C": "27",
          "D": "0"
         },
         "boundAtN0": {
          "lo": "-29/19",
          "hi": "-29/19"
         },
         "target": {
          "lo": "-855435038691829/562949953421312",
          "hi": "-6843480309534631/4503599627370496"
         },
         "pieces": [
          {
           "member": "a",
           "kind": "exact",
           "u": "1",
           "value": "-1/2"
          },
          {
           "member": "b",
           "kind": "lemma3.3",
           "u": "1",
           "v": "2",
           "floor": 12
          },
          {
           "member": "c",
           "kind": "lemma3.3",
           "u": "1",
           "v": "3",
           "floor": 18
          },
          {
           "member": "d",
           "kind": "lemma3.3",
           "u": "2",
           "v": "4",
           "floor": 24
          }
         ]
        }
       ],
       "finite": {
        "ok": true,
        "enumerated": 1090,
        "closed": 1090,
        "skipped": [],
        "undecided": []
       }
      }
     ]
    },
    {
     "label": "U6: c = 2a",
     "parts": [
      {
       "closures": [
        {
         "ok": true,
         "tailMember": null,
         "N0": 19,
         "validityFloor": 12,
         "expr": {
          "A": "-2",
          "B": "0",
          "C": "9",
          "D": "0"
         },
         "boundAtN0": {
          "lo": "-29/19",
          "hi": "-29/19"
         },
         "target": {
          "lo": "-855435038691829/562949953421312",
          "hi": "-6843480309534631/4503599627370496"
         },
         "pieces": [
          {
           "member": "a",
           "kind": "exact",
           "u": "1",
           "value": "-1/2"
          },
          {
           "member": "b",
           "kind": "lemma3.3",
           "u": "0",
           "v": "1",
           "floor": 6
          },
          {
           "member": "c",
           "kind": "exact",
           "u": "2",
           "value": "-1/2"
          },
          {
           "member": "d",
           "kind": "lemma3.3",
           "u": "0",
           "v": "2",
           "floor": 12
          }
         ]
        }
       ],
       "finite": {
        "ok": true,
        "enumerated": 101,
        "closed": 101,
        "skipped": [],
        "undecided": []
       }
      }
     ]
    }
   ],
   "coverage": [
    {
     "subfamily": "U1: b = 2a",
     "pointsChecked": 144
    },
    {
     "subfamily": "U2: c = 2b-a (AP)",
     "pointsChecked": 276
    },
    {
     "subfamily": "U3: c = 3b-2a",
     "pointsChecked": 132
    },
    {
     "subfamily": "U4: 2c = 3b+a",
     "pointsChecked": 132
    },
    {
     "subfamily": "U5: 2c = 3b-a",
     "pointsChecked": 132
    },
    {
     "subfamily": "U6: c = 2a",
     "pointsChecked": 132
    }
   ],
   "ontoChecked": 4324
  },
  "2d = 2c+b": {
   "family": "2d = 2c+b",
   "status": "CLOSED",
   "cones": {
    "i": {
     "base": "-1/5",
     "dip": "-8/5",
     "exceptions": [
      {
       "key": "1,-1,-1",
       "delta": "1/2"
      },
      {
       "key": "2,0,-1",
       "delta": "-1/2"
      },
      {
       "key": "1,-2,-1",
       "delta": "-1/2"
      },
      {
       "key": "1,0,-1",
       "delta": "2"
      },
      {
       "key": "1,-1,0",
       "delta": "-1/2"
      }
     ]
    },
    "ii": {
     "closures": [
      {
       "ok": true,
       "tailMember": "a",
       "N0": 13,
       "validityFloor": 6,
       "expr": {
        "A": "-2",
        "B": "0",
        "C": "6",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-20/13",
        "hi": "-20/13"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "exact",
         "u": "1",
         "value": "-1/2"
        },
        {
         "member": "b",
         "kind": "exact",
         "u": "2",
         "value": "-1/2"
        },
        {
         "member": "c",
         "kind": "lemma3.3",
         "u": "0",
         "v": "1",
         "floor": 6
        },
        {
         "member": "d",
         "kind": "lemma3.3",
         "u": "1",
         "v": "1",
         "floor": 6
        }
       ]
      },
      {
       "ok": true,
       "tailMember": "c",
       "N0": 25,
       "validityFloor": 12,
       "expr": {
        "A": "-2",
        "B": "0",
        "C": "12",
        "D": "0"
       },
       "boundAtN0": {
        "lo": "-38/25",
        "hi": "-38/25"
       },
       "target": {
        "lo": "-855435038691829/562949953421312",
        "hi": "-6843480309534631/4503599627370496"
       },
       "pieces": [
        {
         "member": "a",
         "kind": "lemma3.3",
         "u": "0",
         "v": "1",
         "floor": 6
        },
        {
         "member": "b",
         "kind": "lemma3.3",
         "u": "0",
         "v": "2",
         "floor": 12
        },
        {
         "member": "c",
         "kind": "exact",
         "u": "1",
         "value": "-1/2"
        },
        {
         "member": "d",
         "kind": "lemma3.3",
         "u": "1",
         "v": "1",
         "floor": 6
        }
       ]
      }
     ],
     "finite": {
      "ok": true,
      "enumerated": 89,
      "closed": 88,
      "skipped": [
       "1,2,3,4"
      ],
      "undecided": []
     }
    },
    "iii": {
     "base": "-1/5",
     "dip": "-8/5",
     "exceptions": [
      {
       "key": "1,-1,-1",
       "delta": "1/2"
      },
      {
       "key": "2,0,-2",
       "delta": "1/2"
      },
      {
       "key": "3,1,-1",
       "delta": "1/2"
      },
      {
       "key": "4,2,-1",
       "delta": "-1/2"
      },
      {
       "key": "1,-1,-2",
       "delta": "-1/2"
      },
      {
       "key": "2,0,-1",
       "delta": "7/5"
      },
      {
       "key": "4,1,-1",
       "delta": "-1/2"
      },
      {
       "key": "2,-1,-2",
       "delta": "1/2"
      },
      {
       "key": "2,1,-1",
       "delta": "2"
      },
      {
       "key": "1,0,-1",
       "delta": "-2"
      }
     ]
    }
   },
   "subfamilies": {
    "V1": {
     "label": "d = b+2a",
     "closure": {
      "ok": true,
      "tailMember": null,
      "N0": 13,
      "validityFloor": 12,
      "expr": {
       "A": "-5/2",
       "B": "1/2",
       "C": "12",
       "D": "0"
      },
      "boundAtN0": {
       "lo": "-3610513296719883947599892380909653839511202685981549369424330196848999887/2332790265215210560152947481449634602928474832593590655644933187644162048",
       "hi": "-57768212747518143161598278094554461430091296522452901731375844920752219319/37324644243443368962447159703194153646855597321497450490318931002306592768"
      },
      "target": {
       "lo": "-855435038691829/562949953421312",
       "hi": "-6843480309534631/4503599627370496"
      },
      "pieces": [
       {
        "member": "a",
        "kind": "lemma3.2",
        "u": "0",
        "v": "1"
       },
       {
        "member": "b",
        "kind": "exact",
        "u": "2",
        "value": "-1/2"
       },
       {
        "member": "c",
        "kind": "lemma3.3",
        "u": "1",
        "v": "2",
        "floor": 12
       },
       {
        "member": "d",
        "kind": "lemma3.3",
        "u": "2",
        "v": "2",
        "floor": 12
       }
      ]
     },
     "finite": {
      "ok": true,
      "enumerated": 22,
      "closed": 22,
      "skipped": [],
      "undecided": []
     }
    },
    "V2": {
     "label": "c = a+b",
     "parts": [
      {
       "closure": {
        "ok": true,
        "tailMember": null,
        "N0": 19,
        "validityFloor": 6,
        "expr": {
         "A": "-2",
         "B": "0",
         "C": "9",
         "D": "0"
        },
        "boundAtN0": {
         "lo": "-29/19",
         "hi": "-29/19"
        },
        "target": {
         "lo": "-855435038691829/562949953421312",
         "hi": "-6843480309534631/4503599627370496"
        },
        "pieces": [
         {
          "member": "a",
          "kind": "lemma3.3",
          "u": "0",
          "v": "1",
          "floor": 6
         },
         {
          "member": "b",
          "kind": "exact",
          "u": "2",
          "value": "-1/2"
         },
         {
          "member": "c",
          "kind": "lemma3.3",
          "u": "2",
          "v": "1",
          "floor": 6
         },
         {
          "member": "d",
          "kind": "lemma3.3",
          "u": "3",
          "v": "1",
          "floor": 6
         }
        ]
       },
       "finite": {
        "ok": true,
        "enumerated": 101,
        "closed": 101,
        "skipped": [],
        "undecided": []
       }
      },
      {
       "finite": {
        "ok": true,
        "enumerated": 1,
        "closed": 0,
        "skipped": [
         "1,2,3,4"
        ],
        "undecided": []
       }
      },
      {
       "closure": {
        "ok": true,
        "tailMember": null,
        "N0": 19,
        "validityFloor": 6,
        "expr": {
         "A": "-2",
         "B": "0",
         "C": "9",
         "D": "0"
        },
        "boundAtN0": {
         "lo": "-29/19",
         "hi": "-29/19"
        },
        "target": {
         "lo": "-855435038691829/562949953421312",
         "hi": "-6843480309534631/4503599627370496"
        },
        "pieces": [
         {
          "member": "a",
          "kind": "lemma3.3",
          "u": "0",
          "v": "1",
          "floor": 6
         },
         {
          "member": "b",
          "kind": "exact",
          "u": "2",
          "value": "-1/2"
         },
         {
          "member": "c",
          "kind": "lemma3.3",
          "u": "2",
          "v": "1",
          "floor": 6
         },
         {
          "member": "d",
          "kind": "lemma3.3",
          "u": "3",
          "v": "1",
          "floor": 6
         }
        ]
       },
       "finite": {
        "ok": true,
        "enumerated": 101,
        "closed": 101,
        "skipped": [],
        "undecided": []
       }
      }
     ]
    },
    "V3": {
     "label": "d = 2a",
     "delegated": "family d = 2a"
    },
    "V4": {
     "label": "d = a+b",
     "delegated": "family d = a+b"
    },
    "V5": {
     "label": "d = 2c-2a",
     "closure": {
      "ok": true,
      "tailMember": null,
      "N0": 6,
      "validityFloor": 1,
      "expr": {
       "A": "-3",
       "B": "5/2",
       "C": "0",
       "D": "1"
      },
      "boundAtN0": {
       "lo": "-98888885874346653192521589708117975608913935809966971192384430887315827/55213970774324510299478046898216203619608871777363092441300193790394368",
       "hi": "-14239999565905918059723108917968988473256190503021055335924745722773550995/7950811791502729483124838753343133321223677535940285311547227905816788992"
      },
      "target": {
       "lo": "-855435038691829/562949953421312",
       "hi": "-6843480309534631/4503599627370496"
      },
      "pieces": [
       {
        "member": "a",
        "kind": "lemma3.2",
        "u": "0",
        "v": "1"
       },
       {
        "member": "b",
        "kind": "lemma3.2",
        "u": "2",
        "v": "-2"
       },
       {
        "member": "c",
        "kind": "lemma-halfpi",
        "u": "1",
        "v": "1"
       },
       {
        "member": "d",
        "kind": "exact",
        "u": "2",
        "value": "-1"
       }
      ]
     },
     "finite": {
      "ok": true,
      "enumerated": 1,
      "closed": 1,
      "skipped": [],
      "undecided": []
     }
    },
    "V6": {
     "label": "c = 2a",
     "closure": {
      "ok": true,
      "tailMember": null,
      "N0": 19,
      "validityFloor": 12,
      "expr": {
       "A": "-2",
       "B": "0",
       "C": "9",
       "D": "0"
      },
      "boundAtN0": {
       "lo": "-29/19",
       "hi": "-29/19"
      },
      "target": {
       "lo": "-855435038691829/562949953421312",
       "hi": "-6843480309534631/4503599627370496"
      },
      "pieces": [
       {
        "member": "a",
        "kind": "exact",
        "u": "1",
        "value": "-1/2"
       },
       {
        "member": "b",
        "kind": "lemma3.3",
        "u": "0",
        "v": "2",
        "floor": 12
       },
       {
        "member": "c",
        "kind": "exact",
        "u": "2",
        "value": "-1/2"
       },
       {
        "member": "d",
        "kind": "lemma3.3",
        "u": "2",
        "v": "1",
        "floor": 6
       }
      ]
     },
     "finite": {
      "ok": true,
      "enumerated": 50,
      "closed": 50,
      "skipped": [],
      "undecided": []
     }
    },
    "V7": {
     "label": "2c = 3a",
     "closure": {
      "ok": true,
      "tailMember": null,
      "N0": 7,
      "validityFloor": 1,
      "expr": {
       "A": "-5/2",
       "B": "2",
       "C": "0",
       "D": "1"
      },
      "boundAtN0": {
       "lo": "-5688281488803560828390950540748133832870964062274401580827925584436735/3450873173395281893717377931138512726225554486085193277581262111899648",
       "hi": "-4459612687221991689458505223946536921719814875259441271164824251621319863/2705484567941901004674424298012593977360834717090791529623709495729324032"
      },
      "target": {
       "lo": "-855435038691829/562949953421312",
       "hi": "-6843480309534631/4503599627370496"
      },
      "pieces": [
       {
        "member": "a",
        "kind": "exact",
        "u": "2",
        "value": "-1/2"
       },
       {
        "member": "b",
        "kind": "lemma3.2",
        "u": "0",
        "v": "2"
       },
       {
        "member": "c",
        "kind": "exact",
        "u": "3",
        "value": "-1"
       },
       {
        "member": "d",
        "kind": "lemma-halfpi",
        "u": "3",
        "v": "1"
       }
      ]
     },
     "finite": {
      "ok": true,
      "enumerated": 5,
      "closed": 5,
      "skipped": [],
      "undecided": []
     }
    }
   },
   "coverage": [
    {
     "subfamily": "V1",
     "pointsChecked": 27
    },
    {
     "subfamily": "V2",
     "pointsChecked": 99
    },
    {
     "subfamily": "V3",
     "pointsChecked": 27
    },
    {
     "subfamily": "V4",
     "pointsChecked": 59
    },
    {
     "subfamily": "V5",
     "pointsChecked": 23
    },
    {
     "subfamily": "V6",
     "pointsChecked": 46
    },
    {
     "subfamily": "V7",
     "pointsChecked": 17
    }
   ],
   "ontoChecked": 1876
  },
  "2d = 3c": {
   "family": "2d = 3c",
   "status": "CLOSED",
   "cones": {
    "W1": {
     "base": "-4/5",
     "dip": "-8/5",
     "exceptions": [
      {
       "key": "1,-1,-1",
       "delta": "-1/4"
      },
      {
       "key": "1,1,-1",
       "delta": "-1/4"
      },
      {
       "key": "1,0,-1",
       "delta": "-1/2"
      }
     ]
    },
    "W3a": {
     "base": "-4/5",
     "dip": "-8/5",
     "exceptions": [
      {
       "key": "1,-1,-1",
       "delta": "-1/4"
      },
      {
       "key": "1,1,-1",
       "delta": "1/2"
      },
      {
       "key": "1,0,-1",
       "delta": "1/2"
      }
     ]
    },
    "W3b": {
     "base": "-13/10",
     "dip": "-8/5",
     "exceptions": [
      {
       "key": "1,-1",
       "delta": "3/4"
      }
     ]
    },
    "W3c": {
     "base": "-4/5",
     "dip": "-8/5",
     "exceptions": [
      {
       "key": "2,0,-2",
       "delta": "1/4"
      },
      {
       "key": "1,-1,-3",
       "delta": "1/2"
      },
      {
       "key": "3,1,-1",
       "delta": "-1/4"
      },
      {
       "key": "1,1,-1",
       "delta": "1/2"
      },
      {
       "key": "1,0,-2",
       "delta": "1"
      },
      {
       "key": "2,1,-1",
       "delta": "1/2"
      },
      {
       "key": "1,0,-1",
       "delta": "19/20"
      }
     ]
    },
    "W3d": {
     "base": "-4/5",
     "dip": "-8/5",
     "exceptions": [
      {
       "key": "1,-1",
       "delta": "29/20"
      },
      {
       "key": "1,-2",
       "delta": "1"
      },
      {
       "key": "2,-1",
       "delta": "1/2"
      },
      {
       "key": "2,-2",
       "delta": "1/4"
      },
      {
       "key": "1,-3",
       "delta": "1/2"
      },
      {
       "key": "3,-1",
       "delta": "-1/4"
      }
     ]
    },
    "W3e": {
     "base": "-4/5",
     "dip": "-8/5",
     "exceptions": [
      {
       "key": "1,-1,-1",
       "delta": "1/2"
      },
      {
       "key": "2,0,-2",
       "delta": "1/4"
      },
      {
       "key": "1,-1,-3",
       "delta": "1/2"
      },
      {
       "key": "3,1,-1",
       "delta": "-1/4"
      },
      {
       "key": "1,-1,-2",
       "delta": "1"
      },
      {
       "key": "2,0,-1",
       "delta": "1/2"
      },
      {
       "key": "1,0,-1",
       "delta": "19/20"
      }
     ]
    },
    "W2": {
     "closure": {
      "ok": true,
      "tailMember": null,
      "N0": 4,
      "validityFloor": 1,
      "expr": {
       "A": "-2",
       "B": "1/2",
       "C": "0",
       "D": "0"
      },
      "boundAtN0": {
       "lo": "-373594260075109531292991881501728902311632578033638075053106335887130063/220855883097298041197912187592864814478435487109452369765200775161577472",
       "hi": "-5977508161201752500687870104027662434898174795286321021436263145362302135/3533694129556768659166595001485837031654967793751237916243212402585239552"
      },
      "target": {
       "lo": "-855435038691829/562949953421312",
       "hi": "-6843480309534631/4503599627370496"
      },
      "pieces": [
       {
        "member": "a",
        "kind": "lemma3.2",
        "u": "0",
        "v": "1"
       },
       {
        "member": "b",
        "kind": "exact",
        "u": "1",
        "value": "0"
       },
       {
        "member": "c",
        "kind": "exact",
        "u": "2",
        "value": "-1"
       },
       {
        "member": "d",
        "kind": "exact",
        "u": "3",
        "value": "0"
       }
      ]
     },
     "finite": {
      "ok": true,
      "enumerated": 3,
      "closed": 3,
      "skipped": [],
      "undecided": []
     }
    }
   },
   "subfamilies": {
    "X1": {
     "label": "2b = 3gam",
     "parts": [
      {
       "closure": {
        "ok": true,
        "tailMember": null,
        "N0": 3,
        "validityFloor": 1,
        "expr": {
         "A": "-5/2",
         "B": "1/2",
         "C": "0",
         "D": "0"
        },
        "boundAtN0": {
         "lo": "-26940119942898757703525724457607268746117945284711192278335375070549271/13803492693581127574869511724554050904902217944340773110325048447598592",
         "hi": "-3879377271777421109307704321895446697353037667746523508666855781327316151/1987702947875682370781209688335783330305919383985071327886806976454197248"
        },
        "target": {
         "lo": "-855435038691829/562949953421312",
         "hi": "-6843480309534631/4503599627370496"
        },
        "pieces": [
         {
          "member": "a",
          "kind": "lemma3.2",
          "u": "0",
          "v": "1"
         },
         {
          "member": "b",
          "kind": "exact",
          "u": "3",
          "value": "0"
         },
         {
          "member": "c",
          "kind": "exact",
          "u": "4",
          "value": "-1/2"
         },
         {
          "member": "d",
          "kind": "exact",
          "u": "6",
          "value": "-1"
         }
        ]
       },
       "finite": {
        "ok": true,
        "enumerated": 1,
        "closed": 1,
        "skipped": [],
        "undecided": []
       }
      },
      {
       "closure": {
        "ok": true,
        "tailMember": null,
        "N0": 3,
        "validityFloor": 1,
        "expr": {
         "A": "-5/2",
         "B": "1/2",
         "C": "0",
         "D": "0"
        },
        "boundAtN0": {
         "lo": "-26940119942898757703525724457607268746117945284711192278335375070549271/13803492693581127574869511724554050904902217944340773110325048447598592",
         "hi": "-3879377271777421109307704321895446697353037667746523508666855781327316151/1987702947875682370781209688335783330305919383985071327886806976454197248"
        },
        "target": {
         "lo": "-855435038691829/562949953421312",
         "hi": "-6843480309534631/4503599627370496"
        },
        "pieces": [
         {
          "member": "a",
          "kind": "lemma3.2",
          "u": "0",
          "v": "1"
         },
         {
          "member": "b",
          "kind": "exact",
          "u": "3",
          "value": "0"
         },
         {
          "member": "c",
          "kind": "exact",
          "u": "4",
          "value": "-1/2"
         },
         {
          "member": "d",
          "kind": "exact",
          "u": "6",
          "value": "-1"
         }
        ]
       },
       "finite": {
        "ok": true,
        "enumerated": 1,
        "closed": 1,
        "skipped": [],
        "undecided": []
       }
      },
      {
       "closure": {
        "ok": true,
        "tailMember": null,
        "N0": 3,
        "validityFloor": 1,
        "expr": {
         "A": "-5/2",
         "B": "1/2",
         "C": "0",
         "D": "0"
        },
        "boundAtN0": {
         "lo": "-26940119942898757703525724457607268746117945284711192278335375070549271/13803492693581127574869511724554050904902217944340773110325048447598592",
         "hi": "-3879377271777421109307704321895446697353037667746523508666855781327316151/1987702947875682370781209688335783330305919383985071327886806976454197248"
        },
        "target": {
         "lo": "-855435038691829/562949953421312",
         "hi": "-6843480309534631/4503599627370496"
        },
        "pieces": [
         {
          "member": "a",
          "kind": "lemma3.2",
          "u": "0",
          "v": "1"
         },
         {
          "member": "b",
          "kind": "exact",
          "u": "3",
          "value": "0"
         },
         {
          "member": "c",
          "kind": "exact",
          "u": "4",
          "value": "-1/2"
         },
         {
          "member": "d",
          "kind": "exact",
          "u": "6",
          "value": "-1"
         }
        ]
       },
       "finite": {
        "ok": true,
        "enumerated": 1,
        "closed": 1,
        "skipped": [],
        "undecided": []
       }
      }
     ],
     "rays": [
      {
       "finite": {
        "ok": true,
        "enumerated": 1,
        "closed": 1,
        "skipped": [],
        "undecided": []
       }
      },
      {
       "finite": {
        "ok": true,
        "enumerated": 1,
        "closed": 1,
        "skipped": [],
        "undecided": []
       }
      }
     ]
    },
    "X2": {
     "label": "a+b = c",
     "closure": {
      "ok": true,
      "tailMember": null,
      "N0": 7,
      "validityFloor": 6,
      "expr": {
       "A": "-5/2",
       "B": "0",
       "C": "6",
       "D": "0"
      },
      "boundAtN0": {
       "lo": "-23/14",
       "hi": "-23/14"
      },
      "target": {
       "lo": "-855435038691829/562949953421312",
       "hi": "-6843480309534631/4503599627370496"
      },
      "pieces": [
       {
        "member": "a",
        "kind": "lemma3.3",
        "u": "0",
        "v": "1",
        "floor": 6
       },
       {
        "member": "b",
        "kind": "lemma3.3",
        "u": "2",
        "v": "-1",
        "floor": 6
       },
       {
        "member": "c",
        "kind": "exact",
        "u": "2",
        "value": "-1/2"
       },
       {
        "member": "d",
        "kind": "exact",
        "u": "3",
        "value": "-1"
       }
      ]
     },
     "finite": {
      "ok": true,
      "enumerated": 11,
      "closed": 11,
      "skipped": [],
      "undecided": []
     }
    },
    "X3": {
     "label": "a = gam",
     "closure": {
      "ok": true,
      "tailMember": null,
      "N0": 4,
      "validityFloor": 1,
      "expr": {
       "A": "-2",
       "B": "1/2",
       "C": "0",
       "D": "0"
      },
      "boundAtN0": {
       "lo": "-373594260075109531292991881501728902311632578033638075053106335887130063/220855883097298041197912187592864814478435487109452369765200775161577472",
       "hi": "-5977508161201752500687870104027662434898174795286321021436263145362302135/3533694129556768659166595001485837031654967793751237916243212402585239552"
      },
      "target": {
       "lo": "-855435038691829/562949953421312",
       "hi": "-6843480309534631/4503599627370496"
      },
      "pieces": [
       {
        "member": "a",
        "kind": "exact",
        "u": "1",
        "value": "0"
       },
       {
        "member": "b",
        "kind": "lemma3.2",
        "u": "0",
        "v": "1"
       },
       {
        "member": "c",
        "kind": "exact",
        "u": "2",
        "value": "-1"
       },
       {
        "member": "d",
        "kind": "exact",
        "u": "3",
        "value": "0"
       }
      ]
     },
     "finite": {
      "ok": true,
      "enumerated": 3,
      "closed": 3,
      "skipped": [],
      "undecided": []
     }
    },
    "X4": {
     "label": "4a = 3c",
     "closure": {
      "ok": true,
      "tailMember": null,
      "N0": 3,
      "validityFloor": 1,
      "expr": {
       "A": "-5/2",
       "B": "1/2",
       "C": "0",
       "D": "0"
      },
      "boundAtN0": {
       "lo": "-26940119942898757703525724457607268746117945284711192278335375070549271/13803492693581127574869511724554050904902217944340773110325048447598592",
       "hi": "-3879377271777421109307704321895446697353037667746523508666855781327316151/1987702947875682370781209688335783330305919383985071327886806976454197248"
      },
      "target": {
       "lo": "-855435038691829/562949953421312",
       "hi": "-6843480309534631/4503599627370496"
      },
      "pieces": [
       {
        "member": "a",
        "kind": "exact",
        "u": "3",
        "value": "0"
       },
       {
        "member": "b",
        "kind": "lemma3.2",
        "u": "0",
        "v": "1"
       },
       {
        "member": "c",
        "kind": "exact",
        "u": "4",
        "value": "-1/2"
       },
       {
        "member": "d",
        "kind": "exact",
        "u": "6",
        "value": "-1"
       }
      ]
     },
     "finite": {
      "ok": true,
      "enumerated": 1,
      "closed": 1,
      "skipped": [],
      "undecided": []
     }
    },
    "X5": {
     "label": "a+b = d",
     "delegated": "family d = a+b"
    },
    "R1346": {
     "label": "{1,3,4,6} ray",
     "finite": {
      "ok": true,
      "enumerated": 1,
      "closed": 1,
      "skipped": [],
      "undecided": []
     }
    },
    "R4569": {
     "label": "{4,5,6,9} ray",
     "finite": {
      "ok": true,
      "enumerated": 1,
      "closed": 1,
      "skipped": [],
      "undecided": []
     }
    },
    "R2469": {
     "label": "{2,4,6,9} ray",
     "finite": {
      "ok": true,
      "enumerated": 1,
      "closed": 1,
      "skipped": [],
      "undecided": []
     }
    },
    "R67812": {
     "label": "{6,7,8,12} ray",
     "finite": {
      "ok": true,
      "enumerated": 1,
      "closed": 1,
      "skipped": [],
      "undecided": []
     }
    }
   },
   "coverage": [
    {
     "subfamily": "X1",
     "pointsChecked": 35
    },
    {
     "subfamily": "X2",
     "pointsChecked": 45
    },
    {
     "subfamily": "R1346",
     "pointsChecked": 1
    },
    {
     "subfamily": "X3",
     "pointsChecked": 45
    },
    {
     "subfamily": "R2469",
     "pointsChecked": 1
    },
    {
     "subfamily": "X5",
     "pointsChecked": 22
    },
    {
     "subfamily": "R4569",
     "pointsChecked": 1
    },
    {
     "subfamily": "X4",
     "pointsChecked": 11
    },
    {
     "subfamily": "R67812",
     "pointsChecked": 1
    }
   ],
   "ontoChecked": 919
  }
 },
 "meta": {
  "date": "2026-09-01",
  "git": "8d7fcb2",
  "ms": 1767314
 }
}