{
 "conventions": "tetrahedron vertices 1=A,2=B,3=C,4=D; |AB|=P2,|AC|=P1,|BC|=P3,|DA|=y12,|DB|=y23,|DC|=y31 (signed); face v is opposite to vertex v; C_ab signed cofactors of the 5x5 Cayley-Menger matrix; l_ab = signed length of the edge opposite to ab; u^{\u00b1}_ab = C_ab \u00b1 l_ab w, w = sqrt(R); x_(gamma,eps) = prod_e u_e^{eps_e} / prod_{v in gamma} C_vv; D(x)=Li2(x)-Li2(1/x)",
 "vertex": {
  "F0": [
   [
    "1/2",
    [
     [
      1,
      2
     ],
     [
      1,
      3
     ],
     [
      2,
      3
     ]
    ],
    [
     1,
     -1,
     -1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      2
     ],
     [
      1,
      3
     ],
     [
      2,
      3
     ]
    ],
    [
     -1,
     1,
     -1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      2
     ],
     [
      1,
      3
     ],
     [
      2,
      3
     ]
    ],
    [
     -1,
     -1,
     1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      2
     ],
     [
      1,
      3
     ],
     [
      2,
      3
     ]
    ],
    [
     -1,
     -1,
     -1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      2
     ],
     [
      1,
      4
     ],
     [
      2,
      4
     ]
    ],
    [
     1,
     1,
     1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      2
     ],
     [
      1,
      4
     ],
     [
      2,
      4
     ]
    ],
    [
     -1,
     1,
     1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      2
     ],
     [
      1,
      4
     ],
     [
      2,
      4
     ]
    ],
    [
     -1,
     1,
     -1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      2
     ],
     [
      1,
      4
     ],
     [
      2,
      4
     ]
    ],
    [
     -1,
     -1,
     1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      3
     ],
     [
      1,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     1,
     1,
     1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      3
     ],
     [
      1,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     -1,
     1,
     1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      3
     ],
     [
      1,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     -1,
     1,
     -1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      3
     ],
     [
      1,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     -1,
     -1,
     1
    ]
   ],
   [
    "1/2",
    [
     [
      2,
      3
     ],
     [
      2,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     1,
     1,
     1
    ]
   ],
   [
    "1/2",
    [
     [
      2,
      3
     ],
     [
      2,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     -1,
     1,
     1
    ]
   ],
   [
    "1/2",
    [
     [
      2,
      3
     ],
     [
      2,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     -1,
     1,
     -1
    ]
   ],
   [
    "1/2",
    [
     [
      2,
      3
     ],
     [
      2,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     -1,
     -1,
     1
    ]
   ],
   [
    "1",
    [
     [
      1,
      2
     ],
     [
      2,
      3
     ],
     [
      3,
      4
     ],
     [
      1,
      4
     ]
    ],
    [
     1,
     1,
     -1,
     -1
    ]
   ],
   [
    "1",
    [
     [
      1,
      2
     ],
     [
      2,
      4
     ],
     [
      3,
      4
     ],
     [
      1,
      3
     ]
    ],
    [
     1,
     -1,
     -1,
     1
    ]
   ],
   [
    "1",
    [
     [
      1,
      3
     ],
     [
      2,
      3
     ],
     [
      2,
      4
     ],
     [
      1,
      4
     ]
    ],
    [
     1,
     1,
     -1,
     -1
    ]
   ]
  ],
  "Fe": [
   [
    "3/4",
    [
     [
      1,
      2
     ],
     [
      1,
      3
     ],
     [
      2,
      3
     ]
    ],
    [
     1,
     1,
     1
    ]
   ],
   [
    "1/4",
    [
     [
      1,
      2
     ],
     [
      1,
      3
     ],
     [
      2,
      3
     ]
    ],
    [
     1,
     -1,
     1
    ]
   ],
   [
    "1/4",
    [
     [
      1,
      2
     ],
     [
      1,
      3
     ],
     [
      2,
      3
     ]
    ],
    [
     -1,
     1,
     1
    ]
   ],
   [
    "1/4",
    [
     [
      1,
      2
     ],
     [
      1,
      3
     ],
     [
      2,
      3
     ]
    ],
    [
     -1,
     -1,
     1
    ]
   ],
   [
    "1/4",
    [
     [
      1,
      2
     ],
     [
      1,
      4
     ],
     [
      2,
      4
     ]
    ],
    [
     1,
     1,
     -1
    ]
   ],
   [
    "1/4",
    [
     [
      1,
      2
     ],
     [
      1,
      4
     ],
     [
      2,
      4
     ]
    ],
    [
     1,
     -1,
     1
    ]
   ],
   [
    "1/4",
    [
     [
      1,
      2
     ],
     [
      1,
      4
     ],
     [
      2,
      4
     ]
    ],
    [
     1,
     -1,
     -1
    ]
   ],
   [
    "1/4",
    [
     [
      1,
      2
     ],
     [
      1,
      4
     ],
     [
      2,
      4
     ]
    ],
    [
     -1,
     -1,
     -1
    ]
   ],
   [
    "1/4",
    [
     [
      1,
      3
     ],
     [
      1,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     1,
     1,
     -1
    ]
   ],
   [
    "1/4",
    [
     [
      1,
      3
     ],
     [
      1,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     1,
     -1,
     1
    ]
   ],
   [
    "1/4",
    [
     [
      1,
      3
     ],
     [
      1,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     1,
     -1,
     -1
    ]
   ],
   [
    "1/4",
    [
     [
      1,
      3
     ],
     [
      1,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     -1,
     -1,
     -1
    ]
   ],
   [
    "1/4",
    [
     [
      2,
      3
     ],
     [
      2,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     1,
     1,
     1
    ]
   ],
   [
    "1/4",
    [
     [
      2,
      3
     ],
     [
      2,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     1,
     1,
     -1
    ]
   ],
   [
    "1/4",
    [
     [
      2,
      3
     ],
     [
      2,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     1,
     -1,
     1
    ]
   ],
   [
    "1/4",
    [
     [
      2,
      3
     ],
     [
      2,
      4
     ],
     [
      3,
      4
     ]
    ],
    [
     -1,
     1,
     1
    ]
   ],
   [
    "1/2",
    [
     [
      2,
      3
     ],
     [
      2,
      3
     ]
    ],
    [
     -1,
     -1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      2
     ],
     [
      2,
      3
     ],
     [
      3,
      4
     ],
     [
      1,
      4
     ]
    ],
    [
     -1,
     -1,
     1,
     1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      2
     ],
     [
      2,
      4
     ],
     [
      3,
      4
     ],
     [
      1,
      3
     ]
    ],
    [
     -1,
     -1,
     -1,
     -1
    ]
   ],
   [
    "1/2",
    [
     [
      1,
      3
     ],
     [
      2,
      3
     ],
     [
      2,
      4
     ],
     [
      1,
      4
     ]
    ],
    [
     -1,
     -1,
     1,
     1
    ]
   ]
  ]
 },
 "vertex_structure": {
  "F0": "master function: 1/2 sum over 4 vertices (triangle cycles) of 4 sign patterns + sum over 3 four-cycles; in the orientation o_e -> o_e^{s_e}, s=(-1,-1,1,-1,1,1) for e=(12,13,14,23,24,34) the patterns are {+++,-++,+-+,++-} at every vertex and -(++++) for every four-cycle",
  "Fe": "= 1/2 master(orientation (1,1,-1,1,-1,-1)) + 1/2 * G, G = D(12,13,23;+++) + D(12,13,23;--+) + D(23,24,34;+++) + D(23,24,34;-++) + D(1/o_23) + D(12,24,34,13;+--+) + D(12,24,34,13;----)  (edge function of the special edge DA, y12=-Q/2)"
 },
 "tube": {
  "p": {
   "terms": [
    [
     0,
     1,
     -1
    ],
    [
     0,
     7,
     1
    ],
    [
     0,
     13,
     1
    ],
    [
     2,
     3,
     1
    ],
    [
     2,
     7,
     -1
    ]
   ],
   "p": {
    "0": "-P1**2 - P2**2 + P3**2 - 2*X1*X2",
    "1": "-P1**2 + 2*P1*P2 - 2*P1*X2 - P2**2 - 2*P2*X1 + P3**2",
    "2": "-P1**2 - 2*P1*P3 + 2*P1*X1 + 2*P1*X2 + P2**2 - P3**2 + 2*P3*X1",
    "3": "-P1**2 + P2**2 - P3**2 + 2*X1**2 + 2*X1*X2",
    "7": "-P1**2 + P2**2 + P3**2 - 2*X1*X2 - 2*X2**2",
    "13": "-P1**2 + P2**2 + 2*P2*P3 + 2*P2*X1 + 2*P2*X2 + P3**2 + 2*P3*X2"
   },
   "N": {
    "0": {
     "const": "4",
     "letters": [
      [
       [
        1,
        0,
        0,
        -1,
        0,
        0
       ],
       1
      ],
      [
       [
        0,
        1,
        0,
        0,
        -1,
        0
       ],
       1
      ],
      [
       [
        1,
        0,
        0,
        1,
        0,
        0
       ],
       1
      ],
      [
       [
        0,
        1,
        0,
        0,
        1,
        0
       ],
       1
      ]
     ]
    },
    "1": {
     "const": "-4",
     "letters": [
      [
       [
        1,
        0,
        0,
        -1,
        0,
        0
       ],
       1
      ],
      [
       [
        0,
        1,
        0,
        0,
        -1,
        0
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        -1
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        1
       ],
       1
      ]
     ]
    },
    "2": {
     "const": "4",
     "letters": [
      [
       [
        1,
        0,
        0,
        -1,
        0,
        0
       ],
       1
      ],
      [
       [
        1,
        1,
        0,
        0,
        0,
        -1
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        1
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        1,
        1
       ],
       1
      ]
     ]
    },
    "3": {
     "const": "4",
     "letters": [
      [
       [
        1,
        0,
        0,
        -1,
        0,
        0
       ],
       1
      ],
      [
       [
        1,
        0,
        0,
        1,
        0,
        0
       ],
       1
      ],
      [
       [
        1,
        1,
        0,
        0,
        0,
        -1
       ],
       1
      ],
      [
       [
        1,
        1,
        0,
        0,
        0,
        1
       ],
       1
      ]
     ]
    },
    "7": {
     "const": "4",
     "letters": [
      [
       [
        0,
        1,
        0,
        0,
        -1,
        0
       ],
       1
      ],
      [
       [
        0,
        1,
        0,
        0,
        1,
        0
       ],
       1
      ],
      [
       [
        1,
        1,
        0,
        0,
        0,
        -1
       ],
       1
      ],
      [
       [
        1,
        1,
        0,
        0,
        0,
        1
       ],
       1
      ]
     ]
    },
    "13": {
     "const": "-4",
     "letters": [
      [
       [
        0,
        1,
        0,
        0,
        1,
        0
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        -1
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        1,
        1
       ],
       1
      ],
      [
       [
        1,
        1,
        0,
        0,
        0,
        1
       ],
       1
      ]
     ]
    }
   },
   "D": {
    "0,1": {
     "const": "2",
     "letters": [
      [
       [
        0,
        1,
        0,
        0,
        -1,
        0
       ],
       1
      ],
      [
       [
        1,
        0,
        0,
        -1,
        0,
        0
       ],
       1
      ]
     ]
    },
    "0,7": {
     "const": "-2",
     "letters": [
      [
       [
        0,
        1,
        0,
        0,
        -1,
        0
       ],
       1
      ],
      [
       [
        0,
        1,
        0,
        0,
        1,
        0
       ],
       1
      ]
     ]
    },
    "0,13": {
     "const": "2",
     "letters": [
      [
       [
        1,
        0,
        0,
        0,
        1,
        1
       ],
       1
      ],
      [
       [
        0,
        1,
        0,
        0,
        1,
        0
       ],
       1
      ]
     ]
    },
    "2,3": {
     "const": "2",
     "letters": [
      [
       [
        1,
        1,
        0,
        0,
        0,
        -1
       ],
       1
      ],
      [
       [
        1,
        0,
        0,
        -1,
        0,
        0
       ],
       1
      ]
     ]
    },
    "2,7": {
     "const": "-2",
     "letters": [
      [
       [
        1,
        1,
        0,
        0,
        0,
        -1
       ],
       1
      ],
      [
       [
        0,
        1,
        0,
        1,
        0,
        1
       ],
       1
      ]
     ]
    }
   },
   "uv": {
    "0,1": [
     "-(P1 + X1)*(P2 + X2)/((P1 - P2 - P3)*(P1 - P2 + P3))",
     "-(P1 - X1)*(P2 - X2)/((P1 - P2 - P3)*(P1 - P2 + P3))"
    ],
    "0,7": [
     "(P1 - X1)*(P1 + X1)/((P3 - X1 - X2)*(P3 + X1 + X2))",
     "(P2 - X2)*(P2 + X2)/((P3 - X1 - X2)*(P3 + X1 + X2))"
    ],
    "0,13": [
     "-(P1 - X1)*(P1 + X1)*(P2 - X2)/((P1 - P2 - P3)*(P1 + P2 + P3)*(P3 + X1 + X2))",
     "-(P2 + X2)*(P2 + P3 + X1)**2/((P1 - P2 - P3)*(P1 + P2 + P3)*(P3 + X1 + X2))"
    ],
    "2,3": [
     "(P1 - P2 + P3)*(P1 + P2 + P3)/((P1 + X1)*(P3 + X1 + X2))",
     "(P1 - X1)*(P3 - X1 - X2)/((P1 + X1)*(P3 + X1 + X2))"
    ],
    "2,7": [
     "(P1 - X1)*(P1 - P2 + P3)*(P1 + P2 + P3)/((P2 - X2)*(P2 + X2)*(P3 + X1 + X2))",
     "(P1 + P3 + X2)**2*(P3 - X1 - X2)/((P2 - X2)*(P2 + X2)*(P3 + X1 + X2))"
    ]
   }
  },
  "m": {
   "terms": [
    [
     2,
     3,
     1
    ],
    [
     5,
     13,
     1
    ],
    [
     7,
     13,
     1
    ],
    [
     8,
     9,
     -1
    ]
   ],
   "p": {
    "2": "-P1**2 - 2*P1*P3 + 2*P1*X1 - 2*P1*X2 + P2**2 - P3**2 + 2*P3*X1",
    "3": "-P1**2 + P2**2 - P3**2 + 2*X1**2 - 2*X1*X2",
    "5": "-P1**2 + 2*P1*P2 + 2*P1*X2 - P2**2 - 2*P2*X1 + P3**2",
    "7": "-P1**2 + P2**2 + P3**2 + 2*X1*X2 - 2*X2**2",
    "8": "-P1**2 + P2**2 + 2*P2*P3 + 2*P2*X1 - 2*P2*X2 + P3**2 - 2*P3*X2",
    "9": "-P1**2 + 2*P1*P2 - 2*P1*X2 - P2**2 + 2*P2*X1 + P3**2",
    "13": "-P1**2 - 2*P1*P3 - 2*P1*X1 + 2*P1*X2 + P2**2 - P3**2 - 2*P3*X1"
   },
   "N": {
    "2": {
     "const": "4",
     "letters": [
      [
       [
        1,
        0,
        0,
        -1,
        0,
        0
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        1
       ],
       1
      ],
      [
       [
        1,
        -1,
        0,
        0,
        0,
        -1
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        1,
        1
       ],
       1
      ]
     ]
    },
    "3": {
     "const": "4",
     "letters": [
      [
       [
        1,
        0,
        0,
        -1,
        0,
        0
       ],
       1
      ],
      [
       [
        1,
        0,
        0,
        1,
        0,
        0
       ],
       1
      ],
      [
       [
        1,
        -1,
        0,
        0,
        0,
        -1
       ],
       1
      ],
      [
       [
        1,
        -1,
        0,
        0,
        0,
        1
       ],
       1
      ]
     ]
    },
    "5": {
     "const": "4",
     "letters": [
      [
       [
        1,
        0,
        0,
        -1,
        0,
        0
       ],
       1
      ],
      [
       [
        0,
        1,
        0,
        0,
        1,
        0
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        -1
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        1
       ],
       1
      ]
     ]
    },
    "7": {
     "const": "4",
     "letters": [
      [
       [
        0,
        1,
        0,
        0,
        -1,
        0
       ],
       1
      ],
      [
       [
        0,
        1,
        0,
        0,
        1,
        0
       ],
       1
      ],
      [
       [
        1,
        -1,
        0,
        0,
        0,
        -1
       ],
       1
      ],
      [
       [
        1,
        -1,
        0,
        0,
        0,
        1
       ],
       1
      ]
     ]
    },
    "8": {
     "const": "4",
     "letters": [
      [
       [
        0,
        1,
        0,
        0,
        -1,
        0
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        -1
       ],
       1
      ],
      [
       [
        1,
        -1,
        0,
        0,
        0,
        1
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        1,
        1
       ],
       1
      ]
     ]
    },
    "9": {
     "const": "4",
     "letters": [
      [
       [
        0,
        1,
        0,
        0,
        -1,
        0
       ],
       1
      ],
      [
       [
        1,
        0,
        0,
        1,
        0,
        0
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        -1
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        1
       ],
       1
      ]
     ]
    },
    "13": {
     "const": "4",
     "letters": [
      [
       [
        1,
        0,
        0,
        1,
        0,
        0
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        1
       ],
       1
      ],
      [
       [
        1,
        -1,
        0,
        0,
        0,
        1
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        1,
        1
       ],
       1
      ]
     ]
    }
   },
   "D": {
    "2,3": {
     "const": "2",
     "letters": [
      [
       [
        1,
        -1,
        0,
        0,
        0,
        -1
       ],
       1
      ],
      [
       [
        1,
        0,
        0,
        -1,
        0,
        0
       ],
       1
      ]
     ]
    },
    "5,13": {
     "const": "-2",
     "letters": [
      [
       [
        1,
        0,
        0,
        0,
        1,
        1
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        1
       ],
       1
      ]
     ]
    },
    "7,13": {
     "const": "-2",
     "letters": [
      [
       [
        1,
        -1,
        0,
        0,
        0,
        1
       ],
       1
      ],
      [
       [
        0,
        1,
        0,
        1,
        0,
        1
       ],
       1
      ]
     ]
    },
    "8,9": {
     "const": "-2",
     "letters": [
      [
       [
        0,
        1,
        0,
        0,
        -1,
        0
       ],
       1
      ],
      [
       [
        0,
        0,
        0,
        1,
        -1,
        -1
       ],
       1
      ]
     ]
    }
   },
   "uv": {
    "2,3": [
     "(P1 - P2 + P3)*(P1 + P2 + P3)/((P1 + X1)*(P3 + X1 - X2))",
     "(P1 - X1)*(P3 - X1 + X2)/((P1 + X1)*(P3 + X1 - X2))"
    ],
    "5,13": [
     "-(P1 - X1)*(P2 + X2)*(P1 - P2 - P3)/((P1 + X1)*(P1 + P2 + P3)*(P3 + X1 - X2))",
     "(P1 - P2 + P3)*(P2 + P3 + X1)**2/((P1 + X1)*(P1 + P2 + P3)*(P3 + X1 - X2))"
    ],
    "7,13": [
     "(P2 - X2)*(P2 + X2)*(P3 - X1 + X2)/((P1 + X1)*(P1 - P2 + P3)*(P1 + P2 + P3))",
     "(P1 + P3 + X2)**2*(P3 + X1 - X2)/((P1 + X1)*(P1 - P2 + P3)*(P1 + P2 + P3))"
    ],
    "8,9": [
     "(P1 + P2 + P3)*(P3 + X1 - X2)/((P1 + X1)*(P1 - P2 + P3))",
     "-(P2 - X2)*(P1 - P2 - P3)/((P1 + X1)*(P1 - P2 + P3))"
    ]
   }
  }
 },
 "orbits": {
  "vertex_e": {
   "S12": [
    0,
    1,
    2
   ],
   "S23": [
    1,
    2,
    0
   ],
   "S31": [
    0,
    2,
    1
   ]
  },
  "tube": {
   "12": [
    0,
    1,
    2
   ],
   "13": [
    0,
    2,
    1
   ],
   "23": [
    1,
    2,
    0
   ]
  },
  "coefficients": {
   "F0": "-1/4",
   "Fe": "-1/2",
   "Fminus": "-1",
   "Fplus": "1"
  }
 },
 "tube_minus_selection": {
  "n_four_term_symbol_solutions": 12,
  "selected": "candidate 4 of minus_offsets.json",
  "offset_free_on_sample": [
   4,
   5,
   6,
   7
  ],
  "rejected_first_choice": "candidate 0 [(1,5),(1,8),(2,3),(7,13)] was written first without a numerical test; it is off by -pi^2 in 98 of 360 sampled evaluations (full-table judgement failed on gen/ndg/sft/iso/rays)"
 }
}