{
 "description": "Bloch-Wigner block form of the four vertex functions of V(X;P). See vertex_functions_note.md. Authoritative together with eval_vertex_blocks.py.",
 "edge_order": [
  "l12",
  "l13",
  "l23",
  "l14",
  "l24",
  "l34"
 ],
 "tetrahedron": "vertices 1=A,2=B,3=C (base), 4=D (apex); l12=|AB|=P2, l13=|AC|=P1, l23=|BC|=P3, l14,l24,l34 = apex edges (linear in X, may be negative for F0)",
 "lengths": {
  "F0": [
   "P2",
   "P1",
   "P3",
   "(X1+X2-X3)/2",
   "(X2+X3-X1)/2",
   "(X1+X3-X2)/2"
  ],
  "Fe": [
   "P2",
   "P1",
   "P3",
   "(X1+X2+X3)/2",
   "(X1+X3-X2)/2",
   "(X2+X3-X1)/2"
  ]
 },
 "faces": {
  "f4": [
   "l12",
   "l13",
   "l23"
  ],
  "f3": [
   "l12",
   "l14",
   "l24"
  ],
  "f2": [
   "l13",
   "l14",
   "l34"
  ],
  "f1": [
   "l23",
   "l24",
   "l34"
  ]
 },
 "cycles": {
  "c12|34": [
   "l13",
   "l14",
   "l23",
   "l24"
  ],
  "c13|24": [
   "l12",
   "l14",
   "l23",
   "l34"
  ],
  "c14|23": [
   "l12",
   "l13",
   "l24",
   "l34"
  ]
 },
 "classes": {
  "E": [
   1,
   1,
   1,
   1,
   1,
   1
  ],
  "S": [
   1,
   1,
   1,
   1,
   -1,
   -1
  ]
 },
 "class_comment": "class c: replace l_e -> eps_e l_e in faces and cycles; q_c(z)=prod_k(z-f_k)-z prod_j(z-c_j)=q2 z^2+q1 z+q0; disc = R = -2 det CM for every class; p^c_a = -(2 q2 a + q1), a in {0,f_k,c_j}; w=sqrt(R)",
 "block": "B[x;y] = P2(z,zb), z=(x-w)/(y-w), zb=(x+w)/(y+w); R>0: P2 = Re Li2(z) - Re Li2(zb) + 1/2 log|z zb| log|(1-z)/(1-zb)|; R<0: P2 = 2i D_BW(z), D_BW(z)=Im Li2(z)+arg(1-z) log|z|",
 "F0": [
  [
   -2,
   [
    "E",
    "f1"
   ],
   [
    "E",
    "0"
   ]
  ],
  [
   -2,
   [
    "E",
    "f2"
   ],
   [
    "E",
    "0"
   ]
  ],
  [
   -2,
   [
    "E",
    "f3"
   ],
   [
    "E",
    "0"
   ]
  ],
  [
   -2,
   [
    "E",
    "f4"
   ],
   [
    "E",
    "0"
   ]
  ],
  [
   2,
   [
    "E",
    "c12|34"
   ],
   [
    "E",
    "0"
   ]
  ],
  [
   2,
   [
    "E",
    "c13|24"
   ],
   [
    "E",
    "0"
   ]
  ],
  [
   2,
   [
    "E",
    "c14|23"
   ],
   [
    "E",
    "0"
   ]
  ]
 ],
 "Fe": [
  [
   -1,
   [
    "E",
    "f1"
   ],
   [
    "E",
    "0"
   ]
  ],
  [
   1,
   [
    "E",
    "c14|23"
   ],
   [
    "E",
    "0"
   ]
  ],
  [
   1,
   [
    "S",
    "f4"
   ],
   [
    "S",
    "0"
   ]
  ],
  [
   1,
   [
    "S",
    "f3"
   ],
   [
    "S",
    "0"
   ]
  ],
  [
   1,
   [
    "S",
    "f2"
   ],
   [
    "S",
    "0"
   ]
  ],
  [
   -1,
   [
    "S",
    "c12|34"
   ],
   [
    "S",
    "0"
   ]
  ],
  [
   -1,
   [
    "S",
    "c13|24"
   ],
   [
    "S",
    "0"
   ]
  ],
  [
   1,
   [
    "S",
    "0"
   ],
   [
    "E",
    "f4"
   ]
  ],
  [
   -1,
   [
    "S",
    "f4"
   ],
   [
    "E",
    "0"
   ]
  ]
 ],
 "coefficients_in_V": {
  "F0": "-1/4",
  "Fe": "-1/2"
 },
 "orbits_vertex_e": {
  "S12": [
   0,
   1,
   2
  ],
  "S23": [
   1,
   2,
   0
  ],
  "S31": [
   0,
   2,
   1
  ]
 }
}