{
 "script": "part4_exact_checks",
 "passed": 13,
 "failed": 0,
 "seconds": 99.4,
 "checks": [
  {
   "label": "rem:bernoulli-general",
   "desc": "the three points lie in the upper half disk D^+",
   "status": "PASS",
   "method": "exact rational arithmetic",
   "detail": ""
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "pair terms a_ij = rho1 rho1 - rho2 are positive at the three points",
   "status": "PASS",
   "method": "exact rational arithmetic",
   "detail": "{(0, 1): 0.046106106266290345, (0, 2): 0.12675905469487603, (1, 2): 0.018762056328987687}"
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "T^2/(4 a12 a13 a23) > 1, so no Hermitian determinantal kernel",
   "status": "PASS",
   "method": "exact rational arithmetic",
   "detail": "ratio = 9517717790593398661531421149299339000162892188214447234593931084345745631210802384823607/2430837625185067815869656635768991603454329006925359469903536830670798654926728852823607 = 3.9154066450"
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "the ratio is 3.9154... as printed",
   "status": "PASS",
   "method": "numerical (floating point)",
   "detail": "3.9154066450"
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "the four points lie in D^+ and the configuration is symmetric under z -> -conj z",
   "status": "PASS",
   "method": "exact rational arithmetic",
   "detail": ""
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "rho_2(z,z) = 0 (correlation functions vanish on the diagonal)",
   "status": "PASS",
   "method": "exact rational arithmetic",
   "detail": ""
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "P has degree 4, constant term 1, rational coefficients",
   "status": "PASS",
   "method": "exact rational arithmetic",
   "detail": "tau^0: 1; tau^1: -4700693125000/123602168041; tau^2: 10820185818448421389171672037573001707261081651677011994738137938888246429303249856667207922697424893172321491810879687500000000000000/20231885199339142839241952040952947540597893918462506791516297010849354523143059180486650317100961353055451574680866345962330862777; tau^3: -66532559179492487326137906520943706905425506307161450969312245689146291239043310038784189821840667724609375000000000000000000000000000/20231885199339142839241952040952947540597893918462506791516297010849354523143059180486650317100961353055451574680866345962330862777; tau^4: 79660451379755257838986212118509190067717726596122533854029546862707140407566810173493254964209074584319883188815026293396949768066406250000000000000000000000000000000000000000000000000/10705972508193725305582367148243079497497393826458078353455991693219374301588182796030580204208806023224673663204031494082654571683603194065413790649563458912862357089034957447356529"
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "coefficients match the printed P = 1 - 38.031 tau + 534.81 tau^2 - 3288.5 tau^3 + 7440.7 tau^4",
   "status": "PASS",
   "method": "numerical (floating point)",
   "detail": "[1.0, -38.0308, 534.8086, -3288.5002, 7440.7487]"
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "discriminant of P is negative (exact)",
   "status": "PASS",
   "method": "exact rational arithmetic",
   "detail": "-1.628590e+04"
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "P is squarefree: gcd(P, P') = 1 (exact)",
   "status": "PASS",
   "method": "exact rational arithmetic",
   "detail": ""
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "P has exactly two real roots (Sturm), hence one pair of simple nonreal roots",
   "status": "PASS",
   "method": "exact rational arithmetic",
   "detail": "real roots: 2"
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "the nonreal roots are 0.08879 +- 0.00176 i as printed",
   "status": "PASS",
   "method": "numerical (floating point)",
   "detail": "(0.088790337 - 0.0017573251j), (0.088790337 + 0.0017573251j)"
  },
  {
   "label": "rem:bernoulli-general",
   "desc": "every Pfaffian used (27) is of an antisymmetric matrix and satisfies Pf^2 = det",
   "status": "PASS",
   "method": "exact rational arithmetic",
   "detail": ""
  }
 ]
}