A. residual set R(10^6)
  |R(10^6)| = 16703 | first: [45, 117, 153, 245, 261, 333, 369, 405, 477, 549, 585, 605] | |R(2000)| = 39
  (0.4 s)
B. wheel identities (exact polynomials in x_j, y_j)
  trees: {2: 5, 3: 16, 4: 45} | identities checked for m = 2, 3, 4 | all-ones values {2: [5], 3: [16], 4: [45]}
  (0.0 s)
C. substitutions of Theorems 1.3 and 1.4
  Theorem 1.3 (I), (II) and Theorem 1.4 identities checked
  (0.0 s)
D. Corollary 2.7, Lemma 2.8 (series-parallel duals), Lemma 4.1 (explicit graphs, Kirchhoff)
  300 random SP networks; Euclid networks for coprime a, b <= 40; Z_s for odd s <= 41; Z'_27
  (0.0 s)
E. Theorem 1.3 / Lemma 5.1: primes q = 3 mod 4 below 1000000
  form (I): 19668 | form (II): 19654 (q = 3 counted in (I), a = b = 1)
  (0.5 s)
F. Theorem 1.4 on random admissible parameters
  3000 instances
  (0.1 s)
G. Theorem 1.5: all certificates
  16703 certificates, by family {'F3': 602, 'F1': 15330, 'F2': 771}, failures 0, certified set = R: True
  (0.0 s)
H. Theorem 1.1 on explicit plane maps
  random plane networks: 400 (nonseparable G: 400; m = 2 with Lemma 2.8: 80); stars with SP arms: 150
  control gluing mu_k -> t_{k+1}: 80 of 400 maps self-dual (information only)
  certificate graphs: 16703 built and checked ({'F3': 602, 'F1': 15330, 'F2': 771}; largest G has 368 edges), passed 16703
  (15.8 s)
I. Theorem 1.2 on explicit plane maps (one edge of X replaced by a gadget)
  180 substitutions: tau multiplied by k^2, self-dual, nonseparable
  (0.1 s)
J. Proposition 7.1: q = tau(H) prime, H 2-edge-connected -> q does not divide tau(H/uv)
  300 graphs, 1226 vertex pairs
  (0.0 s)
TOTAL failures: 0 | time 17 s
