  ok   13544211: graded data have Hilbert function [1, 3, 5, 4, 4, 2, 1, 1]
  ok   13544211 graded (seed 2): closed, H [1, 3, 5, 4, 4, 2, 1, 1], gamma_f = 0, b^6 in (I : m^2); N1 triple 38 <= 40
   13544211 random seed 0: inconsistent draw, rejected
   13544211 random seed 1: inconsistent draw, rejected
   13544211 random seed 2: inconsistent draw, rejected
   13544211 random seed 3: inconsistent draw, rejected
   13544211 random seed 4: inconsistent draw, rejected
   13544211 random seed 5: inconsistent draw, rejected
   13544211 random seed 6: inconsistent draw, rejected
   13544211 random seed 7: inconsistent draw, rejected
  ok   13544211 random, depth-1 tails zero (seed 0): closed, H [1, 3, 5, 4, 4, 2, 1, 1], gamma_f = 0, b^6 in (I : m^2); N1 triple 35 <= 40
  ok   13544211 random, depth-1 tails zero (seed 1): closed, H [1, 3, 5, 4, 4, 2, 1, 1], gamma_f = 0, b^6 in (I : m^2); N1 triple 34 <= 40
   13544211: 2 samples with random tails accepted, 8 draws rejected (inconsistent)
   time 30.1 s
  ok   13543311: graded data have Hilbert function [1, 3, 5, 4, 3, 3, 1, 1]
  ok   13543311 graded (seed 2): closed, H [1, 3, 5, 4, 3, 3, 1, 1], gamma_f = 0, b^6 in (I : m^2); N1 triple 38 <= 38
  ok   13543311 random (seed 0): closed, H [1, 3, 5, 4, 3, 3, 1, 1], gamma_f = 0, b^6 in (I : m^2); N1 triple 34 <= 38
   13543311 random seed 1: inconsistent draw, rejected
   13543311 random seed 2: inconsistent draw, rejected
   13543311 random seed 3: inconsistent draw, rejected
   13543311 random seed 4: inconsistent draw, rejected
   13543311 random seed 5: inconsistent draw, rejected
   13543311 random seed 6: inconsistent draw, rejected
   13543311 random seed 7: inconsistent draw, rejected
  ok   13543311 random, depth-1 tails zero (seed 0): closed, H [1, 3, 5, 4, 3, 3, 1, 1], gamma_f = 0, b^6 in (I : m^2); N1 triple 36 <= 38
   13543311: 2 samples with random tails accepted, 7 draws rejected (inconsistent)
   time 65.5 s
  ok   13542222: graded data have Hilbert function [1, 3, 5, 4, 2, 2, 2, 2]
  ok   13542222 graded (seed 2): closed, H [1, 3, 5, 4, 2, 2, 2, 2], gamma_f = 0, b^6 in (I : m^2); N1 triple 38 <= 40
  ok   13542222 random (seed 0): closed, H [1, 3, 5, 4, 2, 2, 2, 2], gamma_f = 0, b^6 in (I : m^2); N1 triple 38 <= 40
  ok   13542222 random (seed 1): closed, H [1, 3, 5, 4, 2, 2, 2, 2], gamma_f = 0, b^6 in (I : m^2); N1 triple 38 <= 40
   13542222: 2 samples with random tails accepted, 0 draws rejected (inconsistent)
   time 83.1 s
  ok   135432111: graded data have Hilbert function [1, 3, 5, 4, 3, 2, 1, 1, 1]
  ok   135432111 graded (seed 2): closed, H [1, 3, 5, 4, 3, 2, 1, 1, 1], gamma_f = 0, b^7 in (I : m^2); N1 triple 38 <= 41
   135432111 random seed 0: inconsistent draw, rejected
   135432111 random seed 1: inconsistent draw, rejected
   135432111 random seed 2: inconsistent draw, rejected
   135432111 random seed 3: inconsistent draw, rejected
   135432111 random seed 4: inconsistent draw, rejected
   135432111 random seed 5: inconsistent draw, rejected
   135432111 random seed 6: inconsistent draw, rejected
   135432111 random seed 7: inconsistent draw, rejected
   135432111 random, depth-1 tails zero seed 0: inconsistent draw, rejected
   135432111 random, depth-1 tails zero seed 1: inconsistent draw, rejected
   135432111 random, depth-1 tails zero seed 2: inconsistent draw, rejected
  ok   135432111 random, depth-1 tails zero (seed 3): closed, H [1, 3, 5, 4, 3, 2, 1, 1, 1], gamma_f = 0, b^7 in (I : m^2); N1 triple 35 <= 41
   135432111 random, depth-1 tails zero seed 4: inconsistent draw, rejected
   135432111 random, depth-1 tails zero seed 5: inconsistent draw, rejected
   135432111 random, depth-1 tails zero seed 6: inconsistent draw, rejected
   135432111 random, depth-1 tails zero seed 7: inconsistent draw, rejected
   135432111: 1 samples with random tails accepted, 15 draws rejected (inconsistent)
   time 120.0 s
  ok   135422211: graded data have Hilbert function [1, 3, 5, 4, 2, 2, 2, 1, 1]
  ok   135422211 graded (seed 2): closed, H [1, 3, 5, 4, 2, 2, 2, 1, 1], gamma_f = 0, b^7 in (I : m^2); N1 triple 38 <= 38
   135422211 random seed 0: inconsistent draw, rejected
   135422211 random seed 1: inconsistent draw, rejected
   135422211 random seed 2: inconsistent draw, rejected
   135422211 random seed 3: inconsistent draw, rejected
   135422211 random seed 4: inconsistent draw, rejected
   135422211 random seed 5: inconsistent draw, rejected
   135422211 random seed 6: inconsistent draw, rejected
  ok   135422211 random (seed 7): closed, H [1, 3, 5, 4, 2, 2, 2, 1, 1], gamma_f = 0, b^7 in (I : m^2); N1 triple 36 <= 38
  ok   135422211 random, depth-1 tails zero (seed 0): closed, H [1, 3, 5, 4, 2, 2, 2, 1, 1], gamma_f = 0, b^7 in (I : m^2); N1 triple 36 <= 38
   135422211: 2 samples with random tails accepted, 7 draws rejected (inconsistent)
   time 151.0 s
  ok   1354221111: graded data have Hilbert function [1, 3, 5, 4, 2, 2, 1, 1, 1, 1]
  ok   1354221111 graded (seed 2): closed, H [1, 3, 5, 4, 2, 2, 1, 1, 1, 1], gamma_f = 0, b^8 in (I : m^2); N1 triple 40 <= 40
   1354221111 random seed 0: inconsistent draw, rejected
   1354221111 random seed 1: inconsistent draw, rejected
  ok   1354221111 random (seed 2): closed, H [1, 3, 5, 4, 2, 2, 1, 1, 1, 1], gamma_f = 0, b^8 in (I : m^2); N1 triple 37 <= 40
   1354221111 random seed 3: inconsistent draw, rejected
   1354221111 random seed 4: inconsistent draw, rejected
   1354221111 random seed 5: inconsistent draw, rejected
   1354221111 random seed 6: inconsistent draw, rejected
   1354221111 random seed 7: inconsistent draw, rejected
  ok   1354221111 random, depth-1 tails zero (seed 0): closed, H [1, 3, 5, 4, 2, 2, 1, 1, 1, 1], gamma_f = 0, b^8 in (I : m^2); N1 triple 36 <= 40
   1354221111: 2 samples with random tails accepted, 7 draws rejected (inconsistent)
   time 220.8 s

Summary (profile: [(kind, seed, N1 length)], rejected draws):
   ('13544211', [('graded', 2, 38), ('random, depth-1 tails zero', 0, 35), ('random, depth-1 tails zero', 1, 34)], 8)
   ('13543311', [('graded', 2, 38), ('random', 0, 34), ('random, depth-1 tails zero', 0, 36)], 7)
   ('13542222', [('graded', 2, 38), ('random', 0, 38), ('random', 1, 38)], 0)
   ('135432111', [('graded', 2, 38), ('random, depth-1 tails zero', 3, 35)], 15)
   ('135422211', [('graded', 2, 38), ('random', 7, 36), ('random, depth-1 tails zero', 0, 36)], 7)
   ('1354221111', [('graded', 2, 40), ('random', 2, 37), ('random, depth-1 tails zero', 0, 36)], 7)

Part A: 135432111, gcd h = z^3, graded algebra: the N1 triple certified by stabilization
  ok   graded algebra closed with H = [1, 3, 5, 4, 3, 2, 1, 1, 1]
   J_4 = [y*z^3, z^4]  gcd = z^3
  ok   gcd of J_4 is z^3
  ok   N1 triple: certified local length 38 (stable at N = 13), local standard basis 38; <= 41
   [info] negative control without the turning term (Thm 3.15 triple): local length 40 (Thm 3.15 bound 47)
time 222.3 s
ALL CHECKS PASSED
