Part A: closedness criterion for the pure top over Gamma_0 (D_3 of dimension 6)
   random: closed True, conditions True, H = [1, 3, 6, 6, 2, 2, 1]; perturbed: closed False, conditions False
   random: closed True, conditions True, H = [1, 3, 6, 6, 2, 2, 1]; perturbed: closed False, conditions False
   delta: contains X^2 T_1: closed True, conditions True, H = [1, 3, 6, 6, 2, 2, 1]; perturbed: closed False, conditions False
   delta: contains X^2 T_1: closed True, conditions True, H = [1, 3, 6, 6, 2, 2, 1]; perturbed: closed False, conditions False
   delta: X T_2: closed True, conditions True, H = [1, 3, 6, 6, 2, 2, 1]; perturbed: closed False, conditions False
   delta: X T_2: closed True, conditions True, H = [1, 3, 6, 6, 2, 2, 1]; perturbed: closed True, conditions True
   alpha: line z = 0 + 2: closed True, conditions True, H = [1, 3, 6, 6, 2, 2, 1]; perturbed: closed False, conditions False
   alpha: line z = 0 + 2: closed True, conditions True, H = [1, 3, 6, 6, 2, 2, 1]; perturbed: closed False, conditions False
   gamma: nu_3(C5) + 1: closed True, conditions True, H = [1, 3, 6, 6, 2, 2, 1]; perturbed: closed False, conditions False
   gamma: nu_3(C5) + 1: closed True, conditions True, H = [1, 3, 6, 6, 2, 2, 1]; perturbed: closed False, conditions False
   accepted members per type: {'random': 2, 'delta: contains X^2 T_1': 2, 'delta: X T_2': 2, 'alpha: line z = 0 + 2': 2, 'gamma: nu_3(C5) + 1': 2}
  ok   (S) criterion (c1)-(c4) = direct closedness with H = (1,3,6,6,2,2,1), at least one member per type
Part B: the incidence count
  ok   (B1, S) dim A_D = 13 - rank beta_D on 7 flags: (dim A_D, rank beta) = [(7, 6), (7, 6), (7, 6), (10, 3), (8, 5), (9, 4), (9, 4)]
  ok   (B2, U) the 3x3 minors of (z o, y o) on nu_3(C4) generate the unit ideal of QQ[a,b]: rank beta >= 3 on every D containing nu_3(C4)
   nu_3(C4) = [1/6*X^3, 1/2*X^2*Y, 1/2*X*Y^2 + 1/2*a*X^2*Z, 1/6*Y^3 + 1/2*b*X^2*Z + a*X*Y*Z]
  ok   (B2, S) rank beta = 3 on C[X,Y]_3 and on nu_3(C5) for (a,b,c) = (1,2,-1), (0,0,1)
  ok   (B3, A) W = <(Y^2,Z^3), (Z^2,Y^3), (YZ, Y^2Z+YZ^2)>: r_W = 5 = 5, dim A_D = 7 = 7
  ok   (B3, S) dim A_D = 12 - r_W for D = X^2 T_1 + W: (r_W, dim A_D) = [(5, 7), (5, 7), (5, 7), (2, 10), (3, 9), (4, 8), (4, 8)]
   alpha: line z=0, V general: dim A_D = 7, dim ker L_1 = 14, dim ker L_0 = 14, sigma = 8, sigma + 2 dim A_D = 22
   alpha: line y=0 through X: dim A_D = 8, dim ker L_1 = 15, dim ker L_0 = 16, sigma = 5, sigma + 2 dim A_D = 21
   gamma: nu_3(C5) + G: dim A_D = 7, dim ker L_1 = 14, dim ker L_0 = 14, sigma = 7, sigma + 2 dim A_D = 21
   delta: X T_2 (r_W = 2): dim A_D = 10, dim ker L_1 = 17, dim ker L_0 = 20, sigma = 6, sigma + 2 dim A_D = 26
   delta: general W: dim A_D = 7, dim ker L_1 = 14, dim ker L_0 = 14, sigma = 12, sigma + 2 dim A_D = 26
  ok   (B4, S) dim ker L_eps <= 2 dim A_D and sigma + 2 dim A_D <= 29 on the representatives
   count: Q = Gr(4,8) x C^4 x T_4^2 x T_3^2 has dimension 70, the section has rank 16, components have dimension >= 54; bad part <= 29 + 4 + 20 = 53
  ok   (U) 53 < 54
Part C: Macaulay bounds for four cubics
  ok   (U) 6^<3> = 7, 6^<4> = 7, 6^<5> = 7, 6^<6> = 6 (all 7 = maximal growth from 6; so H_{S/K}(j) <= 6 for j >= 3 when B is finite)
Part D: nonpure tops, general D_3 containing C
   secant, n = 2: base scheme of four general cubics through B_C has Hilbert polynomial 2
   secant, n = 3: base scheme of four general cubics through B_C has Hilbert polynomial 3
   tangent, n = 2: base scheme of four general cubics through B_C has Hilbert polynomial 2
   tangent, n = 3: base scheme of four general cubics through B_C has Hilbert polynomial 3
  ok   (S) a random D_3 containing C has base scheme of length n = dim C
(4.3 s)
ALL CHECKS PASSED
