=== Part G: base schemes of length four with sum e_p = 5, and the subschemes Gamma of length three (U)
  ok   nu_3(B_A) = <X^3, X^2Y, X^2Z, XZ^2>, and B_A has degree 4
  ok   nu_3(B_B) = <X^3, X^2Y, X^2Z, Y^3>, and B_B has degree 4
  ok   A-fat    Gamma of length 3 inside B; dim nu_4 = nu_5 = nu_6 = 3; S_1 o nu_4 in D_3; nu_4 = [X^3*Z, X^3*Y, X^4]
  ok   A-curv0  Gamma of length 3 inside B; dim nu_4 = nu_5 = nu_6 = 3; S_1 o nu_4 in D_3; nu_4 = [X^2*Z^2, X^3*Z, X^4]
  ok   A-curv1  Gamma of length 3 inside B; dim nu_4 = nu_5 = nu_6 = 3; S_1 o nu_4 in D_3; nu_4 = [-2/3*X^3*Y + X^2*Z^2, X^3*Z, X^4]
  ok   B-fat    Gamma of length 3 inside B; dim nu_4 = nu_5 = nu_6 = 3; S_1 o nu_4 in D_3; nu_4 = [X^3*Z, X^3*Y, X^4]
  ok   B-dblY   Gamma of length 3 inside B; dim nu_4 = nu_5 = nu_6 = 3; S_1 o nu_4 in D_3; nu_4 = [Y^4, X^3*Y, X^4]
  ok   B-dblZ   Gamma of length 3 inside B; dim nu_4 = nu_5 = nu_6 = 3; S_1 o nu_4 in D_3; nu_4 = [X^3*Z, Y^4, X^4]
  ok   B_A: local length 4, socle of dimension 2 (spanned by eta, zeta^2)
  ok   A-fat    graded datum (D_3, nu_4, nu_5, generic F) has H = [1, 3, 6, 4, 3, 3, 1]
  ok   A-curv0  graded datum (D_3, nu_4, nu_5, generic F) has H = [1, 3, 6, 4, 3, 3, 1]
  ok   A-curv1  graded datum (D_3, nu_4, nu_5, generic F) has H = [1, 3, 6, 4, 3, 3, 1]
  ok   B-fat    graded datum (D_3, nu_4, nu_5, generic F) has H = [1, 3, 6, 4, 3, 3, 1]
  ok   B-dblY   graded datum (D_3, nu_4, nu_5, generic F) has H = [1, 3, 6, 4, 3, 3, 1]
  ok   B-dblZ   graded datum (D_3, nu_4, nu_5, generic F) has H = [1, 3, 6, 4, 3, 3, 1]
  ok   A-fat    sixth powers of coordinate-type points in nu_6: [X]
  ok   A-curv0  sixth powers of coordinate-type points in nu_6: [X]
  ok   A-curv1  sixth powers of coordinate-type points in nu_6: [X]
  ok   B-fat    sixth powers of coordinate-type points in nu_6: [X]
  ok   B-dblY   sixth powers of coordinate-type points in nu_6: [X, Y]
  ok   B-dblZ   sixth powers of coordinate-type points in nu_6: [X, Y]
=== Part X: excess weights k(p) - 3 (U)
  ok   general pencils of I*_3: e_X = 5 on B_A, e_X = 4 and e_Y = 1 on B_B
  ok   A-fat    k(X) = 6: weight 3 * e_X = 15, excess gives 42 (fails)
  ok   A-curv0  k(X) = 6: weight 3 * e_X = 15, excess gives 42 (fails)
  ok   A-curv1  k(X) = 6: weight 3 * e_X = 15, excess gives 42 (fails)
  ok   B-fat    k(X) = 6, k(Y) = 4: 27 + 3*4 + 1*1 = 40
  ok   B-dblY   k(X) = 6, k(Y) = 6: 27 + 3*4 + 3*1 = 42
  ok   B-dblZ   k(X) = 6, k(Y) = 6: 27 + 3*4 + 3*1 = 42
=== Part D3: rank condition of [15, Lemma D.3] at [X] (U)
  ok   D_A: dim K = 7, rank of x o K modulo D_3 = 3 (>= 3 needed)
  ok   D_B: dim K = 7, rank of x o K modulo D_3 = 3 (>= 3 needed)
=== Part D4: transverse sextic X^5 Y on B_A (U)
  ok   R = Y^4: x o R = z o R = 0, and y o R = 4Y^3 (theta(w) = -<w, 4Y^3>/120 = -(1/5) coeff of y^3)
  ok   I*_3 = D_A^perp has dim 6; the cubics without y^3 form a 5-space
  ok   the pencil (xy^2+yz^2+z^3, xyz+y^2z) lies in I*_3, has no y^3, and meets at [X] with length 5 = e(b_X)
   (two elements of b_X with colength e(b_X) generate a reduction (Rees); so general pencils of the 5-space are reductions)
=== Part W: weak-ideal multiplicities e(K_v) (U) and sanity on I* (S)
  ok   B-dblY   F = X^6 + X^5*Y + Y^6 lies in nu_6(Gamma)
  ok   B-dblY   nonpure 27 + sum e(K_v) <= 27 + X:10+Y:3 = 40 <= 41
  ok   B-dblY   (S) random triples of I* have local length 40 = 27 + sum e(K_v)
  ok   B-dblY   F = Y^6 lies in nu_6(Gamma)
  ok   B-dblY   Y^6     27 + sum e(K_v) <= 27 + X:10+Y:4 = 41 <= 41
  ok   B-dblY   (S) random triples of I* have local length 41 = 27 + sum e(K_v)
  ok   B-dblZ   F = X^6 + Y^6 + X^5*Z lies in nu_6(Gamma)
  ok   B-dblZ   nonpure 27 + sum e(K_v) <= 27 + X:10+Y:3 = 40 <= 41
  ok   B-dblZ   (S) random triples of I* have local length 40 = 27 + sum e(K_v)
  ok   B-dblZ   F = Y^6 lies in nu_6(Gamma)
  ok   B-dblZ   Y^6     27 + sum e(K_v) <= 27 + X:10+Y:4 = 41 <= 41
  ok   B-dblZ   (S) random triples of I* have local length 41 = 27 + sum e(K_v)
  ok   A-curv0  F = X^4*Z^2 lies in nu_6(Gamma)
  ok   A-curv0  nonpure 27 + sum e(K_v) <= 27 + X:14 = 41 <= 41
  ok   A-curv0  (S) random triples of I* have local length 41 = 27 + sum e(K_v)
  ok   A-curv1  F = -2/5*X^5*Y + X^4*Z^2 lies in nu_6(Gamma)
  ok   A-curv1  nonpure 27 + sum e(K_v) <= 27 + X:14 = 41 <= 41
  ok   A-curv1  (S) random triples of I* have local length 41 = 27 + sum e(K_v)
  ok     (S) B-dblY F = X^6 + X^5*Y + Y^6: e(I*) = 40
  ok     (S) B-dblY F = 2*X^6 - 3*X^5*Y + 5*Y^6: e(I*) = 40
  ok     (S) B-dblY F = X^5*Y + 7*Y^6: e(I*) = 40
  ok     (S) B-dblY F = X^6 - 2*Y^6: e(I*) = 40
  ok     (S) B-dblY F = 3*X^6 + X^5*Y: e(I*) = 40
=== Part F: the aligned stratum B_A, Gamma fat, F = X^5 Z (U + A)
  ok   aligned  F = X^5Z: 48 closedness conditions in 42 tail coefficients; elimination with constant pivots solves all, 14 free (+ 12 free cubic tail coefficients): one family over an affine space
  ok     (S) random member: H = [1, 3, 6, 4, 3, 3, 1], e(I) <= 36 (bound 41)
  ok     (S) random member: H = [1, 3, 6, 4, 3, 3, 1], e(I) <= 36 (bound 41)
  ok     (S) random member: H = [1, 3, 6, 4, 3, 3, 1], e(I) <= 36 (bound 41)
  ok   transverse F = X^5Y: 48 closedness conditions in 42 tail coefficients; elimination with constant pivots solves all, 13 free (+ 12 free cubic tail coefficients): one family over an affine space
  ok     (S) random member: H = [1, 3, 6, 4, 3, 3, 1], e(I) <= 36 (bound 37)
  ok     (S) random member: H = [1, 3, 6, 4, 3, 3, 1], e(I) <= 36 (bound 37)
  ok     (S) random member: H = [1, 3, 6, 4, 3, 3, 1], e(I) <= 36 (bound 37)
  ok   anchor (A): Phi = X^5Z + Z^4, Psi = X^4Y (tails in the family), H = [1, 3, 6, 4, 3, 3, 1]; (2y^3+xyz, 5z^3-x^5, xy^2-x^2z^2) in I, local length 38 (standard basis), stabilization (38, 10)
=== Part D4s: the deformation M_lambda of the Cor D.4 rerun on the graded transverse member (S, discriminating)
  ok   lambda = 0: H ok, e(I_lambda) = 42 (graded member 42; the bound of the deformation is 37)
  ok   lambda = 1: H ok, e(I_lambda) = 37 (graded member 42; the bound of the deformation is 37)
  ok   lambda = 3: H ok, e(I_lambda) = 37 (graded member 42; the bound of the deformation is 37)
time 12.2 s
ALL CHECKS PASSED
