(U1) excess bounds, [15, Thm 3.12] with refined weights
  [ok] Gamma = {X,P}, B = Gamma: 27 + 5 + 4 = 36 < 42
  [ok] Gamma = {X,P}, B = Gamma + q: 27 + 5 + 4 + 1 = 37 < 42
  [ok] Gamma = {X,P}, B = (double point at X) + P: 27 + 10 + 4 = 41 < 42
  [ok] Gamma = {X,P}, B = X + (double point at P): 27 + 5 + 8 = 40 < 42
  [ok] Gamma = Gamma_0, B = Gamma_0 or Gamma_0 + q: <= 27 + 10 + 1 = 38 < 42
  [ok] Gamma = Gamma_0, B curvilinear of length 3 or fat at X: Theorem 3.12 gives 27 + 15 = 42 and 27 + 20 = 47 (open here)
  [ok] Macaulay: 3^<3> = 3, so l(B) <= 3
(U2)/(A) collinear B = V(z, y^3)
  [ok] collinear B = V(z, y^3): dim D_3 = 3, D_4, D_5, D_6 = nu(Gamma_0) of dim 2
  [ok] collinear B = V(z, y^3): I*_3 = (I_B)_3 (dim 7, generated by elements of I_B)
  [ok] collinear B = V(z, y^3): graded data give H = (1,3,6,3,2,2,2,1,1)
    top of M_Q: X^8 - 6720*Y^3
  [ok] collinear B = V(z, y^3): M_Q closed, dim 21, H = (1,3,6,3,2,2,2,1,1), with the graded data D_3..D_7
  [ok] collinear B = V(z, y^3): the triple annihilates M_Q
    triple [x^2*z, x^8 + y^3, x^2*y^2 + z^3]: local length 40 (standard basis), 40 (stabilization)
  [ok] collinear B = V(z, y^3): local length 40 <= 41 by both certificates
(U2)/(A) conic B = V(xz - y^2, yz, z^2)
  [ok] conic B = V(xz - y^2, yz, z^2): dim D_3 = 3, D_4, D_5, D_6 = nu(Gamma_0) of dim 2
  [ok] conic B = V(xz - y^2, yz, z^2): I*_3 = (I_B)_3 (dim 7, generated by elements of I_B)
  [ok] conic B = V(xz - y^2, yz, z^2): graded data give H = (1,3,6,3,2,2,2,1,1)
    top of M_Q: X^8 - 6720*Y^3
  [ok] conic B = V(xz - y^2, yz, z^2): M_Q closed, dim 21, H = (1,3,6,3,2,2,2,1,1), with the graded data D_3..D_7
  [ok] conic B = V(xz - y^2, yz, z^2): the triple annihilates M_Q
    triple [-x*y^2 + x^2*z, x^8 + y^3, x^2*y^2 + z^3]: local length 40 (standard basis), 40 (stabilization)
  [ok] conic B = V(xz - y^2, yz, z^2): local length 40 <= 41 by both certificates
(U2)/(A) fat B = V(y^2, yz, z^2)
  [ok] fat B = V(y^2, yz, z^2): dim D_3 = 3, D_4, D_5, D_6 = nu(Gamma_0) of dim 2
  [ok] fat B = V(y^2, yz, z^2): I*_3 = (I_B)_3 (dim 7, generated by elements of I_B)
  [ok] fat B = V(y^2, yz, z^2): graded data give H = (1,3,6,3,2,2,2,1,1)
    top of M_Q: X^8 - 20160*X*Z^2
  [ok] fat B = V(y^2, yz, z^2): M_Q closed, dim 21, H = (1,3,6,3,2,2,2,1,1), with the graded data D_3..D_7
  [ok] fat B = V(y^2, yz, z^2): the triple annihilates M_Q
    triple [x^6*y + x*y^2, x^8 + y^3 + x*z^2, x^3*z + x*y*z + z^3]: local length 41 (standard basis), 41 (stabilization)
  [ok] fat B = V(y^2, yz, z^2): local length 41 <= 41 by both certificates
(S) observation: two sampled undeformed triples of I* for each of the three data
    collinear B = V(z, y^3): [42, 42]
  [ok] collinear B = V(z, y^3): the two sampled undeformed triples of I* have local lengths greater than 41
    conic B = V(xz - y^2, yz, z^2): [42, 42]
  [ok] conic B = V(xz - y^2, yz, z^2): the two sampled undeformed triples of I* have local lengths greater than 41
    fat B = V(y^2, yz, z^2): [43, 43]
  [ok] fat B = V(y^2, yz, z^2): the two sampled undeformed triples of I* have local lengths greater than 41
28 checks, 0 failed
ALL CHECKS PASSED
