Part C: cube branch
  ok   P7 in <Y^7, X Y^6, Y^6 Z>
  ok   shear effects 56 X Y^6, 56 Y^6 Z (quadratic), 336 X Y^5, 336 Y^5 Z (cubic)
  ok   P6 in <X^2Y^4, XY^5, XY^4Z, Y^6, Y^5Z, Y^4Z^2, Y^3Z^3>
   x o P6 = 2*al*X*Y^4 + sg*Y^4*Z ;  z o P6 = sg*X*Y^4 + 2*dl*Y^4*Z + 3*ep*Y^3*Z^2
  ok   rank condition: x o P6, z o P6 in D_5 = <Y^5, G5> give (2al, sg, 0) ~ (sg, 2dl, 3ep): sg^2 = 4 al dl, al ep = sg ep = 0 (minors)
  ok   forced coefficients: x^2 o al X^2Y^4 = 2 al Y^4 vs y^4 o Y^8 = 1680 Y^4; z^3 o ep Y^3Z^3 = 6 ep Y^3 vs y^5 o Y^8 = 6720 Y^3 ([y^5]g_5 = -ep/1120)
  ok   al != 0 (after z -> z + c x): y^3 z o Phi in T_{<=1}
  ok   al = sg = dl = ep = 0: y^3 z o Phi in T_{<=1}
  ok   x^2 o eta X^2 Y^3 = 2 eta Y^3, so [y^5] f_5 = -eta/3360 (6720 = y^5 o Y^8 coefficient)
  ok   YZ-coefficient of (xyz + r4) o Phi in degree 2 is 4 C + 48 dl [y^3 z] r4
  ok   eta = C = 0: 8 dl V, V = x y^2 - B/(8 dl) y^3 z - (A/1680) y^6: V o Phi in T_{<=1}, x y^2 kills D_5 = <Y^5, Y^4 Z>
Part S: N1 sanity (binary branch), gcd h = z^3 is the worst case 41
   135432111 trial 0: H = [1, 3, 5, 4, 3, 2, 1, 1, 1] ok, N1 complete intersection local length 38 (stable at N = 13)
   135432111 trial 1: H = [1, 3, 5, 4, 3, 2, 1, 1, 1] ok, N1 complete intersection local length 38 (stable at N = 12)
  ok   135432111: N1 sanity, 2 accepted algebras, all local lengths <= 41
time 219.8 s
ALL CHECKS PASSED
