Part I: tangent in
  ok   P7 in <Y^7, 56 X Y^6, 56 Y^6 Z> + C Y^5 Z^2 (gauge, quadratic shears): P7 = eps Y^5 Z^2 after normalization
  ok   x -> x + yz: 10 eps X Y^4 Z on F (from eps Y^5 Z^2), 5 X Y^4 on T; x -> x + y^3: 336 X Y^5 on F, nothing in degree 5 on T
   X-parts: P6 -> P6_22*X*Y^5 + P6_16*X*Y^4*Z  T5 -> T5_16*X*Y^4 + T5_11*X*Y^3*Z ; conditions [-2*eps*T5_16 + P6_16, -2*eps*T5_11, T5_11]
  ok   X-parts of the tails: P6 = a X Y^5 + b X Y^4 Z, T5 = c X Y^4 + d X Y^3 Z; the conditions give d = 0 and b = 2 eps c
   (hand: with c = [X Y^4]T5, the shear x -> x - (c/5) yz removes c X Y^4 from T5 and 2 eps c X Y^4 Z from P6;
    the shear x -> x + t y^3 removes a X Y^5; so P6, T5 become binary)
  ok   eps != 0: 40 eps U, U = x y^2 - v/(40 eps) y^4 z - (u/1680) y^6, kills F and T into T_{<=1}
  ok   eps = 0: z o F - (s0/336) y^3 o F - (2 delta/5) y o T has degree <= 4 and X-part v X Y^3 in degree 4 (so v = 0, as D_4 is binary)
  ok   eps = 0, v = 0: U = x y^2 - (u/1680) y^6 kills F and T into T_{<=1}
Part O: tangent out
  ok   P7 in <X^2 Y^5, X Y^6, Y^7> + C Z Y^6, and Z (y^2 o Y^8) = 56 Z Y^6 (quadratic shear z -> z + e y^2)
  ok   shear z -> z + t x y: Z(xy o X Y^5) = 5 Z Y^4 on T, Z(xy o lam X^2 Y^5) = 10 lam Z X Y^4 on F, Z(xy o Y^8) = 0; z -> z + e y^3: 336 Z Y^5 on F, degree 4 on T
   Z-parts after the derivative conditions: P6 -> P6_16*X*Y^4*Z + P6_15*Y^5*Z ; T5 -> T5_11*X*Y^3*Z + T5_10*Y^4*Z
  ok   x o T - y^3 o F/336 has no part of degree >= 5; x o F - 2 lam T - (al/56) y^2 o F has no part of degree >= 6
   Z-part of the quartic head of the first: T5_11*Y^3*Z ; of the quintic head of the second: (-2*lam*T5_11)*X*Y^3*Z + (-2*lam*T5_10 + P6_16)*Y^4*Z
  ok   these Z-parts must vanish (D_4, D_5 have no Z): they give D = [Z X Y^3]T5 = 0 and B = 2 lam C ([Z X Y^4]P6, [Z Y^4]T5)
   (z4, z5 printed above; hand: the shear z -> z - (C/5) x y then z -> z + e y^3 makes P6, T5 free of Z)
  ok   U = y z^2 kills F and T into T_{<=1} (P7, P6, T5 free of Z, z o P5 in D_4)
Part S: N1 sanity in the binary branch (secant: kappa = 9 and 7 at [Y], [Z]; tangent: [Y] double), bound 38
   135422211 trial 0 rejected (binary H [1, 2, 3, 3, 2, 2, 2, 1, 1])
   135422211 trial 1: H = [1, 3, 5, 4, 2, 2, 2, 1, 1] ok, N1 complete intersection local length 38 (stable at N = 12)
  ok   135422211: N1 sanity, 1 accepted algebras, all local lengths <= 38
time 186.5 s
ALL CHECKS PASSED
