Part T1: G = x^2 + t b^(s-1), b = y (nonzero at all roots), K = x r, P = p
  ok   s = 5, roots 1111: length 32 == 32
  ok   s = 5, roots 211: length 32 == 32
  ok   s = 5, roots 22: length 32 == 32
  ok   s = 5, roots 31: length 32 == 32
  ok   s = 5, roots 4: length 32 == 32
  ok   s = 5, random higher terms (gamma_f = 0), p = z^4: length 32 <= 32
  ok   s = 6, roots 1111: length 36 == 36
  ok   s = 6, roots 211: length 36 == 36
  ok   s = 6, roots 22: length 36 == 36
  ok   s = 6, roots 31: length 36 == 36
  ok   s = 6, roots 4: length 36 == 36
  ok   s = 6, random higher terms (gamma_f = 0), p = z^4: length 32 <= 36
  ok   s = 7, roots 1111: length 40 == 40
  ok   s = 7, roots 211: length 40 == 40
  ok   s = 7, roots 22: length 40 == 40
  ok   s = 7, roots 31: length 40 == 40
  ok   s = 7, roots 4: length 40 == 40
  ok   s = 7, random higher terms (gamma_f = 0), p = z^4: length 32 <= 40
  ok   certified s = 7, p = z^4: 40 (N = 11) == 40
Part T2: s = 8, p = z^3 (y + z): G = x^2 + t y^7 + sigma z^3 y (kappa = 4 at the root of y + z)
  ok   length 41 == 24 + 2 + 5*3 = 41
  ok   certified: 41 (N = 12) == 41
Part T3: (1,3,5,4,5,2,1), F = Y^6: f + t(w + s b^5), w = z(y^3 + z^3), K = x r, P = g + nu y^7 (order 5)
  ok   g = z (y^4 + 2 y^2 z^2 + z^4 + y z^3) (simple root at [Y]): length 41 (expected 41)
  ok   g = z^2 (y^3 + 2 y z^2 + 5 z^3) (double root at [Y]; other roots avoid w = 0 and b = 0): length 42 (expected 42)
Part M: exploratory e(I*) for the bad stratum of (1,3,5,5,5,2): Q_D = Y^2, D_4 = binary quartics, D_5 = <Y^5, G>
  G = Z^5: min local length of 3 general combinations = 48 (Prop. 3.17 needs <= 41)
  G = Y^3 Z^2 + Z^5: min local length of 3 general combinations = 47 (Prop. 3.17 needs <= 41)
  G random: min local length of 3 general combinations = 47 (Prop. 3.17 needs <= 41)
ALL CHECKS PASSED
