(U1) bounds
  [ok] curvilinear Gamma: 27 + 4*3 = 39 < 42
  [ok] fat Gamma, plain excess: 27 + 4*4 = 43 > 41
  [ok] fat Gamma, free quartic tail: 27 + 3*4 = 39 < 42
(U2) rank condition of Lemma D.3 for D_3 = X^2 T_1
  [ok] x o K has rank >= 3 modulo D_3 (rank 3)
(U3) the kernel of theta generates a reduction of m_X^2
  [ok] I*_3 = (y,z)^2 S_1 has dimension 7
  [ok] the kernel of theta (the y^3-coefficient) on I*_3 has dimension 6 and equals the span of xy^2, xyz, xz^2, y^2z, yz^2, z^3
  [ok] negative control: adding y^3 to the six cubics gives a span different from the kernel
    colengths of two random kernel cubics in the chart: [4, 4, 4, 4]
  [ok] two random cubics of the kernel generate an ideal of colength 4 = e(m^2) at [X] (a reduction of m_X^2)
(S) actual algebras of the fat stratum
    sample 0 (X^6Y): line data (lam, H ok, min local length of 3 random triples) = [(1, True, 39), (-3, True, 39)]
  [ok] sample 0: M_lam has the same H and a triple of length <= 39
    sample 1 (X^7): line data (lam, H ok, min local length of 3 random triples) = [(1, True, 39), (-3, True, 39)]
  [ok] sample 1: M_lam has the same H and a triple of length <= 39
    sample 2 (X^6Y): line data (lam, H ok, min local length of 3 random triples) = [(1, True, 39), (-3, True, 39)]
  [ok] sample 2: M_lam has the same H and a triple of length <= 39
    sample 3 (X^7): line data (lam, H ok, min local length of 3 random triples) = [(1, True, 39), (-3, True, 39)]
  [ok] sample 3: M_lam has the same H and a triple of length <= 39
    sample 4 (X^6Y): line data (lam, H ok, min local length of 3 random triples) = [(1, True, 39), (-3, True, 39)]
  [ok] sample 4: M_lam has the same H and a triple of length <= 39
    sample 5 (X^7): line data (lam, H ok, min local length of 3 random triples) = [(1, True, 39), (-3, True, 39)]
  [ok] sample 5: M_lam has the same H and a triple of length <= 39
    sample 6 (X^6Y): line data (lam, H ok, min local length of 3 random triples) = [(1, True, 39), (-3, True, 39)]
  [ok] sample 6: M_lam has the same H and a triple of length <= 39
    sample 7 (X^7): line data (lam, H ok, min local length of 3 random triples) = [(1, True, 39), (-3, True, 39)]
  [ok] sample 7: M_lam has the same H and a triple of length <= 39
    accepted samples: 8
    accepted with F = X^7: 4, with F = X^6Y: 4
  [ok] at least two accepted samples of each top
17 checks, 0 failed
ALL CHECKS PASSED
