Part A: m = 1 (n = 3), exact arithmetic in Q(w)
  ok  : A1: 12 intersection points, each on exactly 3 of the 9 lines
  ok  : A1: each line contains exactly 4 of the 12 points
  ok  : A2: exactly 4 triples with one point on each line; they partition the 12 points
  ok  : A2: each point lies in Lambda_t for exactly 3 of the 4 pencils (so sum_t E_t = 3E)
  ok  : A3: pencil 0: the two members with u in {-w,-w^2} do not depend on the labelling (6 labellings)
  ok  : A3: pencil 1: the two members with u in {-w,-w^2} do not depend on the labelling (6 labellings)
  ok  : A3: pencil 2: the two members with u in {-w,-w^2} do not depend on the labelling (6 labellings)
  ok  : A3: pencil 3: the two members with u in {-w,-w^2} do not depend on the labelling (6 labellings)
  ok  : A3: 8 cubics (2 in each of the 4 pencils)
  ok  : A4: the 8 cubics agree up to scalars with the list on p. 7 of arXiv:1603.04480v1
  ok  : A5: all 8 cubics smooth (partials x quadrics span the 15 quartics)
  ok  : A6: each cubic passes through the 9 points of Lambda_t and through no point of V_t
  ok  : A7: at each vertex 6 cubics, exactly 2 tangent lines, 3 cubics from 3 different pencils on each (no tangent line is a line of the arrangement)
  ok  : A8: two cubics of one pencil: 9 common vertices, distinct tangents (transversal, 9 = Bezout)
  ok  : A8: 24 pairs from different pencils: 6 common vertices, same tangent at exactly 3; 3*2 + 3*1 = 9 = Bezout, so no further intersection and tangency of order exactly 2
  ok  : A9: 2 tangent directions at each vertex (24 points q in all)
     t =  7: dim S_t =  36, conditions = 60, exact rank = 36, dim I_t = 0, h^1(I_Z(t)) = 24
  ok  : A9: rank at t = 7 equals 36
     t =  8: dim S_t =  45, conditions = 60, exact rank = 45, dim I_t = 0, h^1(I_Z(t)) = 15
  ok  : A9: rank at t = 8 equals 45
     t =  9: dim S_t =  55, conditions = 60, exact rank = 52, dim I_t = 3, h^1(I_Z(t)) = 8
  ok  : A9: rank at t = 9 equals 52
     t = 10: dim S_t =  66, conditions = 60, exact rank = 57, dim I_t = 9, h^1(I_Z(t)) = 3
  ok  : A9: rank at t = 10 equals 57
     t = 11: dim S_t =  78, conditions = 60, exact rank = 60, dim I_t = 18, h^1(I_Z(t)) = 0
  ok  : A9: rank at t = 11 equals 60
     t = 12: dim S_t =  91, conditions = 60, exact rank = 60, dim I_t = 31, h^1(I_Z(t)) = 0
  ok  : A9: rank at t = 12 equals 60
     t = 13: dim S_t = 105, conditions = 60, exact rank = 60, dim I_t = 45, h^1(I_Z(t)) = 0
  ok  : A9: rank at t = 13 equals 60
     hence alpha(I) = 9, tau(I) = 11 and reg(I) = tau(I) + 1 = 12 for m = 1
Part B: the sextic of p. 10 of arXiv:1603.04480v1 (exact, Q(w, b), b^3 = 2)
  ok  : B1: P = (x^2-x-1)^3 + 2
  ok  : B1: P = (x^2-x+1)^3 - 6x^2(x-1)^2  (J = 6 on its roots)
  ok  : B1: Q = (x^2-x+1)^3 + 54x^2(x-1)^2  (J = -54 on its roots)
  ok  : B2: b w - 1 != 0
  ok  : B2: Q(tau) = 0
  ok  : B2: P(tau) != 0
  ok  : B2: 1, tau, ..., tau^5 linearly independent over Q, so Q is the minimal polynomial of tau
  ok  : B3: C_{v,tau} printed on p. 10 is proportional to C_{v0} + tau C_{voo} = -tau x^3 + (tau-1) y^3 + z^3
Part C: intersection numbers of the note for m = 1..60 (from the incidence counts)
  ok  : C: incidence bookkeeping, C~.Z = 36m^2-9, genus check, (2.1), Z.Etilde_v = 0, N and (3.1), N.C~, N.Etilde_v, N.E_q, N^2 = 12(k-4)(k+1) at t = 18m^2-9, N.Z = 18k^2+24k, 2(18m^2-8) <= 36m^2-12, length 60 and 1221
     m = 1 fails the hypotheses of the vanishing argument (b = k/2 - 2 = -1 < 0); it is Part A9
TOTAL failures: 0
