(Mi) the minors of [x; alpha x]: span of dimension <= 1 forces alpha scalar  [U]
  ok   (U) every generator of the ideal of scalar matrices lies in rad(2x2 minors of the 3 x 6 coefficient matrix)   [0.3s]
  ok   (U) conversely the coefficient matrix vanishes at alpha = identity (x times x = 0)   [0.3s]
(D) bad points, r = 3: data in Y_V, tau = 26 + kappa, class bounds, the inequality  [S at actual data; bounds are proved by hand]
  ok   (S) (a) <X^5+Y^5, X^5+2Z^5>, l: x=0, Gamma={X,R0}                  given class concise c=3 kappa=0 tau=26  bad<=29 < floor 38   [0.5s]
  ok   (S) (a) <X^5+Y^5, X^5+2Z^5>, l: x=0, Gamma={X,R0}                  conj  class concise c=3 kappa=0 tau=26  bad<=29 < floor 38   [0.5s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [0.5s]
  ok   (S) (a) same V, l: x=z (through Y, X+Z), Gamma={X,Z}               given class concise c=3 kappa=1 tau=27  bad<=30 < floor 38   [0.8s]
  ok   (S) (a) same V, l: x=z (through Y, X+Z), Gamma={X,Z}               conj  class concise c=3 kappa=1 tau=27  bad<=30 < floor 38   [0.8s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [0.8s]
  ok   (S) (a) same V, l: z=0, Gamma={Z,R0}                               given class concise c=3 kappa=0 tau=26  bad<=29 < floor 38   [1.2s]
  ok   (S) (a) same V, l: z=0, Gamma={Z,R0}                               conj  class concise c=3 kappa=0 tau=26  bad<=29 < floor 38   [1.2s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [1.2s]
  ok   (S) (b) <X^5+3X^2Y^3+Y^5, Z^5>, l: z=0, Gamma={Z,R0}               given class concise c=4 kappa=2 tau=28  bad<=31 < floor 34   [1.6s]
  ok   (S) (b) <X^5+3X^2Y^3+Y^5, Z^5>, l: z=0, Gamma={Z,R0}               conj  class concise c=4 kappa=2 tau=28  bad<=31 < floor 34   [1.6s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [1.6s]
  ok   (S) (b) same V, l: z=0, Gamma double at Z along X                  given class concise c=4 kappa=2 tau=28  bad<=31 < floor 34   [1.9s]
  ok   (S) (b) same V, l: z=0, Gamma double at Z along X                  conj  class concise c=4 kappa=2 tau=28  bad<=31 < floor 34   [1.9s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [1.9s]
  ok   (S) (b) <X^5+Y^5, Z^5>, l: x=0, Gamma={X,R0}                       given class concise c=3 kappa=1 tau=27  bad<=30 < floor 38   [2.3s]
  ok   (S) (b) <X^5+Y^5, Z^5>, l: x=0, Gamma={X,R0}                       conj  class concise c=3 kappa=1 tau=27  bad<=30 < floor 38   [2.3s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [2.3s]
  ok   (S) (c) <X^4Y+Z^5, X^5+2Z^5>, l: z=0, Gamma={Z,R0}                 given class concise c=3 kappa=0 tau=26  bad<=29 < floor 38   [2.7s]
  ok   (S) (c) <X^4Y+Z^5, X^5+2Z^5>, l: z=0, Gamma={Z,R0}                 conj  class concise c=3 kappa=0 tau=26  bad<=29 < floor 38   [2.7s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [2.7s]
  ok   (S) (c) same V, l: y=0, Gamma double at X along Y                  given class concise c=3 kappa=1 tau=27  bad<=30 < floor 38   [3.0s]
  ok   (S) (c) same V, l: y=0, Gamma double at X along Y                  conj  class concise c=3 kappa=1 tau=27  bad<=30 < floor 38   [3.0s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [3.0s]
  ok   (S) (d) <X^5, X^4Y+Z^5+X^2Z^3>, l: y=0, Gamma={X,R0}               given class concise c=4 kappa=2 tau=28  bad<=31 < floor 34   [3.4s]
  ok   (S) (d) <X^5, X^4Y+Z^5+X^2Z^3>, l: y=0, Gamma={X,R0}               conj  class concise c=4 kappa=2 tau=28  bad<=31 < floor 34   [3.4s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [3.4s]
  ok   (S) (d) same V, l: y=0, Gamma double at X along Y                  given class concise c=4 kappa=2 tau=28  bad<=31 < floor 34   [3.7s]
  ok   (S) (d) same V, l: y=0, Gamma double at X along Y                  conj  class concise c=4 kappa=2 tau=28  bad<=31 < floor 34   [3.7s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [3.7s]
  ok   (S) (e) <X^4Y, X^4Z+2X^3Y^2>, l: z=0, Gamma={X,R0}                 given class concise c=3 kappa=0 tau=26  bad<=29 < floor 38   [4.2s]
  ok   (S) (e) <X^4Y, X^4Z+2X^3Y^2>, l: z=0, Gamma={X,R0}                 conj  class concise c=3 kappa=0 tau=26  bad<=29 < floor 38   [4.2s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [4.2s]
  ok   (S) (e) same V, l: y=0, Gamma double at X along Y                  given class concise c=3 kappa=1 tau=27  bad<=30 < floor 38   [4.6s]
  ok   (S) (e) same V, l: y=0, Gamma double at X along Y                  conj  class concise c=3 kappa=1 tau=27  bad<=30 < floor 38   [4.6s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [4.6s]
  ok   (S) (12) <X^4Y, X^4Z>, l: y-z=0, Gamma={X,R0}                      given class X4YZ    c=3 kappa=0 tau=26  bad<=29 < floor 38   [5.0s]
  ok   (S) (12) <X^4Y, X^4Z>, l: y-z=0, Gamma={X,R0}                      conj  class X4YZ    c=3 kappa=0 tau=26  bad<=29 < floor 38   [5.0s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [5.0s]
  ok   (S)    class X4YZ: V = L^4 * Lambda (gcd of the basis contains a 4th power of a linear form)   [5.0s]
  ok   (S) (12) same V, l: z=0, Gamma double at X along Z                 given class X4YZ    c=3 kappa=1 tau=27  bad<=30 < floor 38   [5.4s]
  ok   (S) (12) same V, l: z=0, Gamma double at X along Z                 conj  class X4YZ    c=3 kappa=1 tau=27  bad<=30 < floor 38   [5.4s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [5.4s]
  ok   (S)    class X4YZ: V = L^4 * Lambda (gcd of the basis contains a 4th power of a linear form)   [5.4s]
  ok   (S) bin-bad <Y^5, Y^3Z^2+Z^5>, l: x=0, Gamma={Y,X}                 given class binary  c=4 kappa=2 tau=28  bad<=31 < floor 34   [5.8s]
  ok   (S) bin-bad <Y^5, Y^3Z^2+Z^5>, l: x=0, Gamma={Y,X}                 conj  class binary  c=4 kappa=2 tau=28  bad<=31 < floor 34   [5.8s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [5.8s]
  ok   (S) bin-bad same V, l: x=0, Gamma={Y,Z}                            given class binary  c=4 kappa=2 tau=28  bad<=31 < floor 34   [6.3s]
  ok   (S) bin-bad same V, l: x=0, Gamma={Y,Z}                            conj  class binary  c=4 kappa=2 tau=28  bad<=31 < floor 34   [6.3s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [6.3s]
  ok   (S) bin-bad same V, l: x=0, Gamma double at Y along Z              given class binary  c=4 kappa=2 tau=28  bad<=31 < floor 34   [6.7s]
  ok   (S) bin-bad same V, l: x=0, Gamma double at Y along Z              conj  class binary  c=4 kappa=2 tau=28  bad<=31 < floor 34   [6.7s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [6.7s]
  ok   (S) bin-bad same V, l: x=0, Gamma double at Y along X              given class binary  c=4 kappa=2 tau=28  bad<=31 < floor 34   [6.9s]
  ok   (S) bin-bad same V, l: x=0, Gamma double at Y along X              conj  class binary  c=4 kappa=2 tau=28  bad<=31 < floor 34   [6.9s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [6.9s]
  ok   (S) bin, other line: <Y^5, Z^5+(Y+Z)^5>, l: z=0, Gamma={Z,Y+Z}     given class binary  c=3 kappa=1 tau=27  bad<=30 < floor 38   [7.3s]
  ok   (S) bin, other line: <Y^5, Z^5+(Y+Z)^5>, l: z=0, Gamma={Z,Y+Z}     conj  class binary  c=3 kappa=1 tau=27  bad<=30 < floor 38   [7.3s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [7.3s]
  ok   (S) bin, other line: <Y^5+Z^5, Z^5+2(Y+Z)^5>, l: z=0, Gamma={Z,Y+Z} given class binary  c=3 kappa=1 tau=27  bad<=30 < floor 38   [7.7s]
  ok   (S) bin, other line: <Y^5+Z^5, Z^5+2(Y+Z)^5>, l: z=0, Gamma={Z,Y+Z} conj  class binary  c=3 kappa=1 tau=27  bad<=30 < floor 38   [7.7s]
  ok   (S)    invariants agree under the GL_3 conjugation (class, r, c, kappa, tau)   [7.7s]
(D2) bad points, r = 2 (u random in nu_4(B)): tau = 26 + kappa, kappa <= 4, lambda + 4 + 26 + kappa < 42  [S]
  ok   (S) r2 secant <X^5,Y^5>, l: x=0, Gamma={X,R0}                      given c=5 kappa=3 tau=29  bad<=36 < floor 42   [8.2s]
  ok   (S) r2 secant <X^5,Y^5>, l: x=0, Gamma={X,R0}                      conj  c=5 kappa=3 tau=29  bad<=36 < floor 42   [8.2s]
  ok   (S) r2 secant <X^5,Y^5>, l: x=0, Gamma={X,Y}                       given c=4 kappa=4 tau=30  bad<=37 < floor 42   [8.6s]
  ok   (S) r2 secant <X^5,Y^5>, l: x=0, Gamma={X,Y}                       conj  c=4 kappa=4 tau=30  bad<=37 < floor 42   [8.6s]
  ok   (S) r2 secant <X^5,P^5>, l: x=0, Gamma={X,P}                       given c=4 kappa=4 tau=30  bad<=37 < floor 42   [9.1s]
  ok   (S) r2 secant <X^5,P^5>, l: x=0, Gamma={X,P}                       conj  c=4 kappa=4 tau=30  bad<=37 < floor 42   [9.1s]
  ok   (S) r2 tangent <X^5,X^4Y>, l: x=0, Gamma double at X along Y       given c=4 kappa=4 tau=30  bad<=37 < floor 42   [9.5s]
  ok   (S) r2 tangent <X^5,X^4Y>, l: x=0, Gamma double at X along Y       conj  c=4 kappa=4 tau=30  bad<=37 < floor 42   [9.5s]
  ok   (S) r2 tangent <Y^5,Y^4X>, l: x=0, Gamma={Y,R0}                    given c=5 kappa=3 tau=29  bad<=36 < floor 42   [9.9s]
  ok   (S) r2 tangent <Y^5,Y^4X>, l: x=0, Gamma={Y,R0}                    conj  c=5 kappa=3 tau=29  bad<=36 < floor 42   [9.9s]
  ok   (S) r2 bin-bad <Y^5,Z^5>, l: x=0, Gamma={Y,Z}                      given c=4 kappa=4 tau=30  bad<=37 < floor 42   [10.3s]
  ok   (S) r2 bin-bad <Y^5,Z^5>, l: x=0, Gamma={Y,Z}                      conj  c=4 kappa=4 tau=30  bad<=37 < floor 42   [10.3s]
  ok   (S) r2 bin-bad <Y^5,Z^5>, l: x=0, Gamma={Y,X}                      given c=5 kappa=3 tau=29  bad<=36 < floor 42   [10.7s]
  ok   (S) r2 bin-bad <Y^5,Z^5>, l: x=0, Gamma={Y,X}                      conj  c=5 kappa=3 tau=29  bad<=36 < floor 42   [10.7s]
  ok   (S) r2 bin-bad tangent <Y^5,Y^4Z>, l: x=0, Gamma double at Y along X given c=5 kappa=3 tau=29  bad<=36 < floor 42   [11.2s]
  ok   (S) r2 bin-bad tangent <Y^5,Y^4Z>, l: x=0, Gamma double at Y along X conj  c=5 kappa=3 tau=29  bad<=36 < floor 42   [11.2s]
(L1) lines l with dim x_l o V <= 1: projective dimension <= 1  [S]
  ok   (S) (a) <X^5+Y^5, X^5+2Z^5>                                        dim = 0   [11.2s]
  ok   (S) (b) <X^5+3X^2Y^3+Y^5, Z^5>                                     dim = 1   [11.2s]
  ok   (S) (b) <X^5+Y^5, Z^5>                                             dim = 1   [11.2s]
  ok   (S) (c) <X^4Y+Z^5, X^5+2Z^5>                                       dim = 0   [11.2s]
  ok   (S) (d) <X^5, X^4Y+Z^5+X^2Z^3>                                     dim = 1   [11.3s]
  ok   (S) (e) <X^4Y, X^4Z+2X^3Y^2>                                       dim = 0   [11.3s]
  ok   (S) (12) <X^4Y, X^4Z>                                              dim = 1   [11.3s]
  ok   (S) bin-bad <Y^5, Y^3Z^2+Z^5>                                      dim = 1   [11.3s]
  ok   (S) bin, other line: <Y^5, Z^5+(Y+Z)^5>                            dim = 1   [11.4s]
  ok   (S) bin, other line: <Y^5+Z^5, Z^5+2(Y+Z)^5>                       dim = 0   [11.4s]
  ok   (S) r2 secant <X^5,Y^5>                                            dim = 1   [11.4s]
  ok   (S) r2 secant <X^5,P^5>                                            dim = 1   [11.4s]
  ok   (S) r2 tangent <X^5,X^4Y>                                          dim = 1   [11.4s]
  ok   (S) r2 tangent <Y^5,Y^4X>                                          dim = 1   [11.4s]
  ok   (S) r2 bin-bad <Y^5,Z^5>                                           dim = 1   [11.4s]
  ok   (S) r2 bin-bad tangent <Y^5,Y^4Z>                                  dim = 1   [11.5s]
(LAM) local dimension of Lambda_V = {(l, Gamma) : V in nu_5(l u Gamma)} at the sample (l_0, Gamma_0), in a chart of
      P^2* x Hilb_2(P^2) (lines l = l_0 + s1 m1 + s2 m2; Gamma = V(l_G, q) with l_G = l_G0 + a k1 + b k2, q = q_0 + c1 n1 + c2 n2):
      <= 3 where V is non-binary for l_0, and = 4 (Gamma free) where V is binary for l_0  [S]
  ok   (S) (a) <X^5+Y^5, X^5+2Z^5>, l: x=0, Gamma={X,R0}                  local dim 2 (non-binary for l_0)   [11.6s]
  ok   (S) (a) same V, l: x=z (through Y, X+Z), Gamma={X,Z}               local dim 1 (non-binary for l_0)   [11.7s]
  ok   (S) (a) same V, l: z=0, Gamma={Z,R0}                               local dim 2 (non-binary for l_0)   [11.7s]
  ok   (S) (b) <X^5+3X^2Y^3+Y^5, Z^5>, l: z=0, Gamma={Z,R0}               local dim 2 (non-binary for l_0)   [11.8s]
  ok   (S) (b) same V, l: z=0, Gamma double at Z along X                  local dim 2 (non-binary for l_0)   [11.9s]
  ok   (S) (b) <X^5+Y^5, Z^5>, l: x=0, Gamma={X,R0}                       local dim 2 (non-binary for l_0)   [11.9s]
  ok   (S) (c) <X^4Y+Z^5, X^5+2Z^5>, l: z=0, Gamma={Z,R0}                 local dim 2 (non-binary for l_0)   [12.0s]
  ok   (S) (c) same V, l: y=0, Gamma double at X along Y                  local dim 2 (non-binary for l_0)   [12.1s]
  ok   (S) (d) <X^5, X^4Y+Z^5+X^2Z^3>, l: y=0, Gamma={X,R0}               local dim 2 (non-binary for l_0)   [12.1s]
  ok   (S) (d) same V, l: y=0, Gamma double at X along Y                  local dim 2 (non-binary for l_0)   [12.2s]
  ok   (S) (e) <X^4Y, X^4Z+2X^3Y^2>, l: z=0, Gamma={X,R0}                 local dim 2 (non-binary for l_0)   [12.2s]
  ok   (S) (e) same V, l: y=0, Gamma double at X along Y                  local dim 1 (non-binary for l_0)   [12.3s]
  ok   (S) (12) <X^4Y, X^4Z>, l: y-z=0, Gamma={X,R0}                      local dim 3 (non-binary for l_0)   [12.4s]
  ok   (S) (12) same V, l: z=0, Gamma double at X along Z                 local dim 3 (non-binary for l_0)   [12.4s]
  ok   (S) bin-bad <Y^5, Y^3Z^2+Z^5>, l: x=0, Gamma={Y,X}                 local dim 4 (binary for l_0)   [12.5s]
  ok   (S) bin-bad same V, l: x=0, Gamma={Y,Z}                            local dim 4 (binary for l_0)   [12.5s]
  ok   (S) bin-bad same V, l: x=0, Gamma double at Y along Z              local dim 4 (binary for l_0)   [12.6s]
  ok   (S) bin-bad same V, l: x=0, Gamma double at Y along X              local dim 4 (binary for l_0)   [12.7s]
  ok   (S) bin, other line: <Y^5, Z^5+(Y+Z)^5>, l: z=0, Gamma={Z,Y+Z}     local dim 1 (non-binary for l_0)   [12.7s]
  ok   (S) bin, other line: <Y^5+Z^5, Z^5+2(Y+Z)^5>, l: z=0, Gamma={Z,Y+Z} local dim 1 (non-binary for l_0)   [12.8s]
  ok   (S) r2 secant <X^5,Y^5>, l: x=0, Gamma={X,R0}                      local dim 3 (non-binary for l_0)   [12.8s]
  ok   (S) r2 secant <X^5,Y^5>, l: x=0, Gamma={X,Y}                       local dim 3 (non-binary for l_0)   [12.9s]
  ok   (S) r2 secant <X^5,P^5>, l: x=0, Gamma={X,P}                       local dim 2 (non-binary for l_0)   [13.0s]
  ok   (S) r2 tangent <X^5,X^4Y>, l: x=0, Gamma double at X along Y       local dim 2 (non-binary for l_0)   [13.0s]
  ok   (S) r2 tangent <Y^5,Y^4X>, l: x=0, Gamma={Y,R0}                    local dim 3 (non-binary for l_0)   [13.1s]
  ok   (S) r2 bin-bad <Y^5,Z^5>, l: x=0, Gamma={Y,Z}                      local dim 4 (binary for l_0)   [13.1s]
  ok   (S) r2 bin-bad <Y^5,Z^5>, l: x=0, Gamma={Y,X}                      local dim 4 (binary for l_0)   [13.2s]
  ok   (S) r2 bin-bad tangent <Y^5,Y^4Z>, l: x=0, Gamma double at Y along X local dim 4 (binary for l_0)   [13.2s]
(N) negative control: a random triple of L_def = (W) + I*_4 + m^5 (the best of Corollary S6.2)  [S]
  ok   (S) Gamma={Y,Z}, V=<Y^5,Z^5> (binary, Gamma = Gamma')              random triple: local length 44 (stab N=11), ds 44, >= 42 (= e(L_def) for a GENERAL triple; evidence only)   [34.9s]
  ok   (S) Gamma={Y,X}, V=<X^5,Y^4Z> (non-binary, concise)                random triple: local length 43 (stab N=11), ds 43, >= 42 (= e(L_def) for a GENERAL triple; evidence only)   [50.7s]
126 checks, total time 50.7 s
ALL CHECKS PASSED
