(U1) local bounds e(K_v) <= colength of an explicit triple, at points of weight three
  germ curv1: colength 1, multiplicity 1 (two random elements: 1)
  ok   curv1: multiplicity 1 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   curv1, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      curv1 l4=1 m5 b4=[u, w]: triple of local length 3 (ds) = 3 (stabilization), positive
   => e(K_v) <= 3 for (curv1, l4 = 1, m5)
  germ curv2: colength 2, multiplicity 2 (two random elements: 2)
  ok   curv2: multiplicity 2 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   curv2, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      curv2 l4=1 m5 b4=[u, w]: triple of local length 5 (ds) = 5 (stabilization), positive
   => e(K_v) <= 5 for (curv2, l4 = 1, m5)
  ok   curv2, l4 = 2: representative [w, u^2] has colength 2 and contains b3
  ok      curv2 l4=2 m5 b4=[w, u^2]: triple of local length 6 (ds) = 6 (stabilization), positive
   => e(K_v) <= 6 for (curv2, l4 = 2, m5)
  ok   curv2, l4 = 2: representative [w, u^2] has colength 2 and contains b3
  ok      curv2 l4=2 tan b4=[w, u^2]: triple of local length 6 (ds) = 6 (stabilization), positive
   => e(K_v) <= 6 for (curv2, l4 = 2, tan)
  germ curv3: colength 3, multiplicity 3 (two random elements: 3)
  ok   curv3: multiplicity 3 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   curv3, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      curv3 l4=1 m5 b4=[u, w]: triple of local length 6 (ds) = 6 (stabilization), positive
   => e(K_v) <= 6 for (curv3, l4 = 1, m5)
  ok   curv3, l4 = 2: representative [w, u^2] has colength 2 and contains b3
  ok      curv3 l4=2 m5 b4=[w, u^2]: triple of local length 9 (ds) = 9 (stabilization), positive
   => e(K_v) <= 9 for (curv3, l4 = 2, m5)
  ok   curv3, l4 = 2: representative [w, u^2] has colength 2 and contains b3
  ok      curv3 l4=2 tan b4=[w, u^2]: triple of local length 9 (ds) = 9 (stabilization), positive
   => e(K_v) <= 9 for (curv3, l4 = 2, tan)
  ok   curv3, l4 = 3: representative [w, u^3] has colength 3 and contains b3
  ok      curv3 l4=3 m5 b4=[w, u^3]: triple of local length 9 (ds) = 9 (stabilization), positive
   => e(K_v) <= 9 for (curv3, l4 = 3, m5)
  ok   curv3, l4 = 3: representative [w, u^3] has colength 3 and contains b3
  ok      curv3 l4=3 tan b4=[w, u^3]: triple of local length 9 (ds) = 9 (stabilization), positive
   => e(K_v) <= 9 for (curv3, l4 = 3, tan)
  germ curv4: colength 4, multiplicity 4 (two random elements: 4)
  ok   curv4: multiplicity 4 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   curv4, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      curv4 l4=1 m5 b4=[u, w]: triple of local length 7 (ds) = 7 (stabilization), positive
   => e(K_v) <= 7 for (curv4, l4 = 1, m5)
  ok   curv4, l4 = 2: representative [w, u^2] has colength 2 and contains b3
  ok      curv4 l4=2 m5 b4=[w, u^2]: triple of local length 10 (ds) = 10 (stabilization), positive
   => e(K_v) <= 10 for (curv4, l4 = 2, m5)
  ok   curv4, l4 = 2: representative [w, u^2] has colength 2 and contains b3
  ok      curv4 l4=2 tan b4=[w, u^2]: triple of local length 10 (ds) = 10 (stabilization), positive
   => e(K_v) <= 10 for (curv4, l4 = 2, tan)
  ok   curv4, l4 = 3: representative [w, u^3] has colength 3 and contains b3
  ok      curv4 l4=3 m5 b4=[w, u^3]: triple of local length 11 (ds) = 11 (stabilization), positive
   => e(K_v) <= 11 for (curv4, l4 = 3, m5)
  ok   curv4, l4 = 3: representative [w, u^3] has colength 3 and contains b3
  ok      curv4 l4=3 tan b4=[w, u^3]: triple of local length 12 (ds) = 12 (stabilization), positive
   => e(K_v) <= 12 for (curv4, l4 = 3, tan)
  germ curv5: colength 5, multiplicity 5 (two random elements: 5)
  ok   curv5: multiplicity 5 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   curv5, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      curv5 l4=1 m5 b4=[u, w]: triple of local length 8 (ds) = 8 (stabilization), positive
   => e(K_v) <= 8 for (curv5, l4 = 1, m5)
  ok   curv5, l4 = 2: representative [w, u^2] has colength 2 and contains b3
  ok      curv5 l4=2 m5 b4=[w, u^2]: triple of local length 11 (ds) = 11 (stabilization), positive
   => e(K_v) <= 11 for (curv5, l4 = 2, m5)
  ok   curv5, l4 = 2: representative [w, u^2] has colength 2 and contains b3
  ok      curv5 l4=2 tan b4=[w, u^2]: triple of local length 11 (ds) = 11 (stabilization), positive
   => e(K_v) <= 11 for (curv5, l4 = 2, tan)
  ok   curv5, l4 = 3: representative [w, u^3] has colength 3 and contains b3
  ok      curv5 l4=3 m5 b4=[w, u^3]: triple of local length 13 (ds) = 13 (stabilization), positive
   => e(K_v) <= 13 for (curv5, l4 = 3, m5)
  ok   curv5, l4 = 3: representative [w, u^3] has colength 3 and contains b3
  ok      curv5 l4=3 tan b4=[w, u^3]: triple of local length 14 (ds) = 14 (stabilization), positive
   => e(K_v) <= 14 for (curv5, l4 = 3, tan)
  germ fat3: colength 3, multiplicity 4 (two random elements: 4)
  ok   fat3: multiplicity 4 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   fat3, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      fat3 l4=1 m5 b4=[u, w]: triple of local length 9 (ds) = 9 (stabilization), positive
   => e(K_v) <= 9 for (fat3, l4 = 1, m5)
  ok   fat3, l4 = 2: representative [w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      fat3 l4=2 m5 b4=[w, u^2, u*w, w^2]: triple of local length 10 (ds) = 10 (stabilization), positive
   => e(K_v) <= 10 for (fat3, l4 = 2, m5)
  ok   fat3, l4 = 2: representative [w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      fat3 l4=2 tan b4=[w, u^2, u*w, w^2]: triple of local length 10 (ds) = 10 (stabilization), positive
   => e(K_v) <= 10 for (fat3, l4 = 2, tan)
  ok   fat3, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      fat3 l4=3 m5 b4=[u^2, u*w, w^2]: triple of local length 12 (ds) = 12 (stabilization), positive
   => e(K_v) <= 12 for (fat3, l4 = 3, m5)
  ok   fat3, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      fat3 l4=3 tan b4=[u^2, u*w, w^2]: triple of local length 12 (ds) = 12 (stabilization), positive
   => e(K_v) <= 12 for (fat3, l4 = 3, tan)
  germ CI4: colength 4, multiplicity 4 (two random elements: 4)
  ok   CI4: multiplicity 4 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   CI4, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      CI4 l4=1 m5 b4=[u, w]: triple of local length 9 (ds) = 9 (stabilization), positive
   => e(K_v) <= 9 for (CI4, l4 = 1, m5)
  ok   CI4, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      CI4 l4=2 m5 b4=[u, u^2, u*w, w^2]: triple of local length 10 (ds) = 10 (stabilization), positive
  ok   CI4, l4 = 2: representative [u + w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      CI4 l4=2 m5 b4=[u + w, u^2, u*w, w^2]: triple of local length 10 (ds) = 10 (stabilization), positive
   => e(K_v) <= 10 for (CI4, l4 = 2, m5)
  ok   CI4, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      CI4 l4=2 tan b4=[u, u^2, u*w, w^2]: triple of local length 10 (ds) = 10 (stabilization), positive
  ok   CI4, l4 = 2: representative [u + w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      CI4 l4=2 tan b4=[u + w, u^2, u*w, w^2]: triple of local length 10 (ds) = 10 (stabilization), positive
   => e(K_v) <= 10 for (CI4, l4 = 2, tan)
  ok   CI4, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      CI4 l4=3 m5 b4=[u^2, u*w, w^2]: triple of local length 12 (ds) = 12 (stabilization), positive
   => e(K_v) <= 12 for (CI4, l4 = 3, m5)
  ok   CI4, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      CI4 l4=3 tan b4=[u^2, u*w, w^2]: triple of local length 12 (ds) = 12 (stabilization), positive
   => e(K_v) <= 12 for (CI4, l4 = 3, tan)
  germ nG4: colength 4, multiplicity 5 (two random elements: 5)
  ok   nG4: multiplicity 5 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   nG4, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      nG4 l4=1 m5 b4=[u, w]: triple of local length 10 (ds) = 10 (stabilization), positive
   => e(K_v) <= 10 for (nG4, l4 = 1, m5)
  ok   nG4, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      nG4 l4=2 m5 b4=[u, u^2, u*w, w^2]: triple of local length 14 (ds) = 14 (stabilization), positive
  ok   nG4, l4 = 2: representative [w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      nG4 l4=2 m5 b4=[w, u^2, u*w, w^2]: triple of local length 11 (ds) = 11 (stabilization), positive
   => e(K_v) <= 14 for (nG4, l4 = 2, m5)
  ok   nG4, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      nG4 l4=2 tan b4=[u, u^2, u*w, w^2]: triple of local length 14 (ds) = 14 (stabilization), positive
  ok   nG4, l4 = 2: representative [w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      nG4 l4=2 tan b4=[w, u^2, u*w, w^2]: triple of local length 11 (ds) = 11 (stabilization), positive
   => e(K_v) <= 14 for (nG4, l4 = 2, tan)
  ok   nG4, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      nG4 l4=3 m5 b4=[u^2, u*w, w^2]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   nG4, l4 = 3: representative [u, w^3] has colength 3 and contains b3
  ok      nG4 l4=3 m5 b4=[u, w^3]: triple of local length 14 (ds) = 14 (stabilization), positive
  ok   nG4, l4 = 3: representative [w^2 + u, w^3] has colength 3 and contains b3
  ok      nG4 l4=3 m5 b4=[w^2 + u, w^3]: triple of local length 14 (ds) = 14 (stabilization), positive
   => e(K_v) <= 15 for (nG4, l4 = 3, m5)
  ok   nG4, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      nG4 l4=3 tan b4=[u^2, u*w, w^2]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   nG4, l4 = 3: representative [u, w^3] has colength 3 and contains b3
  ok      nG4 l4=3 tan b4=[u, w^3]: triple of local length 14 (ds) = 14 (stabilization), positive
  ok   nG4, l4 = 3: representative [w^2 + u, w^3] has colength 3 and contains b3
  ok      nG4 l4=3 tan b4=[w^2 + u, w^3]: triple of local length 14 (ds) = 14 (stabilization), positive
   => e(K_v) <= 15 for (nG4, l4 = 3, tan)
  germ L5a: colength 5, multiplicity 6 (two random elements: 6)
  ok   L5a: multiplicity 6 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   L5a, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      L5a l4=1 m5 b4=[u, w]: triple of local length 11 (ds) = 11 (stabilization), positive
   => e(K_v) <= 11 for (L5a, l4 = 1, m5)
  ok   L5a, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5a l4=2 m5 b4=[u, u^2, u*w, w^2]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   L5a, l4 = 2: representative [u + w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5a l4=2 m5 b4=[u + w, u^2, u*w, w^2]: triple of local length 12 (ds) = 12 (stabilization), positive
   => e(K_v) <= 15 for (L5a, l4 = 2, m5)
  ok   L5a, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5a l4=2 tan b4=[u, u^2, u*w, w^2]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   L5a, l4 = 2: representative [u + w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5a l4=2 tan b4=[u + w, u^2, u*w, w^2]: triple of local length 12 (ds) = 12 (stabilization), positive
   => e(K_v) <= 15 for (L5a, l4 = 2, tan)
  ok   L5a, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      L5a l4=3 m5 b4=[u^2, u*w, w^2]: triple of local length 18 (ds) = 18 (stabilization), positive
  ok   L5a, l4 = 3: representative [u, w^3] has colength 3 and contains b3
  ok      L5a l4=3 m5 b4=[u, w^3]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   L5a, l4 = 3: representative [w^2 + u, w^3] has colength 3 and contains b3
  ok      L5a l4=3 m5 b4=[w^2 + u, w^3]: triple of local length 15 (ds) = 15 (stabilization), positive
   => e(K_v) <= 18 for (L5a, l4 = 3, m5)
  ok   L5a, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      L5a l4=3 tan b4=[u^2, u*w, w^2]: triple of local length 18 (ds) = 18 (stabilization), positive
  ok   L5a, l4 = 3: representative [u, w^3] has colength 3 and contains b3
  ok      L5a l4=3 tan b4=[u, w^3]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   L5a, l4 = 3: representative [w^2 + u, w^3] has colength 3 and contains b3
  ok      L5a l4=3 tan b4=[w^2 + u, w^3]: triple of local length 15 (ds) = 15 (stabilization), positive
   => e(K_v) <= 18 for (L5a, l4 = 3, tan)
  germ L5b: colength 5, multiplicity 6 (two random elements: 6)
  ok   L5b: multiplicity 6 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   L5b, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      L5b l4=1 m5 b4=[u, w]: triple of local length 11 (ds) = 11 (stabilization), positive
   => e(K_v) <= 11 for (L5b, l4 = 1, m5)
  ok   L5b, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5b l4=2 m5 b4=[u, u^2, u*w, w^2]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   L5b, l4 = 2: representative [w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5b l4=2 m5 b4=[w, u^2, u*w, w^2]: triple of local length 12 (ds) = 12 (stabilization), positive
   => e(K_v) <= 15 for (L5b, l4 = 2, m5)
  ok   L5b, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5b l4=2 tan b4=[u, u^2, u*w, w^2]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   L5b, l4 = 2: representative [w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5b l4=2 tan b4=[w, u^2, u*w, w^2]: triple of local length 12 (ds) = 12 (stabilization), positive
   => e(K_v) <= 15 for (L5b, l4 = 2, tan)
  ok   L5b, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      L5b l4=3 m5 b4=[u^2, u*w, w^2]: triple of local length 18 (ds) = 18 (stabilization), positive
  ok   L5b, l4 = 3: representative [u, w^3] has colength 3 and contains b3
  ok      L5b l4=3 m5 b4=[u, w^3]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   L5b, l4 = 3: representative [w^2 + u, w^3] has colength 3 and contains b3
  ok      L5b l4=3 m5 b4=[w^2 + u, w^3]: triple of local length 15 (ds) = 15 (stabilization), positive
   => e(K_v) <= 18 for (L5b, l4 = 3, m5)
  ok   L5b, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      L5b l4=3 tan b4=[u^2, u*w, w^2]: triple of local length 18 (ds) = 18 (stabilization), positive
  ok   L5b, l4 = 3: representative [u, w^3] has colength 3 and contains b3
  ok      L5b l4=3 tan b4=[u, w^3]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   L5b, l4 = 3: representative [w^2 + u, w^3] has colength 3 and contains b3
  ok      L5b l4=3 tan b4=[w^2 + u, w^3]: triple of local length 15 (ds) = 15 (stabilization), positive
   => e(K_v) <= 18 for (L5b, l4 = 3, tan)
  germ L5c: colength 5, multiplicity 6 (two random elements: 6)
  ok   L5c: multiplicity 6 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   L5c, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      L5c l4=1 m5 b4=[u, w]: triple of local length 11 (ds) = 11 (stabilization), positive
   => e(K_v) <= 11 for (L5c, l4 = 1, m5)
  ok   L5c, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5c l4=2 m5 b4=[u, u^2, u*w, w^2]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   L5c, l4 = 2: representative [w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5c l4=2 m5 b4=[w, u^2, u*w, w^2]: triple of local length 12 (ds) = 12 (stabilization), positive
   => e(K_v) <= 15 for (L5c, l4 = 2, m5)
  ok   L5c, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5c l4=2 tan b4=[u, u^2, u*w, w^2]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   L5c, l4 = 2: representative [w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      L5c l4=2 tan b4=[w, u^2, u*w, w^2]: triple of local length 12 (ds) = 12 (stabilization), positive
   => e(K_v) <= 15 for (L5c, l4 = 2, tan)
  ok   L5c, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      L5c l4=3 m5 b4=[u^2, u*w, w^2]: triple of local length 16 (ds) = 16 (stabilization), positive
  ok   L5c, l4 = 3: representative [u, w^3] has colength 3 and contains b3
  ok      L5c l4=3 m5 b4=[u, w^3]: triple of local length 16 (ds) = 16 (stabilization), positive
  ok   L5c, l4 = 3: representative [w^2 + u, w^3] has colength 3 and contains b3
  ok      L5c l4=3 m5 b4=[w^2 + u, w^3]: triple of local length 15 (ds) = 15 (stabilization), positive
   => e(K_v) <= 16 for (L5c, l4 = 3, m5)
  ok   L5c, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      L5c l4=3 tan b4=[u^2, u*w, w^2]: triple of local length 16 (ds) = 16 (stabilization), positive
  ok   L5c, l4 = 3: representative [u, w^3] has colength 3 and contains b3
  ok      L5c l4=3 tan b4=[u, w^3]: triple of local length 17 (ds) = 17 (stabilization), positive
  ok   L5c, l4 = 3: representative [w^2 + u, w^3] has colength 3 and contains b3
  ok      L5c l4=3 tan b4=[w^2 + u, w^3]: triple of local length 15 (ds) = 15 (stabilization), positive
   => e(K_v) <= 17 for (L5c, l4 = 3, tan)
  germ G5: colength 5, multiplicity 5 (two random elements: 5)
  ok   G5: multiplicity 5 (upper bound by two elements, information: equals for the CI/curvilinear/monomial germs)
  ok   G5, l4 = 1: representative [u, w] has colength 1 and contains b3
  ok      G5 l4=1 m5 b4=[u, w]: triple of local length 10 (ds) = 10 (stabilization), positive
   => e(K_v) <= 10 for (G5, l4 = 1, m5)
  ok   G5, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      G5 l4=2 m5 b4=[u, u^2, u*w, w^2]: triple of local length 14 (ds) = 14 (stabilization), positive
  ok   G5, l4 = 2: representative [w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      G5 l4=2 m5 b4=[w, u^2, u*w, w^2]: triple of local length 11 (ds) = 11 (stabilization), positive
  ok   G5, l4 = 2: representative [u + w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      G5 l4=2 m5 b4=[u + w, u^2, u*w, w^2]: triple of local length 11 (ds) = 11 (stabilization), positive
   => e(K_v) <= 14 for (G5, l4 = 2, m5)
  ok   G5, l4 = 2: representative [u, u^2, u*w, w^2] has colength 2 and contains b3
  ok      G5 l4=2 tan b4=[u, u^2, u*w, w^2]: triple of local length 14 (ds) = 14 (stabilization), positive
  ok   G5, l4 = 2: representative [w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      G5 l4=2 tan b4=[w, u^2, u*w, w^2]: triple of local length 11 (ds) = 11 (stabilization), positive
  ok   G5, l4 = 2: representative [u + w, u^2, u*w, w^2] has colength 2 and contains b3
  ok      G5 l4=2 tan b4=[u + w, u^2, u*w, w^2]: triple of local length 11 (ds) = 11 (stabilization), positive
   => e(K_v) <= 14 for (G5, l4 = 2, tan)
  ok   G5, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      G5 l4=3 m5 b4=[u^2, u*w, w^2]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   G5, l4 = 3: representative [u, w^3] has colength 3 and contains b3
  ok      G5 l4=3 m5 b4=[u, w^3]: triple of local length 14 (ds) = 14 (stabilization), positive
  ok   G5, l4 = 3: representative [w^2 + u, w^3] has colength 3 and contains b3
  ok      G5 l4=3 m5 b4=[w^2 + u, w^3]: triple of local length 14 (ds) = 14 (stabilization), positive
   => e(K_v) <= 15 for (G5, l4 = 3, m5)
  ok   G5, l4 = 3: representative [u^2, u*w, w^2] has colength 3 and contains b3
  ok      G5 l4=3 tan b4=[u^2, u*w, w^2]: triple of local length 15 (ds) = 15 (stabilization), positive
  ok   G5, l4 = 3: representative [u, w^3] has colength 3 and contains b3
  ok      G5 l4=3 tan b4=[u, w^3]: triple of local length 14 (ds) = 14 (stabilization), positive
  ok   G5, l4 = 3: representative [w^2 + u, w^3] has colength 3 and contains b3
  ok      G5 l4=3 tan b4=[w^2 + u, w^3]: triple of local length 14 (ds) = 14 (stabilization), positive
   => e(K_v) <= 15 for (G5, l4 = 3, tan)
(U2) global count (WM(b), s = 6): 27 + sum over weight-three points + sum over other points
  configurations examined: 157
  P2: bound > 41 in 10 configurations:
     45  germs ('L5b',), l4 (3,), other points (len, e) (), l(B) = 5
     45  germs ('L5a',), l4 (3,), other points (len, e) (), l(B) = 5
     43  germs ('nG4',), l4 (3,), other points (len, e) ((1, 1),), l(B) = 5
     43  germs ('nG4',), l4 (2,), other points (len, e) ((1, 1),), l(B) = 5
     43  germs ('L5c',), l4 (3,), other points (len, e) (), l(B) = 5
     42  germs ('nG4',), l4 (3,), other points (len, e) (), l(B) = 4
     42  germs ('L5c',), l4 (2,), other points (len, e) (), l(B) = 5
     42  germs ('L5b',), l4 (2,), other points (len, e) (), l(B) = 5
     42  germs ('L5a',), l4 (2,), other points (len, e) (), l(B) = 5
     42  germs ('G5',), l4 (3,), other points (len, e) (), l(B) = 5
  secant: bound > 41 in 6 configurations:
     44  germs ('nG4', 'curv1'), l4 (2, 1), other points (len, e) (), l(B) = 5
     44  germs ('curv1', 'nG4'), l4 (1, 2), other points (len, e) (), l(B) = 5
     42  germs ('fat3', 'curv2'), l4 (2, 1), other points (len, e) (), l(B) = 5
     42  germs ('fat3', 'curv2'), l4 (1, 2), other points (len, e) (), l(B) = 5
     42  germs ('curv2', 'fat3'), l4 (2, 1), other points (len, e) (), l(B) = 5
     42  germs ('curv2', 'fat3'), l4 (1, 2), other points (len, e) (), l(B) = 5
  tangent: bound > 41 in 10 configurations:
     45  germs ('L5b',), l4 (3,), other points (len, e) (), l(B) = 5
     45  germs ('L5a',), l4 (3,), other points (len, e) (), l(B) = 5
     44  germs ('L5c',), l4 (3,), other points (len, e) (), l(B) = 5
     43  germs ('nG4',), l4 (3,), other points (len, e) ((1, 1),), l(B) = 5
     43  germs ('nG4',), l4 (2,), other points (len, e) ((1, 1),), l(B) = 5
     42  germs ('nG4',), l4 (3,), other points (len, e) (), l(B) = 4
     42  germs ('L5c',), l4 (2,), other points (len, e) (), l(B) = 5
     42  germs ('L5b',), l4 (2,), other points (len, e) (), l(B) = 5
     42  germs ('L5a',), l4 (2,), other points (len, e) (), l(B) = 5
     42  germs ('G5',), l4 (3,), other points (len, e) (), l(B) = 5
  ok   every configuration with bound > 41 has a non-curvilinear germ at a point of weight three
  ok   every configuration with bound > 41 has l(B) >= 4 and a germ of multiplicity >= 4 at a point of weight three
(U3) the list of all configurations of (U2), with the local values at the points of weight three (from (U1)) and the bound
   columns: label, germs at the points of weight three, l4 there, other points (length, e), l(B), sum e, local values (U1),
   contribution of the other points, bound 27 + local + others; in each sector sorted by decreasing bound as in (U2)
  sector P2: 57 configurations
   P2-1  germs L5b  l4 3  other -  l(B) 5  sum e 6  local 18  others 0  bound 45  (> 41)
   P2-2  germs L5a  l4 3  other -  l(B) 5  sum e 6  local 18  others 0  bound 45  (> 41)
   P2-3  germs nG4  l4 3  other [(1, 1)]  l(B) 5  sum e 6  local 15  others 1  bound 43  (> 41)
   P2-4  germs nG4  l4 2  other [(1, 1)]  l(B) 5  sum e 6  local 14  others 2  bound 43  (> 41)
   P2-5  germs L5c  l4 3  other -  l(B) 5  sum e 6  local 16  others 0  bound 43  (> 41)
   P2-6  germs nG4  l4 3  other -  l(B) 4  sum e 5  local 15  others 0  bound 42  (> 41)
   P2-7  germs L5c  l4 2  other -  l(B) 5  sum e 6  local 15  others 0  bound 42  (> 41)
   P2-8  germs L5b  l4 2  other -  l(B) 5  sum e 6  local 15  others 0  bound 42  (> 41)
   P2-9  germs L5a  l4 2  other -  l(B) 5  sum e 6  local 15  others 0  bound 42  (> 41)
   P2-10  germs G5  l4 3  other -  l(B) 5  sum e 5  local 15  others 0  bound 42  (> 41)
   P2-11  germs nG4  l4 2  other -  l(B) 4  sum e 5  local 14  others 0  bound 41
   P2-12  germs fat3  l4 3  other [(2, 2)]  l(B) 5  sum e 6  local 12  others 2  bound 41
   P2-13  germs fat3  l4 3  other [(1, 1), (1, 1)]  l(B) 5  sum e 6  local 12  others 2  bound 41
   P2-14  germs fat3  l4 2  other [(2, 2)]  l(B) 5  sum e 6  local 10  others 4  bound 41
   P2-15  germs G5  l4 2  other -  l(B) 5  sum e 5  local 14  others 0  bound 41
   P2-16  germs fat3  l4 3  other [(1, 1)]  l(B) 4  sum e 5  local 12  others 1  bound 40
   P2-17  germs fat3  l4 2  other [(1, 1), (1, 1)]  l(B) 5  sum e 6  local 10  others 3  bound 40
   P2-18  germs fat3  l4 1  other [(2, 2)]  l(B) 5  sum e 6  local 9  others 4  bound 40
   P2-19  germs fat3  l4 1  other [(1, 1), (1, 1)]  l(B) 5  sum e 6  local 9  others 4  bound 40
   P2-20  germs curv5  l4 3  other -  l(B) 5  sum e 5  local 13  others 0  bound 40
   P2-21  germs curv3  l4 2  other [(2, 2)]  l(B) 5  sum e 5  local 9  others 4  bound 40
   P2-22  germs CI4  l4 3  other [(1, 1)]  l(B) 5  sum e 5  local 12  others 1  bound 40
   P2-23  germs nG4  l4 1  other [(1, 1)]  l(B) 5  sum e 6  local 10  others 2  bound 39
   P2-24  germs fat3  l4 3  other -  l(B) 3  sum e 4  local 12  others 0  bound 39
   P2-25  germs fat3  l4 2  other [(1, 1)]  l(B) 4  sum e 5  local 10  others 2  bound 39
   P2-26  germs curv4  l4 3  other [(1, 1)]  l(B) 5  sum e 5  local 11  others 1  bound 39
   P2-27  germs curv4  l4 2  other [(1, 1)]  l(B) 5  sum e 5  local 10  others 2  bound 39
   P2-28  germs curv3  l4 2  other [(1, 1), (1, 1)]  l(B) 5  sum e 5  local 9  others 3  bound 39
   P2-29  germs CI4  l4 3  other -  l(B) 4  sum e 4  local 12  others 0  bound 39
   P2-30  germs CI4  l4 2  other [(1, 1)]  l(B) 5  sum e 5  local 10  others 2  bound 39
   P2-31  germs fat3  l4 1  other [(1, 1)]  l(B) 4  sum e 5  local 9  others 2  bound 38
   P2-32  germs curv5  l4 2  other -  l(B) 5  sum e 5  local 11  others 0  bound 38
   P2-33  germs curv4  l4 3  other -  l(B) 4  sum e 4  local 11  others 0  bound 38
   P2-34  germs curv3  l4 3  other [(2, 2)]  l(B) 5  sum e 5  local 9  others 2  bound 38
   P2-35  germs curv3  l4 3  other [(1, 1), (1, 1)]  l(B) 5  sum e 5  local 9  others 2  bound 38
   P2-36  germs curv3  l4 2  other [(1, 1)]  l(B) 4  sum e 4  local 9  others 2  bound 38
   P2-37  germs L5c  l4 1  other -  l(B) 5  sum e 6  local 11  others 0  bound 38
   P2-38  germs L5b  l4 1  other -  l(B) 5  sum e 6  local 11  others 0  bound 38
   P2-39  germs L5a  l4 1  other -  l(B) 5  sum e 6  local 11  others 0  bound 38
   P2-40  germs CI4  l4 1  other [(1, 1)]  l(B) 5  sum e 5  local 9  others 2  bound 38
   P2-41  germs nG4  l4 1  other -  l(B) 4  sum e 5  local 10  others 0  bound 37
   P2-42  germs fat3  l4 2  other -  l(B) 3  sum e 4  local 10  others 0  bound 37
   P2-43  germs curv4  l4 2  other -  l(B) 4  sum e 4  local 10  others 0  bound 37
   P2-44  germs curv3  l4 3  other [(1, 1)]  l(B) 4  sum e 4  local 9  others 1  bound 37
   P2-45  germs curv3  l4 1  other [(2, 2)]  l(B) 5  sum e 5  local 6  others 4  bound 37
   P2-46  germs curv3  l4 1  other [(1, 1), (1, 1)]  l(B) 5  sum e 5  local 6  others 4  bound 37
   P2-47  germs G5  l4 1  other -  l(B) 5  sum e 5  local 10  others 0  bound 37
   P2-48  germs CI4  l4 2  other -  l(B) 4  sum e 4  local 10  others 0  bound 37
   P2-49  germs fat3  l4 1  other -  l(B) 3  sum e 4  local 9  others 0  bound 36
   P2-50  germs curv4  l4 1  other [(1, 1)]  l(B) 5  sum e 5  local 7  others 2  bound 36
   P2-51  germs curv3  l4 3  other -  l(B) 3  sum e 3  local 9  others 0  bound 36
   P2-52  germs curv3  l4 2  other -  l(B) 3  sum e 3  local 9  others 0  bound 36
   P2-53  germs CI4  l4 1  other -  l(B) 4  sum e 4  local 9  others 0  bound 36
   P2-54  germs curv5  l4 1  other -  l(B) 5  sum e 5  local 8  others 0  bound 35
   P2-55  germs curv3  l4 1  other [(1, 1)]  l(B) 4  sum e 4  local 6  others 2  bound 35
   P2-56  germs curv4  l4 1  other -  l(B) 4  sum e 4  local 7  others 0  bound 34
   P2-57  germs curv3  l4 1  other -  l(B) 3  sum e 3  local 6  others 0  bound 33
  ok   P2: the configurations with bound > 41 in this list are exactly those of (U2) (10)
  sector secant: 62 configurations
   S-1  germs nG4,curv1  l4 2,1  other -  l(B) 5  sum e 6  local 14+3  others 0  bound 44  (> 41)
   S-2  germs curv1,nG4  l4 1,2  other -  l(B) 5  sum e 6  local 3+14  others 0  bound 44  (> 41)
   S-3  germs fat3,curv2  l4 2,1  other -  l(B) 5  sum e 6  local 10+5  others 0  bound 42  (> 41)
   S-4  germs fat3,curv2  l4 1,2  other -  l(B) 5  sum e 6  local 9+6  others 0  bound 42  (> 41)
   S-5  germs curv2,fat3  l4 2,1  other -  l(B) 5  sum e 6  local 6+9  others 0  bound 42  (> 41)
   S-6  germs curv2,fat3  l4 1,2  other -  l(B) 5  sum e 6  local 5+10  others 0  bound 42  (> 41)
   S-7  germs fat3,curv2  l4 1,1  other -  l(B) 5  sum e 6  local 9+5  others 0  bound 41
   S-8  germs fat3,curv1  l4 2,1  other [(1, 1)]  l(B) 5  sum e 6  local 10+3  others 1  bound 41
   S-9  germs fat3,curv1  l4 1,1  other [(1, 1)]  l(B) 5  sum e 6  local 9+3  others 2  bound 41
   S-10  germs curv3,curv2  l4 2,1  other -  l(B) 5  sum e 5  local 9+5  others 0  bound 41
   S-11  germs curv2,fat3  l4 1,1  other -  l(B) 5  sum e 6  local 5+9  others 0  bound 41
   S-12  germs curv2,curv3  l4 1,2  other -  l(B) 5  sum e 5  local 5+9  others 0  bound 41
   S-13  germs curv1,fat3  l4 1,2  other [(1, 1)]  l(B) 5  sum e 6  local 3+10  others 1  bound 41
   S-14  germs curv1,fat3  l4 1,1  other [(1, 1)]  l(B) 5  sum e 6  local 3+9  others 2  bound 41
   S-15  germs nG4,curv1  l4 1,1  other -  l(B) 5  sum e 6  local 10+3  others 0  bound 40
   S-16  germs fat3,curv1  l4 2,1  other -  l(B) 4  sum e 5  local 10+3  others 0  bound 40
   S-17  germs curv4,curv1  l4 2,1  other -  l(B) 5  sum e 5  local 10+3  others 0  bound 40
   S-18  germs curv3,curv1  l4 2,1  other [(1, 1)]  l(B) 5  sum e 5  local 9+3  others 1  bound 40
   S-19  germs curv1,nG4  l4 1,1  other -  l(B) 5  sum e 6  local 3+10  others 0  bound 40
   S-20  germs curv1,fat3  l4 1,2  other -  l(B) 4  sum e 5  local 3+10  others 0  bound 40
   S-21  germs curv1,curv4  l4 1,2  other -  l(B) 5  sum e 5  local 3+10  others 0  bound 40
   S-22  germs curv1,curv3  l4 1,2  other [(1, 1)]  l(B) 5  sum e 5  local 3+9  others 1  bound 40
   S-23  germs curv1,CI4  l4 1,2  other -  l(B) 5  sum e 5  local 3+10  others 0  bound 40
   S-24  germs CI4,curv1  l4 2,1  other -  l(B) 5  sum e 5  local 10+3  others 0  bound 40
   S-25  germs fat3,curv1  l4 1,1  other -  l(B) 4  sum e 5  local 9+3  others 0  bound 39
   S-26  germs curv3,curv2  l4 1,2  other -  l(B) 5  sum e 5  local 6+6  others 0  bound 39
   S-27  germs curv3,curv1  l4 2,1  other -  l(B) 4  sum e 4  local 9+3  others 0  bound 39
   S-28  germs curv2,curv3  l4 2,1  other -  l(B) 5  sum e 5  local 6+6  others 0  bound 39
   S-29  germs curv2,curv2  l4 2,1  other [(1, 1)]  l(B) 5  sum e 5  local 6+5  others 1  bound 39
   S-30  germs curv2,curv2  l4 1,2  other [(1, 1)]  l(B) 5  sum e 5  local 5+6  others 1  bound 39
   S-31  germs curv2,curv2  l4 1,1  other [(1, 1)]  l(B) 5  sum e 5  local 5+5  others 2  bound 39
   S-32  germs curv2,curv1  l4 1,1  other [(2, 2)]  l(B) 5  sum e 5  local 5+3  others 4  bound 39
   S-33  germs curv1,fat3  l4 1,1  other -  l(B) 4  sum e 5  local 3+9  others 0  bound 39
   S-34  germs curv1,curv3  l4 1,2  other -  l(B) 4  sum e 4  local 3+9  others 0  bound 39
   S-35  germs curv1,curv2  l4 1,1  other [(2, 2)]  l(B) 5  sum e 5  local 3+5  others 4  bound 39
   S-36  germs curv1,CI4  l4 1,1  other -  l(B) 5  sum e 5  local 3+9  others 0  bound 39
   S-37  germs CI4,curv1  l4 1,1  other -  l(B) 5  sum e 5  local 9+3  others 0  bound 39
   S-38  germs curv3,curv2  l4 1,1  other -  l(B) 5  sum e 5  local 6+5  others 0  bound 38
   S-39  germs curv3,curv1  l4 1,1  other [(1, 1)]  l(B) 5  sum e 5  local 6+3  others 2  bound 38
   S-40  germs curv2,curv3  l4 1,1  other -  l(B) 5  sum e 5  local 5+6  others 0  bound 38
   S-41  germs curv2,curv2  l4 2,1  other -  l(B) 4  sum e 4  local 6+5  others 0  bound 38
   S-42  germs curv2,curv2  l4 1,2  other -  l(B) 4  sum e 4  local 5+6  others 0  bound 38
   S-43  germs curv2,curv1  l4 2,1  other [(2, 2)]  l(B) 5  sum e 5  local 6+3  others 2  bound 38
   S-44  germs curv2,curv1  l4 2,1  other [(1, 1), (1, 1)]  l(B) 5  sum e 5  local 6+3  others 2  bound 38
   S-45  germs curv2,curv1  l4 1,1  other [(1, 1), (1, 1)]  l(B) 5  sum e 5  local 5+3  others 3  bound 38
   S-46  germs curv1,curv3  l4 1,1  other [(1, 1)]  l(B) 5  sum e 5  local 3+6  others 2  bound 38
   S-47  germs curv1,curv2  l4 1,2  other [(2, 2)]  l(B) 5  sum e 5  local 3+6  others 2  bound 38
   S-48  germs curv1,curv2  l4 1,2  other [(1, 1), (1, 1)]  l(B) 5  sum e 5  local 3+6  others 2  bound 38
   S-49  germs curv1,curv2  l4 1,1  other [(1, 1), (1, 1)]  l(B) 5  sum e 5  local 3+5  others 3  bound 38
   S-50  germs curv4,curv1  l4 1,1  other -  l(B) 5  sum e 5  local 7+3  others 0  bound 37
   S-51  germs curv2,curv2  l4 1,1  other -  l(B) 4  sum e 4  local 5+5  others 0  bound 37
   S-52  germs curv2,curv1  l4 2,1  other [(1, 1)]  l(B) 4  sum e 4  local 6+3  others 1  bound 37
   S-53  germs curv2,curv1  l4 1,1  other [(1, 1)]  l(B) 4  sum e 4  local 5+3  others 2  bound 37
   S-54  germs curv1,curv4  l4 1,1  other -  l(B) 5  sum e 5  local 3+7  others 0  bound 37
   S-55  germs curv1,curv2  l4 1,2  other [(1, 1)]  l(B) 4  sum e 4  local 3+6  others 1  bound 37
   S-56  germs curv1,curv2  l4 1,1  other [(1, 1)]  l(B) 4  sum e 4  local 3+5  others 2  bound 37
   S-57  germs curv3,curv1  l4 1,1  other -  l(B) 4  sum e 4  local 6+3  others 0  bound 36
   S-58  germs curv2,curv1  l4 2,1  other -  l(B) 3  sum e 3  local 6+3  others 0  bound 36
   S-59  germs curv1,curv3  l4 1,1  other -  l(B) 4  sum e 4  local 3+6  others 0  bound 36
   S-60  germs curv1,curv2  l4 1,2  other -  l(B) 3  sum e 3  local 3+6  others 0  bound 36
   S-61  germs curv2,curv1  l4 1,1  other -  l(B) 3  sum e 3  local 5+3  others 0  bound 35
   S-62  germs curv1,curv2  l4 1,1  other -  l(B) 3  sum e 3  local 3+5  others 0  bound 35
  ok   secant: the configurations with bound > 41 in this list are exactly those of (U2) (6)
  sector tangent: 38 configurations
   T-1  germs L5b  l4 3  other -  l(B) 5  sum e 6  local 18  others 0  bound 45  (> 41)
   T-2  germs L5a  l4 3  other -  l(B) 5  sum e 6  local 18  others 0  bound 45  (> 41)
   T-3  germs L5c  l4 3  other -  l(B) 5  sum e 6  local 17  others 0  bound 44  (> 41)
   T-4  germs nG4  l4 3  other [(1, 1)]  l(B) 5  sum e 6  local 15  others 1  bound 43  (> 41)
   T-5  germs nG4  l4 2  other [(1, 1)]  l(B) 5  sum e 6  local 14  others 2  bound 43  (> 41)
   T-6  germs nG4  l4 3  other -  l(B) 4  sum e 5  local 15  others 0  bound 42  (> 41)
   T-7  germs L5c  l4 2  other -  l(B) 5  sum e 6  local 15  others 0  bound 42  (> 41)
   T-8  germs L5b  l4 2  other -  l(B) 5  sum e 6  local 15  others 0  bound 42  (> 41)
   T-9  germs L5a  l4 2  other -  l(B) 5  sum e 6  local 15  others 0  bound 42  (> 41)
   T-10  germs G5  l4 3  other -  l(B) 5  sum e 5  local 15  others 0  bound 42  (> 41)
   T-11  germs nG4  l4 2  other -  l(B) 4  sum e 5  local 14  others 0  bound 41
   T-12  germs fat3  l4 3  other [(2, 2)]  l(B) 5  sum e 6  local 12  others 2  bound 41
   T-13  germs fat3  l4 3  other [(1, 1), (1, 1)]  l(B) 5  sum e 6  local 12  others 2  bound 41
   T-14  germs fat3  l4 2  other [(2, 2)]  l(B) 5  sum e 6  local 10  others 4  bound 41
   T-15  germs curv5  l4 3  other -  l(B) 5  sum e 5  local 14  others 0  bound 41
   T-16  germs G5  l4 2  other -  l(B) 5  sum e 5  local 14  others 0  bound 41
   T-17  germs fat3  l4 3  other [(1, 1)]  l(B) 4  sum e 5  local 12  others 1  bound 40
   T-18  germs fat3  l4 2  other [(1, 1), (1, 1)]  l(B) 5  sum e 6  local 10  others 3  bound 40
   T-19  germs curv4  l4 3  other [(1, 1)]  l(B) 5  sum e 5  local 12  others 1  bound 40
   T-20  germs curv3  l4 2  other [(2, 2)]  l(B) 5  sum e 5  local 9  others 4  bound 40
   T-21  germs CI4  l4 3  other [(1, 1)]  l(B) 5  sum e 5  local 12  others 1  bound 40
   T-22  germs fat3  l4 3  other -  l(B) 3  sum e 4  local 12  others 0  bound 39
   T-23  germs fat3  l4 2  other [(1, 1)]  l(B) 4  sum e 5  local 10  others 2  bound 39
   T-24  germs curv4  l4 3  other -  l(B) 4  sum e 4  local 12  others 0  bound 39
   T-25  germs curv4  l4 2  other [(1, 1)]  l(B) 5  sum e 5  local 10  others 2  bound 39
   T-26  germs curv3  l4 2  other [(1, 1), (1, 1)]  l(B) 5  sum e 5  local 9  others 3  bound 39
   T-27  germs CI4  l4 3  other -  l(B) 4  sum e 4  local 12  others 0  bound 39
   T-28  germs CI4  l4 2  other [(1, 1)]  l(B) 5  sum e 5  local 10  others 2  bound 39
   T-29  germs curv5  l4 2  other -  l(B) 5  sum e 5  local 11  others 0  bound 38
   T-30  germs curv3  l4 3  other [(2, 2)]  l(B) 5  sum e 5  local 9  others 2  bound 38
   T-31  germs curv3  l4 3  other [(1, 1), (1, 1)]  l(B) 5  sum e 5  local 9  others 2  bound 38
   T-32  germs curv3  l4 2  other [(1, 1)]  l(B) 4  sum e 4  local 9  others 2  bound 38
   T-33  germs fat3  l4 2  other -  l(B) 3  sum e 4  local 10  others 0  bound 37
   T-34  germs curv4  l4 2  other -  l(B) 4  sum e 4  local 10  others 0  bound 37
   T-35  germs curv3  l4 3  other [(1, 1)]  l(B) 4  sum e 4  local 9  others 1  bound 37
   T-36  germs CI4  l4 2  other -  l(B) 4  sum e 4  local 10  others 0  bound 37
   T-37  germs curv3  l4 3  other -  l(B) 3  sum e 3  local 9  others 0  bound 36
   T-38  germs curv3  l4 2  other -  l(B) 3  sum e 3  local 9  others 0  bound 36
  ok   tangent: the configurations with bound > 41 in this list are exactly those of (U2) (10)
  ok   (U3) 157 configurations listed (= 157 of (U2)): 131 with bound <= 41 and 26 with bound > 41
(U4) the sub-ideals b4 of colength 2 and 3 between b3 and m for the germs nG4 = (u^2, uw, w^3) and G5 = (uw, u^2 - w^3)
  ok   (U4) nG4: (b3 : m) = b3 + (u, w^2), so the ideals of colength 3 containing b3 are b3 + (s u + t w^2), [s : t] in P^1
  ok   (U4) G5: (b3 : m) = b3 + (w^3) = (u^2, uw, w^3) = nG4 (S/G5 is Gorenstein), so every ideal of colength <= 4 containing G5 contains nG4
  ok   (U4) s != 0: b3 + (u + c w^2) = (u + c w^2, w^3) for every c (c a variable); s = 0: b3 + (w^2) = m^2
  ok   (U4) nG4: u -> c u maps u^2, uw, w^3 to c^2 u^2, c uw, w^3 and u + w^2 to c u + w^2 = c (u + w^2/c); the shears w -> w -+ c u map b3 into b3 and w + c u to w
  ok   (U4) G5: (u, w) -> (t^3 u, t^2 w) maps uw, u^2 - w^3 to t^5 uw, t^6 (u^2 - w^3), u + c w^2 to t^3 (u + c t w^2), and u + c w to t^2 (t u + c w)
   so up to these automorphisms the sub-ideals are the representatives of (U1): colength 3: m^2, (u, w^3), (u + w^2, w^3);
   colength 2: (u) + m^2, (w) + m^2 for nG4 and (u) + m^2, (w) + m^2, (u + w) + m^2 for G5.  For every flag b3 c b4 c b5 with b4 != m^2
   (b5 = m, or b5 = Gamma' containing b4) the triple of (U1) for the representative of (b3, b4) lies in K_v, as b5 contains b4.
   The (U1) values for these germs with b4 != m^2: G5 l4=1 m5 [u, w]: 10; G5 l4=2 m5 [u + w, u^2, u*w, w^2]: 11; G5 l4=2 m5 [u, u^2, u*w, w^2]: 14; G5 l4=2 m5 [w, u^2, u*w, w^2]: 11; G5 l4=2 tan [u + w, u^2, u*w, w^2]: 11; G5 l4=2 tan [u, u^2, u*w, w^2]: 14; G5 l4=2 tan [w, u^2, u*w, w^2]: 11; G5 l4=3 m5 [u, w^3]: 14; G5 l4=3 m5 [w^2 + u, w^3]: 14; G5 l4=3 tan [u, w^3]: 14; G5 l4=3 tan [w^2 + u, w^3]: 14; nG4 l4=1 m5 [u, w]: 10; nG4 l4=2 m5 [u, u^2, u*w, w^2]: 14; nG4 l4=2 m5 [w, u^2, u*w, w^2]: 11; nG4 l4=2 tan [u, u^2, u*w, w^2]: 14; nG4 l4=2 tan [w, u^2, u*w, w^2]: 11; nG4 l4=3 m5 [u, w^3]: 14; nG4 l4=3 m5 [w^2 + u, w^3]: 14; nG4 l4=3 tan [u, w^3]: 14; nG4 l4=3 tan [w^2 + u, w^3]: 14
  ok   (U4) at nG4 and at G5, e(K_v) <= 14 <= 14 for every flag with b4 != m^2 (P2, secant: b5 = m; tangent: b5 = Gamma' containing b4)
ALL CHECKS PASSED
