# reflect_check.py, mp.dps = 50
  a=1.15 N=8 tau=3: max reflection-law defect over 5 orbits = 1.74e-50
  a=2.5 N=12 tau=5: max reflection-law defect over 5 orbits = 2.04e-45
  a=9 N=16 tau=3: max reflection-law defect over 5 orbits = 6.17e-48
  a=2.5 N=6 tau=1: max reflection-law defect over 5 orbits = 1.22e-49
  a=2.5 N=20 tau=3: max reflection-law defect over 5 orbits = 8.22e-49
# caustic parameters of the exact certificates vs geometric closure solver
  a^2=1.7777778 N=4 tau=1: geometric lam = 0.64, exact = 0.64, diff = 0.0
  a^2=2.6666667 N=8 tau=1: geometric lam = 0.228571428571428571428571428571, exact = 0.228571428571428571428571428571, diff = 4.01e-51
  a^2=1.1851852 N=8 tau=3: geometric lam = 0.914285714285714285714285714286, exact = 0.914285714285714285714285714286, diff = 2.67e-51
  a^2=4.0 N=6 tau=1: geometric lam = 0.444444444444444444444444444444, exact = 0.444444444444444444444444444444, diff = 0.0
# repeated traversal control: 3-periodic listed 4 times (N=12), a=2.5
  M=('0.0', '0.0'): relative spread of A*A_M over 8 phases = 5.72e-50
  M=('0.7', '-0.45'): relative spread of A*A_M over 8 phases = 0.487
0.3 33.40637685028750271352797
1.9 33.40637685028750271352797
