[A] k=2 entries<= 2 size<= 5: spaces=1286 colour-law buckets=818 ordered pairs with equal colour law=2672
   T exists=True  S exists=True : 1286 pairs   first example: (((0, 1),), ((0, 1),))
   T exists=True  S exists=False: 549 pairs   first example: (((0, 1), (0, 1)), ((0, 2),))
   T exists=False S exists=True : 549 pairs   first example: (((0, 2),), ((0, 1), (0, 1)))
   T exists=False S exists=False: 288 pairs   first example: (((0, 1), (0, 1), (2, 0)), ((0, 2), (1, 0), (1, 0)))
[B] k=2 entries<= 3 size<= 4: spaces=3875 colour-law buckets=2774 ordered pairs with equal colour law=7061
   T exists=True  S exists=True : 3875 pairs   first example: (((0, 1),), ((0, 1),))
   T exists=True  S exists=False: 882 pairs   first example: (((0, 1), (0, 1)), ((0, 2),))
   T exists=False S exists=True : 882 pairs   first example: (((0, 2),), ((0, 1), (0, 1)))
   T exists=False S exists=False: 1422 pairs   first example: (((0, 1), (0, 3)), ((0, 2), (0, 2)))
[C] k=3 entries<= 2 size<= 4: spaces=27404 colour-law buckets=24779 ordered pairs with equal colour law=33886
   T exists=True  S exists=True : 27404 pairs   first example: (((0, 0, 1),), ((0, 0, 1),))
   T exists=True  S exists=False: 2674 pairs   first example: (((0, 0, 1), (0, 0, 1)), ((0, 0, 2),))
   T exists=False S exists=True : 2674 pairs   first example: (((0, 0, 2),), ((0, 0, 1), (0, 0, 1)))
   T exists=False S exists=False: 1134 pairs   first example: (((0, 0, 1), (0, 0, 1), (0, 2, 0)), ((0, 0, 2), (0, 1, 0), (0, 1, 0)))
[k=2 different-law check] ordered pairs with equal total but different colour law: 4570; each has some F_t with different integrals => not mutually dominating (Jensen).
3-versus-2 example: sigma=3 points of mass (2,2); eta=2 points of mass (3,3):
   mutual domination (explicit kernels, exact): True True
   T exists: False  S exists: False
2-versus-1 example: sigma=2 points of mass (1,1); eta=1 point of mass (2,2):
   mutual domination (explicit kernels, exact): True True
   T exists: True  S exists: False
ALL ASSERTIONS PASSED
python3 finite_exhaustive.py  16.25s user 0.04s system 99% cpu 16.307 total
