EXHAUSTIVE |S|=2 N=12: tables=50388 violations=0 tables with V*=C (information-saturated)=17927 max gain/bound=0.7003
EXHAUSTIVE |S|=3 N=8: tables=75582 violations=0 tables with V*=C (information-saturated)=42471 max gain/bound=0.6912
EXHAUSTIVE |S|=4 N=5: tables=15504 violations=0 tables with V*=C (information-saturated)=12336 max gain/bound=0.5761
GARBLING |S|=3->2 N=8: tables=75582 V*(garbled)>V*(full) in 0; strictly smaller in 13208
CONDITIONAL INDEPENDENCE (Y_i ind. of B given A for both i) N=5 m=4: tables=15504 satisfying=4000 violations of V*(A,B)=V*(A) = 0
TERNARY COUNTEREXAMPLE search N=24: Y=0 tables 265 in 23 covariance classes; Y=1 tables 265 in 23 classes
  using the largest classes: sum(a*b*cell | Y=0)=12 (25 tables), sum(a*b*cell | Y=1)=52 (25 tables)
  shared sums of a*b*cell (Y=0, Y=1) = (12, 52): same marginals and same covariance under each y in both laws
  law 1: Y=0 table ((10, 2, 2), (2, 4, 0), (2, 0, 2)), Y=1 table ((0, 2, 2), (2, 4, 0), (2, 0, 12))
  law 2: Y=0 table ((11, 0, 3), (3, 2, 1), (0, 4, 0)), Y=1 table ((0, 4, 0), (1, 2, 3), (3, 0, 11))
  V* law 1 = 69/160 (0.431250); V* law 2 = 2413/4800 (0.502708); |difference| = 0.071458; C = 51/100 (0.5100); no-information base = 3/10
  best additive policy argmax_i[gA(a_i)+gB(b_i)] found over integer scores 0..10 (lower bound on the true best additive value; 5929/5929 distinct orderings): law 1 0.431250, law 2 0.445104
  joint-minus-additive gap (upper bounds, because the additive value is only a lower bound): law 1 <= 0.000000, law 2 <= 0.057604
  sum_i I(Y_i;S): law 1 0.363800 nats, law 2 0.953189 nats (same pairwise correlation, different information)
BINARY EXACT: largest joint-minus-additive gap over all N=10 binary conditional laws (prior 3/10, two i.i.d. candidates): gap=21/100 (0.210000); V*=0.510000, best additive=0.300000
  Y=0 cells {(0, 0): 0, (0, 1): 5, (1, 0): 5, (1, 1): 0}; Y=1 cells {(0, 0): 5, (0, 1): 0, (1, 0): 0, (1, 1): 5}

real	3m26.850s
user	3m26.729s
sys	0m0.014s
