[selftest] small known cases ok
[atoms lemma] n<=8, <= 6 parts: 805 ordered pairs of integer partitions, maps both ways exist iff the multisets coincide; 0.1s
[scipy cross-check] exact simplex agrees with HiGHS on 199 random instances (25 feasible, 174 infeasible)
[block 1] k=2 entries<=2 points<=4: 494 spaces, 80 total-vector groups; 830 ordered pairs with equal colour law (exhaustive) all mutually dominating; 4390 ordered pairs with equal total vector but different colour law (sampled) none mutually dominating, in 1983 of these ordered pairs (U,V) one has U dominating V (one-sided domination); 23.6s
    outcomes among equal-colour-law pairs (T exists, S exists): (True, True): 494, (True, False): 141, (False, True): 141, (False, False): 54
[block 2] k=2 entries<=3 points<=4: 3875 spaces, 168 total-vector groups; 7061 ordered pairs with equal colour law (exhaustive) all mutually dominating; 17996 ordered pairs with equal total vector but different colour law (sampled) none mutually dominating, in 7409 of these ordered pairs (U,V) one has U dominating V (one-sided domination); 97.4s
    outcomes among equal-colour-law pairs (T exists, S exists): (True, True): 3875, (True, False): 882, (False, True): 882, (False, False): 1422
[block 3] k=2 entries<=1 points<=5: 55 spaces, 35 total-vector groups; 55 ordered pairs with equal colour law (exhaustive) all mutually dominating; 48 ordered pairs with equal total vector but different colour law (sampled) none mutually dominating, in 24 of these ordered pairs (U,V) one has U dominating V (one-sided domination); 0.3s
    outcomes among equal-colour-law pairs (T exists, S exists): (True, True): 55
[block 4] k=3 entries<=1 points<=4: 329 spaces, 124 total-vector groups; 329 ordered pairs with equal colour law (exhaustive) all mutually dominating; 1120 ordered pairs with equal total vector but different colour law (sampled) none mutually dominating, in 250 of these ordered pairs (U,V) one has U dominating V (one-sided domination); 3.0s
    outcomes among equal-colour-law pairs (T exists, S exists): (True, True): 329
[block 5] k=3 entries<=2 points<=3: 3653 spaces, 342 total-vector groups; 4073 ordered pairs with equal colour law (exhaustive) all mutually dominating; 23764 ordered pairs with equal total vector but different colour law (sampled) none mutually dominating, in 3503 of these ordered pairs (U,V) one has U dominating V (one-sided domination); 36.4s
    outcomes among equal-colour-law pairs (T exists, S exists): (True, True): 3653, (True, False): 189, (False, True): 189, (False, False): 42
TOTAL outcomes (T exists, S exists): {(True, True): 8406, (True, False): 1212, (False, True): 1212, (False, False): 1518}
ALL ASSERTIONS PASSED; total 161.6s
