PASS order-feasible pattern counts K=2..7 = 0,1,6,26,98,344 (got [0, 1, 6, 26, 98, 344])
PASS number of normalized vectors for K=4 is 40
PASS K=4 patterns are c=a+b, d=a+b, d=a+c, d=b+c, d=a+b+c, a+d=b+c (got ['a+d=b+c', 'c=a+b', 'd=a+b', 'd=a+b+c', 'd=a+c', 'd=b+c'])
PASS every order-feasible pattern is realized by explicit 0 < x_1 < ... < x_K (K <= 7)
PASS {1..6} has no dissociated 4-subset
PASS each 4-subset of {1..6} contains one of the six listed triples or is {3,4,5,6}
PASS the listed triples carry 3=1+2,4=1+3,5=1+4,5=2+3,6=1+5,6=2+4 and 3+6=4+5
PASS {3,5,6,7} dissociated with sums [0, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 21]
PASS each of the 15 four-subsets of {1,2,3,a,a+1,a+3} carries a relation that is an identity in a
PASS covering argument of the proof of Prop. 3.1(b) (4 triples, 3 quadruples)
PASS the relations b=1+a, c=3+a, c=2+b, c=1+2+a, 1+c=3+b, 2+b=3+a are identities
PASS sample members a in ['4', '7/2', '13/4', '10', '1000/7', '301/100']: six distinct numbers, no dissociated 4-subset
PASS a = 4 gives {1,2,3,4,5,7}
PASS {0,+-1,...,+-6}: 13 numbers, no dissociated 4-subset
PASS {0,+-1,+-2,+-3}: 7 numbers, no dissociated triple
PASS A*: 1287 five-subsets, none dissociated
PASS A* has a dissociated 4-subset ({1,2,4,8})
PASS {0} u A* u (-A*): 27 numbers, no dissociated 5-subset
PASS S24: 134596 six-subsets, none dissociated
PASS u_1..u_6 = 1,2,4,7,13,24 (direct search over intervals; got [1, 2, 4, 7, 13, 24])
PASS {3,6,11,12,13} and {11,17,20,22,23,24} dissociated
PASS {1,2,4} and {3,5,6,7} are maximal dissociated in {1..7} (sizes 3 and 4)
PASS g(1..4) = 1,3,7,13
PASS f(n), n=1..27 = 0,1,1,2,2,2,2, 3 x6, 4 x14 (got [0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4])
PASS f(n) in {4,5} for 28 <= n <= 49
PASS f(n) >= floor(log2 n) for n <= 31; equality on n <= 27 exactly for n <= 13 and 16..27
PASS n = 32 is the first n <= 49 with floor(log2 n) > the proved lower bound
PASS Table 1 columns 2^(K-1)-1 and (3^(K-1)-1)/2: [(1, 0, 0), (2, 1, 1), (3, 3, 4), (4, 7, 13), (5, 15, 40), (6, 31, 121)]
PASS f+(m), m=1..13 = 1,2,2,3,3,3,4,...,4 (got [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4])
PASS f(n) = f+(floor(n/2)) for n = 1..27
PASS f(13) = 3 while f+(13) = 4
PASS floor(log2(2m)) = floor(log2(2m+1)) = floor(log2 m)+1 for m = 1..10^5
PASS (3^(K-1)-1)/2 <= 2^K - 1 exactly for K <= 4 (K = 1..10)
PASS floor(log3(n-1))+1 >= floor(log3 n) and 3^(K-1) <= n-1 for K = floor(log3(n-1))+1, n = 2..10^5
PASS F_2^3: dissociated = independent (dim = rank) and |P| <= 2^dim P - 1 for all 127 sets, equality for all of F_2^3 minus 0
PASS example: relations give p7 = 3(p1+p2)+p5 and the case gives p4 = 2(p1+p2)+p5
PASS every 8-subset of {-8..8} has a dissociated triple (consistent with g(3) = 7)
PASS every 14-subset of {-8..8} has a dissociated 4-subset (consistent with g(4) = 13)
TOTAL: ALL PASS
