phi_1({0,1,2}) = 1/4  phi_2({0,1,2}) = 19/48
phi_2({0,1,3}) = 517/1296  phi_1({0,1,3}) = 1/4
phi_1({0,1,2,3}) = 11/54  phi_1({0,1,2,4}) = 85/432
Proposition 2 closed form OK for alpha = 1..8
pairwise independence check OK (|S| <= 2, alpha = 1..5)
phi_M == phi_G and invariances OK on 60 random (S, alpha)
