Prop 2 closed form, alpha=1..12: True; difference formula: True; iid - lattice > 0 exactly for alpha in [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
phi_1, phi_2 of {0,1,2}: 1/4, 19/48
{0,1,3}: phi_1=1/4, phi_2=517/1296 (claim 1/4, 517/1296); {0,1,2,3}: phi_1=11/54 (claim 11/54); {0,1,2,4}: phi_1-1/5=-7/2160 (claim -7/2160); {0,1,2,3}: phi_1-1/5=1/270 (claim 1/270)
Lemma 2(d) invariance (translation, scaling by 2,3,-1,-2) on 60 random sets, no canonicalisation: True
Remark 8(a) phi_1 = 1/4: 7021 triples (b<=119), violations 0
Remark 8(b) closed form for phi_2: 7021 triples (b<=119), violations 0
Remark 8(c): 41664 4-sets with max <= 64, phi_1 < 1/5 for 21630 (claim 41664 and 21630); max phi_1 = 5/24 at (0, 1, 3, 4)
max phi_1 over canonical 4-sets with diam <= 119: 5/24 = 0.208333 at (0, 1, 3, 4)
