PASS A1 metric axioms of X_1 on {p,x_1..x_16}: triangle violations 0
PASS A2 pattern (3.1) on {p,x_1..x_40}: 39 classes of size > 1, all {(p,x_k),(x_k,x_k+1)}
PASS B1 doubling map f(x_k) = 2^(k-1) is a loose embedding of Y_K, K = 1..40
PASS B2 Remark 3.2 map, M = 2^(m+3) (note): all 2047 nonempty subsets of {p,x_1..x_10}: 2047; 2000 random subsets of {p,x_1..x_40}: 2000
PASS B2 Remark 3.2 map, M = 2^(m+4) (program in original/): all 2047 nonempty subsets of {p,x_1..x_10}: 2047; 2000 random subsets of {p,x_1..x_40}: 2000
PASS B3 negative control: M = 2^m is too small and is detected: 1542 failing subsets
PASS C1 Lemma 2.2 for N = 1..12 (edge 1): Gram det > 0, centroid radius^2 = N/(2N+2) < 1/2
PASS D1 metric of p+G_1..G_6, N=2, heights random: triangle violations 0
PASS D1 metric of p+G_1..G_6, N=2, heights zero: triangle violations 0
PASS D1 metric of p+G_1..G_6, N=2, heights near_half: triangle violations 0
PASS D2 pattern (4.1) on p+G_1..G_6 with formal heights, N=2
PASS D1 metric of p+G_1..G_6, N=3, heights random: triangle violations 0
PASS D1 metric of p+G_1..G_6, N=3, heights zero: triangle violations 0
PASS D1 metric of p+G_1..G_6, N=3, heights near_half: triangle violations 0
PASS D2 pattern (4.1) on p+G_1..G_6 with formal heights, N=3
PASS D1 metric of p+G_1..G_6, N=4, heights random: triangle violations 0
PASS D1 metric of p+G_1..G_6, N=4, heights zero: triangle violations 0
PASS D1 metric of p+G_1..G_6, N=4, heights near_half: triangle violations 0
PASS D2 pattern (4.1) on p+G_1..G_6 with formal heights, N=4
PASS E0 template N=2: edge 1, centroid 0, radius c_N, c_N^-1 exact
PASS E1 Theorem B map on Y_5 = p+G_1..G_5, N=2 (21 points), exact: pattern realized exactly; random rational parameters, trial 1
PASS E0 template N=3: edge 1, centroid 0, radius c_N, c_N^-1 exact
PASS E1 Theorem B map on Y_4 = p+G_1..G_4, N=3 (21 points), exact: pattern realized exactly; random rational parameters, trial 1
PASS F1 Remark 4.2 (N = 1): two cross differences of consecutive gadgets coincide: differences/S: ['-1', '-1/2', '0', '0', '1/2', '1', '1', '3/2', '2']
PASS G1 Proposition 5.1 construction on {p,x_1..x_14}, exact in Q(i): pattern exact at every step; parameters s = ['8', '8', '8', '8', '8', '8', '8', '8', '8', '8', '8', '8', '8']; |g_k| <= 4^(1-k)
PASS H1 hexagonal torus: lambda_1^2 = 1 and the four 2-torsion points pairwise at distance 1/2: squared distances [Fraction(1, 4)]
PASS H2 control: the 2-torsion points of the square torus are not equidistant
PASS I1 RP^3: |xx^T - yy^T|^2 = 2 - 2(x.y)^2 on 200 rational pairs
PASS I2 CP^1: |xx^* - yy^*|^2 = 2 - 2|<x,y>|^2 on 200 rational pairs
TOTAL failures: 0
