=== N1: Lemma 2.1 on random tensors ===
PASS N1 mu_i <= sum_{j != i} mu_j on 8704 random unit tensors (n = 3..7; Gaussian, uniform, sparse, complex, rank 2) :: max violation 1.11e-16
=== N2: Lemma 2.3 (unit ball) ===
PASS N2 f(d_i) <= sum_{j != i} f(d_j) for 6575 tensors in the ball (incl. scaled extremal ones) :: max violation 1.11e-16
PASS N2b R_c(tau) = mu(c,tau)/mu(d_m,tau) nondecreasing in tau (grid of d_m, c, tau)
=== N3: attainment by least squares; distance from d' to G(B) ===
PASS N3a random targets h(lambda), lambda in P_4, P_5 (a third on facets) are reached on the unit sphere :: worst residual 1.4e-12
PASS N3b d': minimisation over the unit ball (60 starts) finds nothing closer than h(P_4); the nearest point of h(P_4) is attained by a unit tensor :: ball min 0.0233299, dist to h(P_4) 0.0233290, attained 0.0233290
PASS N3b d*: minimisation over the unit ball (60 starts) finds nothing closer than h(P_4); the nearest point of h(P_4) is attained by a unit tensor :: ball min 0.0100330, dist to h(P_4) 0.0100300, attained 0.0100300
=== N4: Monte Carlo volumes in [0,1/4]^n (floating point) ===
   n=3: |{Q1>=Q2} \ G(B)| = 0.0000, |G(B) \ {Q1>=Q2}| = 0.0111, |G(B)| = 0.3664  (fractions of the cube, 4e5 points)
   n=4: |{Q1>=Q2} \ G(B)| = 0.1366, |G(B) \ {Q1>=Q2}| = 0.0000, |G(B)| = 0.6964  (fractions of the cube, 4e5 points)
   n=5: |{Q1>=Q2} \ G(B)| = 0.0756, |G(B) \ {Q1>=Q2}| = 0.0000, |G(B)| = 0.8821  (fractions of the cube, 4e5 points)
   n=6: |{Q1>=Q2} \ G(B)| = 0.0300, |G(B) \ {Q1>=Q2}| = 0.0000, |G(B)| = 0.9616  (fractions of the cube, 4e5 points)
PASS N4 volume fractions agree with Remark 3.5 (13.6, 7.6, 3.0 % for n=4,5,6; G(B)\{Q1>=Q2} empty there; n=3: {Q1>=Q2}\G(B) empty and G(B)\{Q1>=Q2} about 1.1 %)
=== N5: Q1 - Q2 on G(B); largest Q2/Q1 for n = 4 ===
PASS N5a no point with Q1 < Q2 among 5e5 points h(lambda), lambda uniform in P_n, n = 4, 5, 6 :: {4: 0, 5: 0, 6: 0}
PASS N5b largest Q2/Q1 found on G(B), n = 4, does not exceed 27/512 = 0.052734 :: best found 0.052734
PASS N5c at (1/4,1/4,1/4,0): Q2/Q1 = 27/512

SUMMARY: 10 checks, 0 failed
