PASS  run B's exact values of E_lat and E_iid: 638 identical, 0 different
PASS  value (3, 1, 4): E_lat=19/1620, E_iid=4/405
PASS  value (4, 1, 4): E_lat=139/17280, E_iid=11/1920
PASS  value (5, 1, 4): E_lat=31/5000, E_iid=7/1875
PASS  value (6, 1, 4): E_lat=647/129600, E_iid=17/6480
PASS  value (7, 1, 4): E_lat=274313/64827000, E_iid=2/1029
PASS  value (8, 1, 4): E_lat=29399/8064000, E_iid=23/15360
PASS  value (14, 1, 4): E_lat=1700176573/839091052800, E_iid=41/82320
PASS  value (3, 1, 6): E_lat=353/81648, E_iid=59/20412
PASS  value (3, 1, 8): E_lat=4399/2099520, E_iid=37/32805
PASS  value (3, 1, 10): E_lat=196897/166281984, E_iid=689/1299078
PASS  value (3, 2, 4): E_lat=6829/777600, E_iid=391/48600
PASS  value (4, 2, 4): E_lat=620539/111974400, E_iid=133/28800
PASS  n=65, d=1: E_lat=4.29527e-04 (note 4.29527e-4), E_iid=97/4119375 (note 97/4119375), ratio 18.2411 (note 18.2411)
PASS  ratios of Table 2: 3:1.1875, 4:1.4040, 5:1.6607, 6:1.9029, 7:2.1771, 8:2.4347, 14:4.0682, 65:18.2411, 120:33.5720
PASS  Remark 7.1: ratio 18.24 at n=65 and 33.57 at n=120 (d=1, p=4): 18.24, 33.57
PASS  Remark 5.3: n E_lat(n,1,4) at n=10,20,40,80,120: ['0.02875', '0.02813', '0.02796', '0.02791', '0.02790'] (note 0.02875, 0.02813, 0.02796, 0.02791, 0.02790)
PASS  Section 1.3: ratio at p=4, n=12: d=10 1.0115 (note 1.0115), d=20 1.000004 (note 1.000004)
PASS  n <= 2: E_lat = E_iid in all 34 cases
PASS  n >= 3: E_lat > E_iid in all 628 cases (p=4: d<=4, n<=120 and d=10,20, n<=12; p=6: d<=4, n<=25; p=8: d<=4, n<=10; p=10: d<=3, n<=6)
PASS  Theorem 5.1 (E_lat >= 4/((p+1)^d (p+2)(p+3)(n-1))) holds in all 628 cases with n >= 3
PASS  Proposition 5.2 (E_iid <= T_p (2^-d - 3^-d) n^(-p/2)) holds in all 662 cases
PASS  Remark 5.3: E_lat(3,1,p)/bound for p=4,6,8,10,30: ['1.2315', '1.0895', '1.0371', '1.0160', '1.000005'] (note 1.2315, 1.0895, 1.0371, 1.0160, 1.000005)
INFO  Remark 7.1: distinct triples (n,d,p) with n >= 3, p >= 4 and a positive exact difference recorded (run B's certificate and scan files and thm4_highp, the original p = 4 file, and run 2): 2354; by p: {4: 1890, 6: 322, 8: 88, 10: 36, 12: 3, 14: 3, 16: 3, 20: 3, 24: 3, 30: 3}
TOTAL failures: 0
