OBSERVED (the Qurʾān, real openings) — table = (sign hold, sign fail, non-sign hold, non-sign fail) letter-group rule: R0: (0, 6, 5, 3) Fisher one-tailed p = 0.02797 R1: (3, 74, 7, 36) Fisher one-tailed p = 0.02435 R2: (4, 80, 8, 39) Fisher one-tailed p = 0.02383 R3: (7, 77, 9, 38) Fisher one-tailed p = 0.06451 R4: (6, 78, 9, 38) Fisher one-tailed p = 0.03943 R5: (6, 78, 11, 36) Fisher one-tailed p = 0.009611 formula-only rule: R0: (0, 5, 5, 4) Fisher one-tailed p = 0.06294 R1: (2, 42, 8, 68) Fisher one-tailed p = 0.2159 R2: (3, 47, 9, 72) Fisher one-tailed p = 0.255 R3: (4, 46, 12, 69) Fisher one-tailed p = 0.1901 R4: (4, 46, 12, 69) Fisher one-tailed p = 0.1901 R5: (4, 46, 14, 67) Fisher one-tailed p = 0.1058 Family A — the Qurʾān, openings shuffled (10000 runs) letter-group rung Qurʾān p ctrl median p k (ctrl<=obs) (k+1)/(N+1) R0 0.02797 1 0 0.00010 conditional on holds>=5: 0 of 5 R1 0.02435 0.7025 60 0.00610 conditional on holds>=10: 18 of 1679 R2 0.02383 0.7028 47 0.00480 conditional on holds>=12: 11 of 746 R3 0.06451 0.6884 249 0.02500 conditional on holds>=16: 108 of 3402 R4 0.03943 0.3504 615 0.06159 conditional on holds>=15: 226 of 2073 R5 0.009611 0.1404 624 0.06249 conditional on holds>=17: 225 of 1927 formula-only rung Qurʾān p ctrl median p k (ctrl<=obs) (k+1)/(N+1) R0 0.06294 1 1 0.00020 conditional on holds>=5: 1 of 5 R1 0.2159 0.6742 1080 0.10809 conditional on holds>=10: 252 of 1679 R2 0.255 0.6755 1150 0.11509 conditional on holds>=12: 146 of 746 R3 0.1901 0.6336 1074 0.10749 conditional on holds>=16: 451 of 3402 R4 0.1901 0.3176 3463 0.34637 conditional on holds>=16: 989 of 2451 R5 0.1058 0.1865 3692 0.36926 conditional on holds>=18: 879 of 2369 elapsed 57s Family B — Ṣaḥīḥ al-Bukhārī (10000 runs) letter-group rung Qurʾān p ctrl median p k (ctrl<=obs) (k+1)/(N+1) R0 0.02797 1 0 0.00010 conditional on holds>=5: 0 of 6 R1 0.02435 0.7025 124 0.01250 conditional on holds>=10: 25 of 1002 R2 0.02383 0.6906 104 0.01050 conditional on holds>=12: 16 of 418 R3 0.06451 0.6867 284 0.02850 conditional on holds>=16: 76 of 2137 R4 0.03943 0.4892 420 0.04210 conditional on holds>=15: 142 of 1799 R5 0.009611 0.2217 434 0.04350 conditional on holds>=17: 138 of 1766 formula-only rung Qurʾān p ctrl median p k (ctrl<=obs) (k+1)/(N+1) R0 0.06294 1 0 0.00010 conditional on holds>=5: 0 of 6 R1 0.2159 0.6742 1084 0.10849 conditional on holds>=10: 159 of 1002 R2 0.255 0.6755 1204 0.12049 conditional on holds>=12: 104 of 418 R3 0.1901 0.6392 1119 0.11199 conditional on holds>=16: 293 of 2137 R4 0.1901 0.4247 2455 0.24558 conditional on holds>=16: 662 of 2207 R5 0.1058 0.255 2644 0.26447 conditional on holds>=18: 602 of 2175 elapsed 397s Family B — Ṣaḥīḥ Muslim (10000 runs) letter-group rung Qurʾān p ctrl median p k (ctrl<=obs) (k+1)/(N+1) R0 0.02797 1 0 0.00010 conditional on holds>=5: 0 of 3 R1 0.02435 0.6904 147 0.01480 conditional on holds>=10: 21 of 972 R2 0.02383 0.6906 114 0.01150 conditional on holds>=12: 12 of 423 R3 0.06451 0.6865 322 0.03230 conditional on holds>=16: 107 of 2101 R4 0.03943 0.4838 435 0.04360 conditional on holds>=15: 150 of 1716 R5 0.009611 0.2088 451 0.04520 conditional on holds>=17: 148 of 1684 formula-only rung Qurʾān p ctrl median p k (ctrl<=obs) (k+1)/(N+1) R0 0.06294 1 0 0.00010 conditional on holds>=5: 0 of 3 R1 0.2159 0.6742 1192 0.11929 conditional on holds>=10: 187 of 972 R2 0.255 0.6392 1318 0.13189 conditional on holds>=12: 116 of 423 R3 0.1901 0.6329 1187 0.11879 conditional on holds>=16: 310 of 2101 R4 0.1901 0.3983 2668 0.26687 conditional on holds>=16: 687 of 2113 R5 0.1058 0.2481 2838 0.28387 conditional on holds>=18: 607 of 2076 elapsed 386s Family B — Sīra of Ibn Hishām (10000 runs) letter-group rung Qurʾān p ctrl median p k (ctrl<=obs) (k+1)/(N+1) R0 0.02797 1 0 0.00010 conditional on holds>=5: 0 of 4 R1 0.02435 0.6904 135 0.01360 conditional on holds>=10: 24 of 1030 R2 0.02383 0.6906 113 0.01140 conditional on holds>=12: 10 of 431 R3 0.06451 0.6867 300 0.03010 conditional on holds>=16: 83 of 2147 R4 0.03943 0.4892 407 0.04080 conditional on holds>=15: 130 of 1737 R5 0.009611 0.2217 413 0.04140 conditional on holds>=17: 128 of 1702 formula-only rung Qurʾān p ctrl median p k (ctrl<=obs) (k+1)/(N+1) R0 0.06294 1 0 0.00010 conditional on holds>=5: 0 of 4 R1 0.2159 0.6742 1125 0.11259 conditional on holds>=10: 184 of 1030 R2 0.255 0.6755 1164 0.11649 conditional on holds>=12: 95 of 431 R3 0.1901 0.6336 1132 0.11329 conditional on holds>=16: 307 of 2147 R4 0.1901 0.4247 2507 0.25077 conditional on holds>=16: 665 of 2133 R5 0.1058 0.255 2701 0.27017 conditional on holds>=18: 598 of 2089 elapsed 388s Family B — Jāhilī poetry (10000 runs) letter-group rung Qurʾān p ctrl median p k (ctrl<=obs) (k+1)/(N+1) R0 0.02797 1 0 0.00010 conditional on holds>=5: 0 of 9 R1 0.02435 0.6904 148 0.01490 conditional on holds>=10: 20 of 925 R2 0.02383 0.6906 104 0.01050 conditional on holds>=12: 7 of 430 R3 0.06451 0.6865 277 0.02780 conditional on holds>=16: 70 of 2153 R4 0.03943 0.3504 561 0.05619 conditional on holds>=15: 192 of 2252 R5 0.009611 0.1324 567 0.05679 conditional on holds>=17: 186 of 2102 formula-only rung Qurʾān p ctrl median p k (ctrl<=obs) (k+1)/(N+1) R0 0.06294 1 0 0.00010 conditional on holds>=5: 0 of 9 R1 0.2159 0.6742 1098 0.10989 conditional on holds>=10: 165 of 925 R2 0.255 0.6755 1188 0.11889 conditional on holds>=12: 104 of 430 R3 0.1901 0.6336 1203 0.12039 conditional on holds>=16: 353 of 2153 R4 0.1901 0.3176 3301 0.33017 conditional on holds>=16: 861 of 2141 R5 0.1058 0.1901 3507 0.35076 conditional on holds>=18: 769 of 2053 elapsed 380s