== T35: construction of Theorem 3.5 (cases with q > Q), exact tails by direct iteration
   q=17 r=1 d=3 Q=16 q>Q:True  point (h,s,c)=(1,9,8)  tail_PSL=3 (period 1), tail_SL=3 (period 1); need >= 3; traces t_k = 2 + h_k for k <= 3: True; OK
   q=19 r=1 d=3 Q=16 q>Q:True  point (h,s,c)=(8,3,14)  tail_PSL=3 (period 6), tail_SL=3 (period 6); need >= 3; traces t_k = 2 + h_k for k <= 6: True; OK
   q=25 r=1 d=3 Q=16 q>Q:True  point (h,s,c)=(6,14,16)  tail_PSL=3 (period 24), tail_SL=3 (period 24); need >= 3; traces t_k = 2 + h_k for k <= 6: True; OK
   q=27 r=1 d=3 Q=16 q>Q:True  point (h,s,c)=(12,10,3)  tail_PSL=3 (period 13), tail_SL=3 (period 13); need >= 3; traces t_k = 2 + h_k for k <= 6: True; OK
   q=49 r=1 d=3 Q=16 q>Q:True  point (h,s,c)=(9,16,26)  tail_PSL=3 (period 48), tail_SL=3 (period 48); need >= 3; traces t_k = 2 + h_k for k <= 6: True; OK
   q=8 r=1 d=2 Q=4 q>Q:True  point (h,s,c)=(5,7,3)  tail_PSL=3 (period 7), tail_SL=3 (period 7); need >= 3; traces t_k = 2 + h_k for k <= 6: True; OK
   q=16 r=1 d=2 Q=4 q>Q:True  point (h,s,c)=(11,7,6)  tail_PSL=3 (period 15), tail_SL=3 (period 15); need >= 3; traces t_k = 2 + h_k for k <= 6: True; OK
   q=487 r=2 d=6 Q=484 q>Q:True  point (h,s,c)=(121,412,223)  tail_PSL=4 (period 486), tail_SL=4 (period 486); need >= 4; traces t_k = 2 + h_k for k <= 7: True; OK
   q=491 r=2 d=6 Q=484 q>Q:True  point (h,s,c)=(285,39,447)  tail_PSL=4 (period 490), tail_SL=4 (period 490); need >= 4; traces t_k = 2 + h_k for k <= 7: True; OK
   q=529 r=2 d=6 Q=484 q>Q:True  point (h,s,c)=(325,468,256)  tail_PSL=4 (period 528), tail_SL=4 (period 528); need >= 4; traces t_k = 2 + h_k for k <= 7: True; OK
   q=625 r=2 d=6 Q=484 q>Q:True  point (h,s,c)=(367,25,36)  tail_PSL=4 (period 208), tail_SL=4 (period 208); need >= 4; traces t_k = 2 + h_k for k <= 7: True; OK
   q=729 r=2 d=6 Q=484 q>Q:True  point (h,s,c)=(567,372,345)  tail_PSL=4 (period 182), tail_SL=4 (period 182); need >= 4; traces t_k = 2 + h_k for k <= 7: True; OK
   q=128 r=2 d=4 Q=64 q>Q:True  point (h,s,c)=(45,63,75)  tail_PSL=4 (period 127), tail_SL=4 (period 127); need >= 4; traces t_k = 2 + h_k for k <= 7: True; OK
   q=256 r=2 d=4 Q=64 q>Q:True  point (h,s,c)=(125,193,223)  tail_PSL=4 (period 255), tail_SL=4 (period 255); need >= 4; traces t_k = 2 + h_k for k <= 7: True; OK
   q=12547 r=3 d=12 Q=12544 q>Q:True  point (h,s,c)=(2076,8595,2715)  tail_PSL=5 (period 697), tail_SL=5 (period 697); need >= 5; traces t_k = 2 + h_k for k <= 8: True; OK
   q=14641 r=3 d=12 Q=12544 q>Q:True  point (h,s,c)=(8672,6880,1690)  tail_PSL=5 (period 14640), tail_SL=5 (period 14640); need >= 5; traces t_k = 2 + h_k for k <= 8: True; OK
   q=15625 r=3 d=12 Q=12544 q>Q:True  point (h,s,c)=(7360,8404,12563)  tail_PSL=5 (period 7812), tail_SL=5 (period 7812); need >= 5; traces t_k = 2 + h_k for k <= 8: True; OK
   q=16807 r=3 d=12 Q=12544 q>Q:True  point (h,s,c)=(536,4227,9359)  tail_PSL=5 (period 16806), tail_SL=5 (period 16806); need >= 5; traces t_k = 2 + h_k for k <= 8: True; OK
   q=19683 r=3 d=12 Q=12544 q>Q:True  point (h,s,c)=(717,3361,10745)  tail_PSL=5 (period 9841), tail_SL=5 (period 9841); need >= 5; traces t_k = 2 + h_k for k <= 8: True; OK
   q=2048 r=3 d=8 Q=1936 q>Q:True  point (h,s,c)=(629,1335,1968)  tail_PSL=5 (period 2047), tail_SL=5 (period 2047); need >= 5; traces t_k = 2 + h_k for k <= 8: True; OK
   q=4096 r=3 d=8 Q=1936 q>Q:True  point (h,s,c)=(3956,540,1475)  tail_PSL=5 (period 273), tail_SL=5 (period 273); need >= 5; traces t_k = 2 + h_k for k <= 8: True; OK
   q=65536 r=4 d=16 Q=44944 q>Q:True  point (h,s,c)=(20629,46304,36559)  tail_PSL=6 (period 13107), tail_SL=6 (period 13107); need >= 6; traces t_k = 2 + h_k for k <= 9: True; OK
   q=258067 r=4 d=24 Q=258064 q>Q:True  point (h,s,c)=(144051,240336,195316)  tail_PSL=6 (period 129033), tail_SL=6 (period 129033); need >= 6; traces t_k = 2 + h_k for k <= 9: True; OK
   q=1048576 r=5 d=32 Q=868624 q>Q:True  point (h,s,c)=(19008,129494,126688)  tail_PSL=7 (period 95325), tail_SL=7 (period 95325); need >= 7; traces t_k = 2 + h_k for k <= 10: True; OK
   24 of 24 cases OK
== BND-construction: q >= 256 with r = floor(log2 q/4) - 1: tail >= r+1 = floor(log2 q/4)
   [bound] q=256 r=1 d=2 Q=4 q>Q:True  point (h,s,c)=(152,11,69)  tail_PSL=3 (period 15), tail_SL=3 (period 15); need >= 3; traces t_k = 2 + h_k for k <= 6: True; OK
   [bound] q=257 r=1 d=3 Q=16 q>Q:True  point (h,s,c)=(110,160,104)  tail_PSL=3 (period 256), tail_SL=3 (period 256); need >= 3; traces t_k = 2 + h_k for k <= 6: True; OK
   [bound] q=1021 r=1 d=3 Q=16 q>Q:True  point (h,s,c)=(617,960,367)  tail_PSL=3 (period 340), tail_SL=3 (period 340); need >= 3; traces t_k = 2 + h_k for k <= 6: True; OK
   [bound] q=729 r=1 d=3 Q=16 q>Q:True  point (h,s,c)=(667,484,452)  tail_PSL=3 (period 91), tail_SL=3 (period 91); need >= 3; traces t_k = 2 + h_k for k <= 6: True; OK
   [bound] q=4096 r=2 d=4 Q=64 q>Q:True  point (h,s,c)=(839,3331,3926)  tail_PSL=4 (period 4095), tail_SL=4 (period 4095); need >= 4; traces t_k = 2 + h_k for k <= 7: True; OK
   [bound] q=4099 r=2 d=6 Q=484 q>Q:True  point (h,s,c)=(1620,3422,763)  tail_PSL=4 (period 2049), tail_SL=4 (period 2049); need >= 4; traces t_k = 2 + h_k for k <= 7: True; OK
   [bound] q=6561 r=2 d=6 Q=484 q>Q:True  point (h,s,c)=(3952,1108,1756)  tail_PSL=4 (period 6560), tail_SL=4 (period 6560); need >= 4; traces t_k = 2 + h_k for k <= 7: True; OK
   [bound] q=65536 r=3 d=8 Q=1936 q>Q:True  point (h,s,c)=(4307,22129,59967)  tail_PSL=5 (period 65535), tail_SL=5 (period 65535); need >= 5; traces t_k = 2 + h_k for k <= 8: True; OK
   [bound] q=65537 r=3 d=12 Q=12544 q>Q:True  point (h,s,c)=(42295,19468,62988)  tail_PSL=5 (period 65536), tail_SL=5 (period 65536); need >= 5; traces t_k = 2 + h_k for k <= 8: True; OK
   [bound] q=1048576 r=4 d=16 Q=44944 q>Q:True  point (h,s,c)=(895778,608623,363875)  tail_PSL=6 (period 349525), tail_SL=6 (period 349525); need >= 6; traces t_k = 2 + h_k for k <= 9: True; OK
   [bound] q=1048583 r=4 d=24 Q=258064 q>Q:True  point (h,s,c)=(673932,998295,299256)  tail_PSL=6 (period 524291), tail_SL=6 (period 524291); need >= 6; traces t_k = 2 + h_k for k <= 9: True; OK
   11 of 11 cases OK
   [T35: 17.2s]
exit=0
