Part A: literal (b) obstruction (spikes y_{4^k} = 1/k^2, other y_n = 2^-n)
   k   m_k      lower bound for sum of any non-increasing majorant on (m_{k-1}, m_k]
   2       16          3.00
   3       64          5.33
   4      256         12.00
   5     1024         30.72
   6     4096         85.33
   7    16384        250.78
   8    65536        768.00
   9   262144       2427.26
   (while sum of y over the same range is < 3.5398)
Part B: D1 tail-index lemma on random instances
   done 200 instances
Part C: D2 corner-step lemma on random instances
   done 150 instances
Part D: D4 shapes + slalom envelope on random instances
   done 60 instances
Part E: Lemma 1 strict upper bound, s_n = 1/((n+1)(n+2)), T_s(m) = 1/(m+1)
  k=1: block [4,16) sum u-bar = 0.298693  <=  5*2^-k = 2.500000
  k=2: block [16,64) sum u-bar = 0.183769  <=  5*2^-k = 1.250000
  k=3: block [64,256) sum u-bar = 0.097219  <=  5*2^-k = 0.625000
  k=4: block [256,1024) sum u-bar = 0.049316  <=  5*2^-k = 0.312500
  k=5: block [1024,4096) sum u-bar = 0.024748  <=  5*2^-k = 0.156250
  k=6: block [4096,16384) sum u-bar = 0.012385  <=  5*2^-k = 0.078125
  k=7: block [16384,65536) sum u-bar = 0.006194  <=  5*2^-k = 0.039062
  k=8: block [65536,262144) sum u-bar = 0.003097  <=  5*2^-k = 0.019531
  k=9: block [262144,1048576) sum u-bar = 0.001549  <=  5*2^-k = 0.009766
Part F: Lemma 3 Tukey maps on random finite instances
   done 200 instances
ALL CHECKS PASSED
