(1) corner bound - P, min over 2e5 random (box, point): 7.533e-04  (OK)
(2) interval property of {s>0: P(q,s)<=0}: violations on 3002 q's: 0
(3) Stein eq. residual max 1.84e-40; f'' range on (0,10): [0.00152858, 0.923832] (must be in (0,1))
(4) equal-coefficient sums, exact:  tau*E|X| vs  N p (1-p)^N  (the closed form when N p < 1)
    p=1/10, N=5: tau E|X| == 2 N p (1-p)^N exactly: True; E|X|/sqrt(N) exact 0.880251; 2 sqrt(Np)(1-p)^(N-1/2) = 0.880251; Iv-S (1.10) as printed, exponent N-1: 0.927866
    p=1/5, N=2: tau E|X| == 2 N p (1-p)^N exactly: True; E|X|/sqrt(N) exact 0.905097; 2 sqrt(Np)(1-p)^(N-1/2) = 0.905097; Iv-S (1.10) as printed, exponent N-1: 1.011929
    p=1/4, N=2: tau E|X| == 2 N p (1-p)^N exactly: True; E|X|/sqrt(N) exact 0.918559; 2 sqrt(Np)(1-p)^(N-1/2) = 0.918559; Iv-S (1.10) as printed, exponent N-1: 1.060660
    p=3/10, N=1: tau E|X| == 2 N p (1-p)^N exactly: True; E|X|/sqrt(N) exact 0.916515; 2 sqrt(Np)(1-p)^(N-1/2) = 0.916515; Iv-S (1.10) as printed, exponent N-1: 1.095445
    p=1/20, N=10: tau E|X| == 2 N p (1-p)^N exactly: True; E|X|/sqrt(N) exact 0.868739; 2 sqrt(Np)(1-p)^(N-1/2) = 0.868739; Iv-S (1.10) as printed, exponent N-1: 0.891307
