C5 = [0.855100455470819, 0.855100455470819]
PASS C5 matches 0.8551004554...  [[0.855100455470819, 0.855100455470819]]
PASS 171/200 < C5  [margin 1.005e-04]
PASS ln(5/4) > (171/256)^2/2 (same fact)  [0.2231435513 > 0.2230911255]
PASS C_4: g((K-1)s_K) and g(K s_K) agree  [[0.853343568496049, 0.853343568496049]]
PASS C_5: g((K-1)s_K) and g(K s_K) agree  [[0.855100455470819, 0.855100455470819]]
PASS C_6: g((K-1)s_K) and g(K s_K) agree  [[0.855984489173815, 0.855984489173815]]
C_4 = [0.853343568496049, 0.853343568496049]  C_5 = [0.855100455470819, 0.855100455470819]  C_6 = [0.855984489173815, 0.855984489173815]
PASS C_5 from the tie formula equals 1.28 sqrt(2 ln 1.25)
PASS C_K strictly increasing for 4 <= K <= 40 (enclosures disjoint)
PASS x_K = ((K-1)/2) ln(K/(K-1)) < 1/2 for K <= 40
PASS sqrt(2/e) > C_5 (limit q -> 0)
q5 = [0.105572809000084, 0.105572809000084]
PASS q5 = 1 - 2/sqrt5 = 0.105572809...
PASS q6 = 1 - sqrt(5/6) < q5  [[0.087129070824723, 0.087129070824723]]
PASS q_5 = 1 - e^{-s_5} with s_5 = (1/2) ln(5/4)  [e^{-s_5} = sqrt(4/5) = 2/sqrt5 exactly]
A'(q5) = [1.538044391650755, 1.538044391650755]
PASS A'(q5) < 1.54 = 77/50  [[1.538044391650755, 1.538044391650755]]
PASS A'(q5) = 1.53804...
PASS sqrt(2) (limit of A' as q -> 0) < 77/50
PASS A'(q) increasing on the grid q = k/1000, k <= 105 (spot check of the analytic proof)
PASS 2 tau = 1.7 > A = 1.54 (Lemma 19, dQ/da >= 0)
PASS 0.8/tau^2 < 28/25 (Lemma 20(i))  [1.107266]
PASS 0.8/A^2 < 17/50 (Lemma 20(i))  [0.337325]
PASS case 1: (a+b)^2/(4ab) = 121/120 and floor(20 * 121/120) = 20
PASS case 2: (theta+A)^2/(4 theta A) * (1/2) < 11/20, so i+j <= 10  [0.545464]
PASS case 3: m1 < A/4 + 3 theta/4 = 1.0225
PASS case 3: m2 < (A^2 + theta^2)/2 = 1.54705 < 31/20  [1.547050]
PASS theta = 17/20 = 0.85, A = 77/50 = 1.54
ALL CONSTANT CHECKS PASSED
