number of admissible pairs checked: 42234  max d: 6000000
k2_lower: lo/k2 - 1                                          max = -3.331e-07 at (d,k)=(6000000, 5999999)  OK
k2_upper: k2/hi - 1                                          max = -3.333e-07 at (d,k)=(6000000, 5999995)  OK
k4ratio: (k4/k2^2)/rhs - 1                                   max = -1.389e-06 at (d,k)=(6000000, 5999999)  OK
F^2 >= Na/b: (Na/b)/F^2 - 1                                  max = -3.331e-07 at (d,k)=(6000000, 5999999)  OK
mean: N k1 / (N a (1/b+1/b^2)) - 1                           max = -2.603e-07 at (d,k)=(6000000, 5999999)  OK
-log sigma >= rhs: rhs - (-log sigma) [abs]                  max = -6.093e-08 at (d,k)=(6000000, 5999999)  OK
decomp: |E|/(N/b) - 1                                        max = -3.648e-01 at (d,k)=(6000000, 3000001)  OK
decomp closed form |E - Eclosed| / max(1,|E|) [abs]          max = 5.887e-09 at (d,k)=(5097866, 5097864)  OK
G2: r1(x)*12x^2 - 1                                          max = -5.970e-09 at (d,k)=(3925, 3922)  OK
G2: -r1(x) [must be <0]                                      max = -2.084e-08 at (d,k)=(6399, 4000)  OK
G2: r2(x)*12x - 1                                            max = -8.336e-07 at (d,k)=(17009, 8705)  OK
G2: -r2(x) [must be <0]                                      max = -4.168e-05 at (d,k)=(6399, 4000)  OK
supdens <= 2e^2/F: S*F/(2e^2) - 1                            max = -9.323e-01 at (d,k)=(999448, 999446)  OK
supdens <= 1/F (sharp): S*F - 1                              max = 7.522e-10 at (d,k)=(999448, 999446)  OK
Markov: (1-p)/sqrt(e rho) - 1                                max = -4.453e-01 at (d,k)=(6000000, 3003706)  OK
note: tolerance 1e-8 for rounding; 'supdens <= 1/F' is an equality when a=1 (-log W exponential).
