Lemma 3.1 identity |S minus union of discs| = sum |Q_j minus B_j| vs 3000x3000 grid count, 8 systems: max |diff| = 4.14e-06
random disc systems: 6000 (kinds: uniform, unequal, bigsmall, perturbed hexagonal lattices; N' < N in 4360, Euler bound attained in 95)
violations: tiling 0, Euler count 0, per-cell moment lemma 0, tangent/per-cell chain 0, refined inequality 0, weighted Phi_beta 0
min over systems of Phi - c_H - 0.06 m = 0.1110 ; min of Phi - (c_H + 0.06 m + 0.0055 m #nonhex) = 0.1055

local minimisation of Phi (free centres in the plane and free radii), 8 starts for each N:
   N=1 : min Phi found = 0.18109   (m = 1.0000, c_H + 0.06 m = 0.13447; slack 0.04663)
   N=2 : min Phi found = 0.45001   (m = 0.5000, c_H + 0.06 m = 0.10447; slack 0.34554)
   N=3 : min Phi found = 0.34511   (m = 0.3333, c_H + 0.06 m = 0.09447; slack 0.25065)
   N=4 : min Phi found = 0.18112   (m = 0.2500, c_H + 0.06 m = 0.08947; slack 0.09165)
   N=5 : min Phi found = 0.26756   (m = 0.1994, c_H + 0.06 m = 0.08643; slack 0.18114)
   N=6 : min Phi found = 0.29727   (m = 0.1640, c_H + 0.06 m = 0.08430; slack 0.21297)
elapsed 38 s
RESULT PASS
