seed=2026 NRAND=600 NADV=40
PART1 Lemma B random: connected cases=600 violations(R>=2)=0 max R=1.693578 (n=9)
Chebyshev n= 1: max critical value=0.000000000000 R=1.0000000000 2rho=1.0000000000 diff=+2.2e-16
Chebyshev n= 2: max critical value=1.000000000000 R=1.4142135624 2rho=1.4142135624 diff=+2.2e-16
Chebyshev n= 3: max critical value=1.000000000000 R=1.5874010520 2rho=1.5874010520 diff=+4.2e-15
Chebyshev n= 4: max critical value=1.000000000000 R=1.6817928305 2rho=1.6817928305 diff=+3.3e-15
Chebyshev n= 5: max critical value=1.000000000000 R=1.7411011266 2rho=1.7411011266 diff=+4.0e-15
Chebyshev n= 6: max critical value=1.000000000000 R=1.7817974363 2rho=1.7817974363 diff=+7.3e-15
Chebyshev n= 7: max critical value=1.000000000000 R=1.8114473285 2rho=1.8114473285 diff=+2.4e-15
Chebyshev n= 8: max critical value=1.000000000000 R=1.8340080864 2rho=1.8340080864 diff=+1.1e-14
Chebyshev n= 9: max critical value=1.000000000000 R=1.8517494246 2rho=1.8517494246 diff=+7.3e-15
Chebyshev n=10: max critical value=1.000000000000 R=1.8660659831 2rho=1.8660659831 diff=+2.8e-14
Chebyshev n=11: max critical value=1.000000000001 R=1.8778618213 2rho=1.8778618213 diff=+7.3e-14
Chebyshev n=12: max critical value=1.000000000027 R=1.8877486254 2rho=1.8877486254 diff=+6.3e-13
WRONG (a) zeros 0,5: max critical value=6.2500 (>1 = disconnected, detected=True); R about mean=2.6926 (>2: True)
WRONG (b) scaled Chebyshev n=10 with level K=3 instead of 1: max critical value=3.000000 (<=3: connected at level 3) R=2.082759 (>2 detected: True); predicted 2rho*3^(1/10)=2.082759
WRONG (c) Chebyshev n=12 radius from z_1 not centroid: R=3.759347 (>2 detected: True)
adversary n=2 runs=40 best_verified_R=1.414213562 2*2^(-1/n)=1.414213562 diff=+1.11e-15 BEATS_1D_runs=0 below2=True max|Im z|=4.91e-08
adversary n=3 runs=40 best_verified_R=1.587401052 2*2^(-1/n)=1.587401052 diff=-6.63e-11 BEATS_1D_runs=0 below2=True max|Im z|=8.30e-08
adversary n=4 runs=40 best_verified_R=1.681792830 2*2^(-1/n)=1.681792831 diff=-6.35e-11 BEATS_1D_runs=0 below2=True max|Im z|=2.72e-05
adversary n=5 runs=40 best_verified_R=1.741101126 2*2^(-1/n)=1.741101127 diff=-6.27e-10 BEATS_1D_runs=0 below2=True max|Im z|=7.12e-06
adversary n=6 runs=40 best_verified_R=1.781797435 2*2^(-1/n)=1.781797436 diff=-8.50e-10 BEATS_1D_runs=0 below2=True max|Im z|=4.59e-05
adversary n=7 runs=40 best_verified_R=1.811447327 2*2^(-1/n)=1.811447329 diff=-1.41e-09 BEATS_1D_runs=0 below2=True max|Im z|=1.29e-05
adversary n=8 runs=40 best_verified_R=1.834008081 2*2^(-1/n)=1.834008086 diff=-5.65e-09 BEATS_1D_runs=0 below2=True max|Im z|=1.73e-04
