path_2                             n=  2 m=   1 g=inf Delta= 1 minpos=                 1.0 meanGr=0.5 rhs=4 margin=-3.0
path_10                            n= 10 m=   9 g=inf Delta= 2 minpos= 0.28462967654657106 meanGr=0.146564373898 rhs=68.2294048278 margin=-67.9447751512554
cycle_5                            n=  5 m=   5 g=  5 Delta= 2 minpos=  0.6180339887498948 meanGr=0.6 rhs=8.33333333333 margin=-7.715299344583439
cycle_17                           n= 17 m=  17 g= 17 Delta= 2 minpos=  0.1845367189266037 meanGr=0.0799369747899 rhs=212.667542707 margin=-212.48300598803792
petersen                           n= 10 m=  15 g=  5 Delta= 3 minpos=  0.9999999999999992 meanGr=0.6 rhs=16.6666666667 margin=-15.666666666666668
heawood                            n= 14 m=  21 g=  6 Delta= 3 minpos=  1.4142135623730938 meanGr=0.362637362637 rhs=38.6060606061 margin=-37.19184704368752
pappus                             n= 18 m=  27 g=  6 Delta= 3 minpos=  1.7320508075688765 meanGr=0.25 rhs=72 margin=-70.26794919243112
desargues                          n= 20 m=  30 g=  6 Delta= 3 minpos=  0.9999999999999984 meanGr=0.211973684211 rhs=94.3513345748 margin=-93.35133457479826
mobius_kantor                      n= 16 m=  24 g=  6 Delta= 3 minpos=  0.9999999999999993 meanGr=0.296875 rhs=53.8947368421 margin=-52.89473684210526
hoffman_singleton                  n= 50 m= 175 g=  5 Delta= 7 minpos=  1.9999999999999967 meanGr=0.56 rhs=89.2857142857 margin=-87.28571428571428
random_3reg_n20_seed114            n= 20 m=  30 g=  5 Delta= 3 minpos=  0.4034570124000778 meanGr=0.215328947368 rhs=92.8811487932 margin=-92.47769178075603
random_3reg_n30_seed35             n= 30 m=  45 g=  5 Delta= 3 minpos=  0.1545253800599562 meanGr=0.119390804598 rhs=251.275633003 margin=-251.12110762273198
atlas_checked=35
representatives_proved_by_Delta_cubed_le_n_squared=12/12
OK: no counterexample; normalization yields a broad elementary proof region.