== predicted mean linear factor (rounding, craters shrink with surface)
  caps       0.859
  ring45-60  0.902
  belt<15    1.081
  far<60     1.016
  near<60    0.995
  caps/ring 0.952  caps/belt 0.795
  P3 dome closure: far side x0.58 vs near side
areas (Mkm2): {'caps': np.float64(3.81), 'ring45-60': np.float64(4.21), 'belt<15': np.float64(7.63), 'far<60': np.float64(13.04), 'near<60': np.float64(10.76)}

== CALC 1: largest craters per equal area (top q per Mkm2), clean
 q=2/Mkm2 | caps: n=8 mean=199.4 med=184.5 | ring45-60: n=8 mean=371.6 med=277.3 | belt<15: n=15 mean=304.8 med=218.5 | far<60: n=26 mean=350.2 med=257.2 | near<60: n=22 mean=239.6 med=181.1
 q=5/Mkm2 | caps: n=19 mean=163.3 med=151.3 | ring45-60: n=21 mean=233.5 med=165.6 | belt<15: n=38 mean=201.7 med=147.7 | far<60: n=65 mean=229.9 med=171.5 | near<60: n=54 mean=172.5 med=138.9
 q=10/Mkm2 | caps: n=38 mean=139.3 med=127.4 | ring45-60: n=42 mean=169.2 med=120.5 | belt<15: n=76 mean=150.9 med=115.1 | far<60: n=130 mean=168.5 med=125.0 | near<60: n=108 mean=133.1 med=111.6
 q=20/Mkm2 | caps: n=76 mean=116.8 med=107.5 | ring45-60: n=84 mean=125.2 med=92.4 | belt<15: n=153 mean=114.7 med=92.3 | far<60: n=261 mean=126.8 med=96.7 | near<60: n=215 mean=102.4 med=84.9
  caps/ring45-60 q=5: mean-ratio 0.699  95% [0.488 1.04 ]
  caps/belt<15 q=5: mean-ratio 0.810  95% [0.59  1.116]
  far/near q=5: mean-ratio 1.333  95% [0.995 1.768]
  caps/ring45-60 q=10: mean-ratio 0.824  95% [0.623 1.101]
  caps/belt<15 q=10: mean-ratio 0.924  95% [0.728 1.152]
  far/near q=10: mean-ratio 1.265  95% [1.02  1.559]
  caps/ring45-60 q=20: mean-ratio 0.933  95% [0.747 1.144]
  caps/belt<15 q=20: mean-ratio 1.018  95% [0.857 1.201]
  far/near q=20: mean-ratio 1.238  95% [1.057 1.44 ]
  expectation: kept size + crowding f -> ratio ~ f^(1/2) (f=1.20 -> 1.10); shrink with surface -> ~1.00

== CALC 1b: shape of the family (R-plot) and best shift
  caps       N=[345, 223, 155, 85, 59, 20, 7, 1]  R=[146.96, 189.98, 264.1, 289.66, 402.12, 272.62, 190.83, 54.52]
  ring45-60  N=[402, 227, 128, 81, 37, 14, 5, 2]  R=[154.98, 175.03, 197.39, 249.82, 228.23, 172.72, 123.37, 98.7]
  belt<15    N=[637, 391, 243, 120, 68, 27, 5, 2]  R=[135.61, 166.48, 206.92, 204.37, 231.62, 183.93, 68.12, 54.5]
  far<60     N=[1256, 716, 456, 276, 146, 40, 17, 9]  R=[156.37, 178.28, 227.09, 274.89, 290.83, 159.36, 135.46, 143.42]
  near<60    N=[852, 483, 302, 131, 79, 36, 11, 1]  R=[128.64, 145.85, 182.39, 158.23, 190.84, 173.93, 106.29, 19.33]
  caps vs ring45-60: best size factor s=1.335  95% [0.735 1.495]
  caps vs belt<15: best size factor s=1.395  95% [1.087 1.498]
  far<60 vs near<60: best size factor s=1.485  95% [1.007 1.5  ]

== CALC 2: simple-to-complex transition (Wang & Wu depths, clean), N= 104493
  caps       p90 d/D: 0.136 0.148 0.156 0.165 0.167 0.149 0.152 0.147 0.118 0.108 0.089 0.077 0.084 0.069  n: [np.int64(4709), np.int64(3154), np.int64(2042), np.int64(1336), np.int64(1026), np.int64(752), np.int64(562), np.int64(375), np.int64(228), np.int64(185), np.int64(154), np.int64(109), np.int64(100), np.int64(73)]
  ring45-60  p90 d/D: 0.143 0.149 0.157 0.158 0.152 0.157 0.157 0.145 0.126 0.114 0.102 0.089 0.074 0.066  n: [np.int64(5014), np.int64(3581), np.int64(2670), np.int64(1775), np.int64(1386), np.int64(854), np.int64(699), np.int64(414), np.int64(296), np.int64(186), np.int64(149), np.int64(111), np.int64(74), np.int64(69)]
  belt<15    p90 d/D: 0.147 0.154 0.158 0.168 0.170 0.171 0.167 0.162 0.138 0.125 0.103 0.093 0.079 0.073  n: [np.int64(7508), np.int64(5075), np.int64(3594), np.int64(2758), np.int64(2132), np.int64(1591), np.int64(1183), np.int64(749), np.int64(437), np.int64(267), np.int64(239), np.int64(180), np.int64(142), np.int64(112)]
  far<60     p90 d/D: 0.145 0.151 0.154 0.161 0.164 0.168 0.163 0.156 0.134 0.125 0.103 0.093 0.085 0.073  n: [np.int64(16398), np.int64(11210), np.int64(8100), np.int64(6067), np.int64(4875), np.int64(3573), np.int64(2615), np.int64(1577), np.int64(942), np.int64(589), np.int64(440), np.int64(347), np.int64(278), np.int64(237)]
  near<60    p90 d/D: 0.145 0.153 0.163 0.167 0.165 0.178 0.172 0.148 0.126 0.112 0.098 0.090 0.075 0.069  n: [np.int64(10110), np.int64(6764), np.int64(4548), np.int64(2986), np.int64(2037), np.int64(1443), np.int64(1119), np.int64(741), np.int64(565), np.int64(370), np.int64(316), np.int64(235), np.int64(193), np.int64(131)]
  bins D(km):   4.4   5.3   6.5   7.9   9.6  11.6  14.1  17.1  20.7  25.1  30.5  37.0  44.9  54.5
  caps       Dt=16.4 km  95% [15.8 17.1]  plateau d/D=0.170 slope=0.71
  ring45-60  Dt=15.5 km  95% [14.8 16.1]  plateau d/D=0.176 slope=0.67
  belt<15    Dt=16.9 km  95% [16.5 17.5]  plateau d/D=0.184 slope=0.77
  far<60     Dt=17.1 km  95% [16.8 17.5]  plateau d/D=0.177 slope=0.70
  near<60    Dt=15.1 km  95% [14.7 15.7]  plateau d/D=0.184 slope=0.74
  ratios: caps/ring 1.057 caps/belt 0.967 far/near 1.131

== CALC 4: old vs fresh (freshness = d/D residual from one global d/D-D curve; thirds within each region), D>=20
  caps       n=923 old: mean 41.7 med 31.4 | fresh: mean 43.3 med 34.2 | old/fresh mean 0.963 med 0.918
  ring45-60  n=919 old: mean 43.6 med 29.0 | fresh: mean 40.1 med 29.5 | old/fresh mean 1.086 med 0.982
  belt<15    n=1441 old: mean 39.2 med 30.7 | fresh: mean 41.5 med 30.7 | old/fresh mean 0.944 med 1.002
  far<60     n=2956 old: mean 41.5 med 29.2 | fresh: mean 40.3 med 30.7 | old/fresh mean 1.028 med 0.950
  near<60    n=1864 old: mean 42.2 med 31.5 | fresh: mean 37.4 med 29.9 | old/fresh mean 1.130 med 1.051
  double ratio caps/ring45-60: 0.886  95% [0.714 1.094]
  double ratio caps/belt<15: 1.019  95% [0.891 1.163]
  double ratio far<60/near<60: 0.910  95% [0.809 1.018]

== CALC 3: predicted ellipticity if craters deformed with the surface (radial mapping, a/c=1.69)
  lat  5: zonal x0.845 meridional x0.835 -> e=1.013 long axis E-W
  lat 20: zonal x0.926 meridional x0.832 -> e=1.114 long axis E-W
  lat 37: zonal x1.086 meridional x0.958 -> e=1.133 long axis E-W
  lat 52: zonal x1.232 meridional x1.136 -> e=1.084 long axis E-W
  lat 67: zonal x1.347 meridional x1.303 -> e=1.033 long axis E-W
  lat 80: zonal x1.405 meridional x1.396 -> e=1.006 long axis E-W
