God's Algorithm out to 12f*

I just completed exploring all positions of the cube out to depth 12 in the face turn metric.

The first table is the count of positions with exactly the given depth.

 d  mod M + inv        mod M      positions
-- ------------ ------------ --------------
 0            1            1              1
 1            2            2             18
 2            8            9            243
 3           48           75           3240
 4          509          934          43239
 5         6198        12077         574908
 6        80178       159131        7618438
 7      1053077      2101575      100803036
 8     13890036     27762103     1332343288
 9    183339529    366611212    17596479795
10   2419418798   4838564147   232248063316
11  31909900767  63818720716  3063288809012
12 420569653153 841134600018 40374425656248

The second table is the count of positions with that depth or less.

 d  mod M + inv        mod M      positions
-- ------------ ------------ --------------
 0            1            1              1
 1            3            3             19
 2           11           12            262
 3           59           87           3502
 4          568         1021          46741
 5         6766        13098         621649
 6        86944       172229        8240087
 7      1140021      2273804      109043123
 8     15030057     30035907     1441386411
 9    198369586    396647119    19037866206
10   2617788384   5235211266   251285929522
11  34527689151  69053931982  3314574738534
12 455097342304 910188532000 43689000394782