No Doubles

There are no doubled ciphertext symbols in the eye messages. When we say "doubles", we mean ciphertext with a gap pattern of AA, as in a "0-gap", or a "distance 1 repeat".

This is quite unlikely to happen by chance, so it's one of several indications that we probably have the right reading order. The expected frequency of doubles, assuming a ciphertext alphabet of 83 symbols, is 1/83, or about 1.2%. In messages as long as the eyes (1036 characters total, minus 9 because the last letter of each message cannot be a double with the nonexistent letter after it), using completely random values (which is similar to the IoC we see for the eyes), we'd expect to see about 12.37 doubles. So it's likely the mechanism specifically prevents doubles.

There are several ways to prevent doubles, but methods like Group Autokey (GAK) can avoid doubles fairly easily by selecting the permutations applied by the PT letters in a particular way. (I'll add that here... I also have a proof that it avoids doubles)