After solving K1, we are able to retrieve Palimpsest which basically describes recycled materials used for ciphering.  After having just finished a vigenere, I would take this to mean that I should do another.  After sucessfully repeating things for K2, I get Abscissa and Layer Two which I would take to mean the next one involves two changes in location which corresponds pretty well with Gary Phillips description of the K3 solution being a double rotational transposition.  So then we get to the end of K3 and it asks if we can see anything between X and Q.

Literally, I can see OGHULBSOLIFBBWFLRV between the X and Q but that doesn’t do us any good.  So then I was thinking, maybe it meant literally “anything”.  If it’s some kind of substitution cipher then we would need two of the same letters separated by 4 different letters to get the aNythiNg to fit.

I found a distance of 3, 5 and 6 but nothing that would work.

At least we can rule out literally finding the enciphered word ANYTHING between X and Q in the ciphertext of K4.

Kryptos Fan