No. Maybe… See comments below.
Ever searching for a new way to attempt a K4 solution, I stumbled upon a series of ciphers that utilize a Polybius square.
In cryptography, the Polybius square, also known as the Polybius checkerboard, is a device invented by the Ancient Greek historian and scholar Polybius for fractionating plaintext characters so that they can be represented by a smaller set of symbols. (Wikipedia)
In classical cryptography, the bifid cipher is a cipher which combines the Polybius square with transposition, and uses fractionation to achieve diffusion. It was invented around 1901 by Felix Delastelle. (Wikipedia)
For those unfamiliar with why these types of ciphers caught my interest, it’s due to the fact that the methods used in enciphering text could potentially give rise to the letter frequencies observed in K4 where they are more flattened than you would see in a substitution or straight transposition.
Using a Polybius square:
I converted the text of K4 into numbers.
In a Bifid cipher you write the coordinates vertically then read them off by rows then pair those numbers and use the Polybius square to translate.
In order, from the top row to the second and then paired:
Using the regular Polybius square to translate:
L I/J S Y G S D N G A W O for the beginning which is enough gibberish that I chose not to translate it all.
Knowing that Bifid ciphers usually used a mixed Polybius square, I used a keyed Polybius square as well (keyword = KRYPTOS)
D B M X S M P F S K V G for the beginning which was gibberish as well.
I feel pretty confident saying that K4 is not a Bifid cipher.