At the beginning of the year Government Attic published the NSA manual "Military Cryptanalytics Part III" by Lambros D. Callimahos (October 1977).

The FOIA request date was July 2012 ... and it had been the subject of FOI requests since the early 1990s. 

https://www.governmentattic.org/39docs/NSAmilitaryCryptalyticsPt3_1977.pdf (25 MB PDF)

It is still quite a bit redacted, but Chapter XI "Principles of cryptodiagnosis" would be useful for people trying to understand the phenomena seen in K4.

First step: manipulating the data

"In all of one's endeavors, the successful cryptanalyst's precept should be kept foremost in mind: "Try the simplest thing first." It is surprising how often this admonishment is disregarded, to the later chagrin of the cryptosinner."

Second step: recognizing the phenomena

Reading through the posts in this group, I can't emphasize the following quote enough...

"After finding a phenomenon - or what is thought to be a phenomenon - an evaluation should follow. It's not enough to say "I think the doublets are high." How many are there? Count them. And, even more important, how many doublets are expected at random in a sample of this size?"

The STETHOSCOPE program presents a variety of fundamental information about a single message:

a. the uniliteral frequency distribution, the monographic IC, and its sigmage
b. the overall digraphic IC, as well as the digraphic ICs on cut A and cut B, and their sigmages
c. the overall trigraphic IC, and the trigraphic ICs on cuts A, B, and C and their sigmages
d. the local roughness (in terms of the observed and expected number of hits, and sigmage), when the message is offset against itself at offsets of 1 to 33
e. width tests, giving average columnar ICs and sigmages of the message if it were written out on widths from 2 to 51
f. the observed and expected number of tetragraphic and pentagraphic repetitions, and their ICs and sigmages
g. a listing of polygraphic repetitions of length 4 or longer
h. if desired, the same categories of statistical information on the delta stream

(here sigmage is the number of standard deviations away from the mean)

Third step: interpreting the phenomena

There is also a reference to I. J. Good "Standard Reagents and Diagnostician's Dictionary", National Security Agency, 1966 ... Good was one of the original Bletchley Park cryptanalysts.
I wonder how long that would take to release...