Repeated column trigrams in K1
I’ve seen ELY in K1 mentioned a few times as a possible K4-relevant artifact, but ELY is only one example of a broader pattern. I have not seen this mentioned elsewhere, so maybe it's useful information for someone.
[edit] I believe this is novel information, not a rehash of tired analysis, hence this post. I wrote it to help another user who was looking into ELY, I thought the following was well-known. Apologies if old news, please correct me. Also, see K4 relevance in later edit. This is NOT a solution to K4, but might help.
If you stack K1 as plaintext / key / ciphertext, several entire vertical columns repeat. In other words, it is not just that the ciphertext has repeated letters, but that the same PT+key+CT column triple blocks recur. Examples include:
- ELY appears 4 times (position is almost regular - 13,
23, 33, 43, 53) - ELY SIU appears twice
- NPV CAJ ELY OIQ FMT appears twice
- other single column triples like EPH, HMS, etc. repeat too
That seems more specific than a normal text repeat. For a column triple to repeat, Sanborn’s plaintext wording, the repeating PALIMPSEST key alignment, and the resulting CT all have to line up.
Since Jim only had a budget of 63 characters (K1 length) it would be unusual to force 29 columns (46%) to occur in a repeated triple unless there was good reason.
For example, imagine he needed ALICE to repeat in 2 specific spots, including exact corresponding keyword fragment (say ALIMP) and CT. He'd need to plot ALICE on said positions (strongly constrained by where (p)ALIMP(sest) happens to land, it is predetermined) then build up a coherent sentence around them. Here is an example. Now imagine having to fill in the space surrounding ALICE/ALIMP with lucid prose.
what here
? |A L I C E| ? ? ? ? ? |A L I C E| ? ? ? ? ... CT
p |A L I M P| s e s t p |A L I M P| s e s t ... keyword
Given that K1’s phrasing was apparently “carefully worded,” I don’t think this should be dismissed as just "ELY appearing by chance". I don’t know what, if anything, it implies for K4, but the phenomenon is better described as repeated PT/key/CT column-triple blocks, not merely repeated CT fragments.
[edit, per mod]: Consider that these repeated sections are useful as alignment edges or strides (see the 13/23/33/43/53 pattern). Or that their content is elements of a transposition or (say) a Polybius square. Or perhaps concatenated as a keystream. Or maybe under some shift they give us the full RDUM strings. Or the indexes and lengths frame text extents in K4. Not sure, but perhaps they connect some dots someone else has been looking for.
Nomenclature: Repeated sections delineated using |x|, eg at position 13, you can see ELY SIU, which you can see again at 43. The more interesting/longer one is at 31 & 51
|13 | <-- See repeat of this 2 column block at 43
B E T W E|E|N S U B T L|e s|H A D
P A L I M|P|S E S T P A|l i|M P S
E M U F P|H|Z L R F A X|y u|S D J
|6|
|31 35| <-- See repeat of this 5 column block at 51
I N G A N D T H|E|A B S E|n c e o f|
E S T P A L I M|P|S E S T|p a l i m|
K Z L D K R N S|H|G N F I|v j y q t|
^ 26 ^
|43 | |51 55| *
L I G H T L I|e s| T H|E N|U A|n c e o f|I q L U S I O N
P S E S T P A|l i| M P|S E|S T|p a l i m|P c E S T P A L
Q U X Q B Q V|y u| V L|L T|R E|v j y q t|M k Y R D M F D
|47 |
Inventory (29 columns):
EPH x2 positions 6, 26
NSZ x2 positions 7, 19
USR x3 positions 9, 49, 59
ELY x4 positions 13, 33, 43, 53
SIU x2 positions 14, 44
HMS x2 positions 15, 25
APD x2 positions 16, 21
NPV x2 positions 31, 51
CAJ x2 positions 32, 52
OIQ x2 positions 34, 54
FMT x2 positions 35, 55
LPQ x2 positions 36, 41
IPM x2 positions 56, 61