Experiment 112

“Double columnar with the same English word both times, with a repeating key before or after”

0084 and 0085 tested double columnar with two keys from the puzzle's words; the dictionary is too large for every pair. The classic field double transposition uses one key word twice, which the whole dictionary allows. Here every dictionary word (true keyword order, repeats dropped or whole word) keys both passes, forward and inverse, with a repeating key of length 1-26 after or before.

revertedstatus
experiment 110parents
3 mintime, all phases
0candidates
0/24known letters
unclocked
1

The experiment method

What the method does with the 24 known letters.

Soldiers once enciphered by shuffling columns under a secret word, then doing it again with the same word, which is easy to remember. Here every word in an English dictionary is used that way, twice in a row, with a short repeating secret word on the tablethe table The right-hand half of the sculpture, 26 rows of the alphabet each shifted one place further, starting from the word KRYPTOS. before or after, against the 24 known lettersthe known letters Sanborn has confirmed that positions 22 to 34 of the message read EASTNORTHEAST and positions 64 to 74 read BERLINCLOCK..

Words in the margin are defined on the glossary page.

1.1

The method at work

The carved letters go in at the top; the reading comes out at the bottom.

OBKRUOXOGHULBSOLIFBBWEASTNORTHEASTOTWTQSJQSSEKZZWATJKLUDIAWINFBBERLINCLOCKWGDKZXTJCDIGKUHUAUEKCARIN: THE COPPER, ALL 97 LETTERS, THE 24 KNOWN PLACES IN ACCENTSHADOW twice: rows of 6, columns read 3 4 2 5 1 6; then the result in rows of 6 again, read the same wayEASTNORTHEASTBERLINCLOCKOSNERTBCNAIKATELTELCSHROafter the first shuffleRUOLLBWVPRTQSZZWIANZZJCAafter the secondthe E of place 22: letter 20, then 36, where the copper has T459,267 routes x 8 tables; dots: lowest and highest scrambled copperkey after: period 22 live06the copper: 4period 24 live0350the copper: 224period 25 live0222the copper: 204key before: period 25 live0242the copper: 199ten shuffled coppersthe copperOUT: NO READING; EVERY COUNT INSIDE THE SCRAMBLED COPPERS' RANGEEASTNORTHEASTBERLINCLOCK
the shuffle

The double column shuffle was the classic hand cipher of the 20th century, and often used one key word twice. Here every dictionary word is that word, the shuffle run twice and also undone.

the check

After both shuffles a repeating secret word on the table must give the copper's letters where the known letters landed; two known letters in one slot of the word must agree.

the bound

459,267 routes, keys of 1 to 26 letters before or after: nothing below period 22, and every count sits inside the range of ten scrambled coppers.

2

Best candidate against the known letters

This experiment produced no candidate: the search ruled everything out before a full text was built. Its product is the bounded negative in section 7.

3

Walkthrough, by hand

Redo the method on a few letters with pencil and paper.

  1. SHADOW gives the column order 3, 4, 2, 5, 1, 6.
  2. Write the 97 letters in rows of 6, read the columns in that order; write the result in rows of 6 again and read it the same way.
  3. Each known letter lands at a new place; with a key of length p after the move, letters sharing a slot must agree.
  4. Repeat for every word, key length and rule, and with the key before the move.
the worksheet: the first steps by hand, on squared paper
SHADOW TWICE: COLUMNS READ IN THE ORDER [3, 4, 2, 5, 1, 6], THEN AGAINplaceletterafter oneafter twocopper there22E2036T23A5225V24S8579Z25T6912L64B275UAfter one shuffle place 22 is letter20: column 4, row 4, the column readsecond. Letter 20 sits in row 4,column 2 of the second grid, readthird: 16 + 16 + 4 = 36.A key of p letters after the move putsplace 22's E in slot 36 mod p.
4

Worked example, generated

The same steps run by the code on the real letters.

SHADOW twice: columns read in the order [3, 4, 2, 5, 1, 6], then again

place  letter  after one  after two  copper there
   22       E         20         36             T
   23       A         52         25             V
   24       S         85         79             Z
   25       T         69         12             L
   64       B         27          5             U
5

Hypothesis, for a cryptanalyst

Family, key space, the constraint under test, and the clues it reads.

Type 1 (C1: 'double matrixes'); the U.S. Army double transposition used one key for both passes, and Scheidt taught field methods (C5: 'simple, can be remembered'). Routes: the 229,634 distinct column orders of 0110, each applied twice, forward and inverse, deduplicated. Key: periodic 1-26 after the move (slot = carved place mod p) or before it, 8 tableau classes, exact by slot agreement. Ten shuffled coppers.

6

Prediction

Written before the run; the result decides it.

Nothing consistent below period 20; counts inside the coppers' range, give or take one period. Zero candidates.

7

Method

  1. Turn every dictionary word into its two column orders; drop repeats.
  2. Apply each twice and take the inverse.
  3. Test periods 1-26 in both orders and 8 classes by slot agreement.
  4. Count per period on K4 and ten shuffled coppers.
8

Result and bounds

The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.

0candidates returned
0passed every gate
0/24known letters, best
–lowest loss
nonechampion before

229,634 distinct column orders from 234,428 words, 459,267 routes x 8 classes x 2 orders, periods 1-26. K4 live below 20: 0. Outside the control range: {'A': [], 'B': []}.

What was searched, as the harness recorded it.

family
double keyword columnar with the same dictionary word twice, then or before a periodic tableau key
words
234,428
distinct column orders
229,634
distinct routes
459,267
duplicates skipped
1
periods
1, 26
classes
8
k4 live by period
A
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 3, 224, 204, 854
B
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 199, 142,078
controls live by period min
A
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 173, 846
B
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 165, 137,750
controls live by period max
A
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 6, 8, 350, 222, 894
B
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 242, 144,613
periods outside control range
A
none
B
none
k4 live below 20
none
n k4 live below 20
0
controls
10 shuffled coppers (seed 112), identical search

How this experiment sits among the others is on the lineage page; its family's open hypotheses are on the families page.

Rendered from the record on 2026-10-18 12:26 UTC; updated after every experiment.
view on GitHub