“Which ways of making a cipher put the doubled letters in one column of seven?”
Experiment 62 found no recipe that makes the copper's doublet column at width 7. This tries recipes built specifically to line doublets up in sevens: a key that feeds on the previous carved letter plus a repeating key of 7, a key with two equal neighbouring letters, the same reshuffle applied to every block of 7, and a key of 28 with a pattern every 7.
Five of the copper's six doubled lettersthe doublets Places where a carved letter is immediately followed by the same letter. sit in the same column when the carved lettersthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. are written in rows of seven, and experiment 56 showed that is no accident. We make thousands of fake coppers from real English with recipes that have a seven built in, and count how often each recipe puts the doublets in one column. The most promising recipe is an autokey cipheran autokey cipher A cipher that uses the message itself, or the scrambled text itself, as the secret word, each letter enciphered with the letter a fixed distance before it. that feeds on the previous carved letter, combined with a repeating secret wordthe secret word The word or string a cipher needs besides the method. of seven letters. Random lettersa shuffled control The same experiment run on the carved letters shuffled into a random order. and scrambled copies of the copper show how often the pattern turns up by luck.
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.
the column
Written in rows of 7, five of the copper's six doubled letters start in one column; experiment 56 showed that is not chance.
the recipes
Each recipe enciphered 4,000 stretches of Carter's book and K1 to K3, and the experiment counted how often the doubled letters lined up as on the copper.
the result
Ciphertext autokey at distance 1 with a 7-letter key does it 1.5% of the time, about five times a shuffled copper, but well short of the 5% the record predicted.
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.
Take a 97-letter stretch of Carter's book and a random secret word of 7 letters.
Encipher the first letter on the sculpture's table with the first key letter.
For each later letter, add its key letter and also the previous carved letter, counted along the sculpture's alphabet KRYPTOSABCDEFGHIJLMNQUVWXZ, and write the result.
A letter repeats its neighbour exactly when the plaintext letter plus its key letter counts to 26, back to K: A is 7th from K (counting K as 0) and N is 19th, so with key letter A in slot 5, every N in slot 5 makes a doublet.
Write the result in rows of 7 and look for a column holding most of the doublets.
Repeat four thousand times per recipe and count.
the worksheet: the first steps by hand, on squared paper
4
Worked example, generated
The same steps run by the code on the real letters.
plaintext SLOWLYDESPARATLYSLOWLYTHEREMAINSOFPASSAGEDEBRIS
key KRYPTOS repeating, plus the previous carved letter
carved DYCCTERFNXBGZCKPEOHJGIQDXPNLXHCMRMRBIWAXHTIXRNP
doublets at 0-based [2]; mod 7 [2]
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Family 7 (Oranchak's construction simulation), aimed at the width-7 doublet column that 0056 showed is real (five of six doublets at 0-based positions 18, 25, 32, 46, 67, all 4 mod 7). A ciphertext doublet c[i] = c[i+1] needs a mechanism tied to i mod 7. Candidates: (1) ciphertext autokey at lag 1 plus a period-7 key, c[i] = p[i] + k[i mod 7] + c[i-1]: a doublet appears exactly when p[i+1] = -k[(i+1) mod 7], so one column fires on a frequent plaintext letter; periods 14 and 28 for comparison. (2) plaintext autokey at lag 1 plus a period-7 key. (3) a period-7 key with two equal neighbouring letters, which passes plaintext doublets through in one column only. (4) a period-7 Vigenere and one fixed reshuffle of every block of 7, in either order. (5) a period-28 key whose steps at slots 4-5, 11-12, 18-19, 25-26 are equal (28 survives the crib sweep). (6) a period-7 Vigenere read out in columns of 7 from a width-14 grid. Plaintexts: 97-letter windows of Carter's Tomb of Tut-ankh-Amen and K1-K3 (C7(d)). 4,000 samples per recipe, KRYPTOS alphabet, random keys. Statistic as in 0056 and 0062: at least 4 doublets with at most one outside the fullest column of 7. Calibrations: random letters and shuffles of K4. Clue entries: C11a ('interval 7'), C1(a).
6
Prediction
Written before the run; the result decides it.
The ciphertext autokey at lag 1 with a period-7 key makes the doublet column in more than 5% of samples, at least ten times the calibrations (which stay below 0.5%). The key with two equal neighbouring letters makes it rarely (below 2%), because English doublets are few. The block reshuffles, the structured key of 28 and the width-14 read-out stay within twice the calibration rate.
7
Method
Draw 97-letter English windows.
Encipher each with each recipe and a fresh random key.
Find the doublets and write the text in rows of 7; note whether at least four doublets fall in one column with at most one elsewhere.
Count the share of samples with the mark, and the mean number of doublets.
Compare with random letters and shuffled K4.
8
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
Doublet-column rate (mean doublets): ciphertext autokey lag 1 plus a period-7 key: 0.0147 (3.76); ciphertext autokey lag 1 plus a period-28 key: 0.0073 (3.69); ciphertext autokey lag 1 plus a period-14 key: 0.0057 (3.74); period-7 Vigenere read out in columns of 7 (width-14 grid): 0.0035 (6.15); period-7 Vigenere, then one reshuffle of every block of 7: 0.0027 (3.74); calibration: shuffled K4: 0.0027 (3.49); period-7 key with two equal neighbouring letters: 0.0025 (3.57); one reshuffle of every block of 7, then period-7 Vigenere: 0.0020 (3.74); plaintext autokey lag 1 plus a period-7 key: 0.0018 (3.71); period-28 key with the same step at slots 4-5, 11-12, 18-19, 25-26: 0.0013 (3.72); calibration: random letters: 0.0010 (3.71).
What was searched, as the harness recorded it.
family
construction simulation for the width-7 doublet column
samples per recipe
4,000
k4
column
yes
doublets
6
plaintext source
Carter vol. 1 (284,914 letters) and K1-K3
rates
ciphertext autokey lag 1 plus a period-7 key
column
0.015
mean doublets
3.76
ciphertext autokey lag 1 plus a period-14 key
column
0.006
mean doublets
3.74
ciphertext autokey lag 1 plus a period-28 key
column
0.007
mean doublets
3.69
plaintext autokey lag 1 plus a period-7 key
column
0.002
mean doublets
3.71
period-7 key with two equal neighbouring letters
column
0.003
mean doublets
3.57
period-7 Vigenere, then one reshuffle of every block of 7
column
0.003
mean doublets
3.74
one reshuffle of every block of 7, then period-7 Vigenere
column
0.002
mean doublets
3.74
period-28 key with the same step at slots 4-5, 11-12, 18-19, 25-26
column
0.001
mean doublets
3.72
period-7 Vigenere read out in columns of 7 (width-14 grid)
column
0.004
mean doublets
6.15
calibration: random letters
column
0.001
mean doublets
3.71
calibration: shuffled K4
column
0.003
mean doublets
3.49
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.