Experiment 62

“Which ways of making a cipher leave the copper's two real fingerprints?”

Experiment 56 showed the width-7 doublet column and the width-21 repeats are real, not artefacts of looking at many widths. This builds thousands of fake K4s from English by constructions that carry a 7 or a 21 in their structure, and counts how often each one leaves either fingerprint, or both.

revertedstatus
experiment 56parents
2 stime, all phases
0candidates
0/24known letters
unclocked
1

The experiment method

What the method does with the 24 known letters.

We now know the copper has two genuine oddities tied to the numbers 7 and 21. A good way to find out what made them is to make fake coppers ourselves, from real English, by different recipes that involve a 7 or a 21, and see which recipes leave the same marks. Random lettersa shuffled control The same experiment run on the carved letters shuffled into a random order. and scrambled copies of the real copper show how often the marks turn up by accident.

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 ACCENThow often each recipe, on 4,000 stretches of English, makes each pattern as strongly as the copperdoubled letters in one column (width 7)pairs 21 apart repeatingciphertext autokey, lag 210.1%5.5%Vigenere, period 70.3%1.6%Vigenere, period 210.2%0.4%Vigenere, period 140.2%0.4%plaintext autokey, lag 70.1%0.4%Vigenere, period 280.1%0.2%Vigenere 27-29 then columnar width 210.2%0.2%columnar width 21 then Vigenere 27-290.3%0.2%columnar width 7 then Vigenere 27-290.2%0.2%ciphertext autokey, lag 70.2%0.1%both at once, in any recipe: 0 of 4,000only ciphertext autokey at distance 21 makes the repeats oftenOUT: NO READING; NO RECIPE MAKES BOTH PATTERNSEASTNORTHEASTBERLINCLOCK
the patterns

Experiment 56 showed that two patterns on the copper are real: five of six doubled letters in one column at width 7, and pairs of letters 21 apart repeating eleven times.

the recipes

Each recipe enciphered 4,000 stretches of Carter's book and K1 to K3, and the experiment counted how often each pattern came out as strong as on the copper.

the result

Ciphertext autokey at distance 21 makes the repeats 5.5% of the time, against well under 1% for most recipes, but nothing made both patterns together, and nothing makes the width-7 column.

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. Take a 97-letter stretch of Carter's book.
  2. Pick a random secret word of 7 letters and encipher the stretch on the sculpture's table, letter by letter.
  3. Find the doubled letters in the result and write it in rows of 7: note the fullest column.
  4. Count how often a pair of letters 21 places apart repeats.
  5. Do this four thousand times for each recipe and count how often both marks appear as strongly as on the copper.
the worksheet: the first steps by hand, on squared paper
THE TWO MARKS, COUNTED BY HAND ON ONE ENCIPHERED STRETCH, AS THE SIMULATOR COUNTS THEM ON 4,0001. Take 97 letters of Carter's book and encipherthem with one recipe, say a 7-letter secret wordon the sculpture's table.2. Find the doubled letters and write the resultin rows of 7: count the doubled letters in thefullest column.3. Write it in rows of 21 and count the letterpairs, one above the other, that occur twice.the coppercountdoubled letters6fullest column at width 75pairs 21 apart occurring twice11A recipe matches the copper only if onestretch reaches 5 in the column and 11repeats at once. None did in 4,000 triesof any recipe.
4

Worked example, generated

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

K4: doublet column mark True, width-21 repeat mark True
5

Hypothesis, for a cryptanalyst

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

Construction simulation (family 7, Oranchak's method) aimed at the two features 0056 confirmed: five of six doublets at one position mod 7, and 11 repeated pairs (c[i], c[i+21]). Plaintexts: 97-letter windows of Carter's Tomb of Tut-ankh-Amen (the K3 source) and the K1-K3 plaintexts. Generators, each 4,000 samples, random keys, KRYPTOS alphabet: Vigenere at periods 7, 14, 21 and 28; plaintext autokey at lags 7 and 21 (C11a 'interval 7'); ciphertext autokey at lags 7 and 21; columnar transposition of width 7 or 21 after a period 27-29 Vigenere; the same transposition before it; and two calibrations, random letters and shuffles of K4. Statistics as in 0056: the fullest doublet column at width 7 as a share of doublets (5 of 6 or stronger: at least 4 doublets and at most one outside the column), and repeats at width 21 >= 11. Report each rate and the joint rate. Diagnostic: no candidates; the calibrations are the controls.

6

Prediction

Written before the run; the result decides it.

No construction leaves both fingerprints in more than 2% of samples. Vigenere or transposition with a 7 in it raises the doublet column, and those with a 21 raise the repeats, but not together. The calibrations show both marks below 1%.

7

Method

  1. Draw 97-letter English windows.
  2. Encrypt each with each generator and a fresh random key.
  3. Compute the doublet column at width 7 and the repeats at width 21.
  4. Count the share of samples with the column, with the repeats, and with both.
  5. Compare with the calibrations.
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
34champion before

Rates (column / repeats / both): ciphertext autokey, lag 21: 0.001 / 0.054 / 0.0000; Vigenere, period 7: 0.003 / 0.015 / 0.0000; Vigenere, period 14: 0.002 / 0.004 / 0.0000; Vigenere, period 21: 0.002 / 0.004 / 0.0000; plaintext autokey, lag 7: 0.002 / 0.004 / 0.0000; columnar width 21 then Vigenere 27-29: 0.003 / 0.002 / 0.0000; plaintext autokey, lag 21: 0.003 / 0.002 / 0.0000; Vigenere 27-29 then columnar width 21: 0.002 / 0.002 / 0.0000; columnar width 7 then Vigenere 27-29: 0.002 / 0.002 / 0.0000; Vigenere, period 28: 0.001 / 0.003 / 0.0000; ciphertext autokey, lag 7: 0.002 / 0.002 / 0.0000; Vigenere 27-29 then columnar width 7: 0.002 / 0.002 / 0.0000; calibration: random letters: 0.002 / 0.002 / 0.0000; calibration: shuffled K4: 0.001 / 0.000 / 0.0000.

What was searched, as the harness recorded it.

family
construction simulation for the width-7 and width-21 fingerprints
samples per generator
4,000
k4
column
yes
repeats
yes
plaintext source
Carter vol. 1 (284,914 letters) and K1-K3
rates
Vigenere, period 7
column
0.003
repeats
0.015
both
0
Vigenere, period 14
column
0.002
repeats
0.004
both
0
Vigenere, period 21
column
0.002
repeats
0.004
both
0
Vigenere, period 28
column
0.001
repeats
0.003
both
0
plaintext autokey, lag 7
column
0.002
repeats
0.004
both
0
ciphertext autokey, lag 7
column
0.002
repeats
0.002
both
0
plaintext autokey, lag 21
column
0.003
repeats
0.002
both
0
ciphertext autokey, lag 21
column
0.001
repeats
0.054
both
0
Vigenere 27-29 then columnar width 7
column
0.002
repeats
0.002
both
0
columnar width 7 then Vigenere 27-29
column
0.002
repeats
0.002
both
0
Vigenere 27-29 then columnar width 21
column
0.002
repeats
0.002
both
0
columnar width 21 then Vigenere 27-29
column
0.003
repeats
0.002
both
0
calibration: random letters
column
0.002
repeats
0.002
both
0
calibration: shuffled K4
column
0.001
repeats
0
both
0

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.
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