Experiment 20

“The short periods come back: a periodic tableau at periods 1 to 52 with alphabets mixed from the puzzle's words”

0005 excluded periods 1-26 and 30-52 under the standard and KRYPTOS alphabets only. Here the plain and cipher alphabets range over the four Friedman mixings of every vocabulary word, which changes every forced key letter and so every consistency check. Family 1 re-entered with a new alphabet source.

revertedstatus
experiment 5parents
26 mintime, all phases
0candidates
0/24known letters
1

The experiment method

What the method does with the 24 known letters.

Earlier we ruled outdead Said of a period, grid or method when the known letters contradict it: no secret word of that kind can produce the carved letters. short secret words because two known letters that would share a letter of the word disagreed. But that reasoning assumed 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. was built from the word KRYPTOS or the plain alphabetthe plain alphabet A to Z in the usual order.. If the table was built from another word, say PALIMPSEST, the same two known letters make a different demand and might agree. There is also a hint in the carved textthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. that letters 21 apart were treated alike. So we rebuild the table from every word the puzzle knowsthe puzzle's words A list of 62 words tied to the sculpture: the earlier secret words, place names, the names of the people involved, the words in the Morse code, and the themes Sanborn has named., in four standard ways, and ask again which short lengths 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. allow.

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 ACCENTsettings that survive the known letters, by key length, over 184,512 alphabet pairs (bar height on a log scale)11021242630425221 and 42: none survives, so the width-21repeats are not a key of that lengththe coppera shuffled copper26: 7,454 survive on the copper and 7,204 on a shuffle, so chanceOUT: NO READING; NO SURVIVING KEY FRAGMENT READS AS A WORDEASTNORTHEASTBERLINCLOCK
the sweep

Repeating keys of length 1 to 52, with the plain and carved alphabets each rebuilt from a puzzle word in four ways (248 alphabets). A setting survives if no two known letters that share a key slot demand different key letters.

the counts

Below 24 nothing survives. At 26 thousands do, but just as many survive on a shuffled copper, so they say nothing about K4. From 27 up almost everything survives, because few known letters share a slot.

the width-21 question

Lengths 21 and 42 have no survivor at all, so the repeats seen when the copper is written in rows of 21 do not come from a repeating key of that length on these alphabets.

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. Build the alphabet from PALIMPSEST: PALIMSETBCDFGHJKNOQRUVWXYZ, and use it for the plaintext; keep KRYPTOS for the ciphertext.
  2. Position 22 is E, index 6; ciphertext F, index 11 in KRYPTOS; Vigenere gives key index 5.
  3. Position 64, which is 42 later, is B, index 8; ciphertext N, index 19; key index 11.
  4. At period 21 or 42 these two positions share a slot, so 5 must equal 11: it does not, and this alphabet pair is dead at 21 and 42.
  5. Try the next pair; eleven such checks apply at period 21.
  6. A pair that passes all eleven would be a real find: read off its forced key letters and see whether they spell a word.
the worksheet: the first steps by hand, on squared paper
KEY LENGTH 21 ON THE SCULPTURE'S TABLE: KNOWN PLACES THAT SHARE A SLOT MUST FORCE THE SAME KEY LETTERplacesslotkey at firstkey at second22 and 641RE23 and 652DL24 and 663UY25 and 674MO26 and 685RI27 and 696IE28 and 707YCPlaces a multiple of 21 apart use the sameslot of a 21-letter key. Each knownletter, over its carved letter, forces akey letter; the pair must agree.One disagreement kills key length 21 forthis table. The experiment repeats thecheck for every alphabet pair built fromthe puzzle's words.
4

Worked example, generated

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

plain alphabet PALIMPSEST/keyword PALIMSETBCDFGHJKNOQRUVWXYZ
cipher alphabet KRYPTOS KRYPTOSABCDEFGHIJLMNQUVWXZ

period 21 collisions: positions 42 apart share a slot

pos  plain  cipher  key index    pos  plain  cipher  key index   agree?
 22    E      F        6         64    B      N       11       no
 23    A      L       16         65    E      Y       22       no
 24    S      R       22         66    R      P       10       no
 25    T      V       15         67    L      V       20       no
 26    N      Q        4         68    I      T        1       no
 27    O      Q        3         69    N      T       14       no
5

Hypothesis, for a cryptanalyst

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

K4's eleven width-21 vertical repeats and the width-7 doublet column (0018, knowledge/04-structure.md) are what a key of period 21 or 42 would leave: positions 21 apart share a key letter, so English bigrams repeat vertically. 0005 and 0011 killed periods 1-26 and 30-52, but only with plain and cipher alphabets in {standard, KRYPTOS}; a tableau built on PALIMPSEST, ABSCISSA or any other word (Scheidt's keyword alphabets, C5, C29) gives different forced key indices and was never swept at these periods. For each pair of alphabets from the pool (standard, KRYPTOS, four mixings of each vocabulary word, 248 in all) and each of three modes, the forced key index at every crib position follows; for each period 1-52 the slots that collide must agree. Period 21 has eleven collisions, so a surviving pair there has chance probability 26 to the minus eleven per trial against 184,512 trials. Survivors at any period get the forced key letters read in the standard, KRYPTOS and keyword-mixed alphabets and scored as English; a vocabulary match is decrypted and submitted. Bounds: complete for this alphabet pool, periods 1-52, and the three modes.

6

Prediction

Written before the run; the result decides it.

No alphabet pair revives periods 1-26 or 30-52 except by chance at the periods with the fewest collisions, 23 to 26, where a few survivors appear per period; 30 to 52 are counted only. Period 21 and 42 have no survivor. No survivor's forced key matches the vocabulary; zero candidates pass.

7

Method

  1. Build the alphabet pool.
  2. For each plain alphabet, cipher alphabet and mode, compute the forced key index at each of the 24 crib positions.
  3. For each period 1-52, group the positions by slot and reject on any disagreement.
  4. Count survivors by period, with a shuffled-K4 control.
  5. For survivors, read the forced indices in each keyword-mixed key alphabet, match the fragment against the vocabulary and K1-K3 windows, score it as English, and decrypt any match.
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

184512 alphabet pairs x modes, periods 1-52. Short periods with survivors: {24: 1, 26: 7454}. Period 21: 0, period 42: 0. 0 vocabulary matches.

What was searched, as the harness recorded it.

family
periodic tableau, alphabets mixed from the vocabulary, periods 1-52
alphabets
248
alphabet pairs x modes
184,512
survivors by period
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
10
0
11
0
12
0
13
0
14
0
15
0
16
0
17
0
18
0
19
0
20
0
21
0
22
0
23
0
24
1
25
0
26
7,454
27
184,512
28
184,512
29
184,512
30
7,339
31
285
32
12
33
0
34
0
35
0
36
0
37
0
38
0
39
0
40
0
41
0
42
0
43
0
44
0
45
0
46
0
47
0
48
1
49
0
50
0
51
287
52
7,454
shuffled k4 survivors by period
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
10
0
11
0
12
0
13
0
14
0
15
0
16
0
17
0
18
0
19
0
20
0
21
0
22
0
23
0
24
0
25
19
26
7,204
27
184,512
28
184,512
29
184,512
30
7,243
31
286
32
0
33
0
34
0
35
0
36
0
37
0
38
0
39
0
40
0
41
0
42
0
43
0
44
0
45
0
46
0
47
0
48
0
49
0
50
19
51
316
52
7,204
short periods with survivors
24
1
26
7,454
period 21 survivors
0
period 42 survivors
0
best english fragments
  1. score
    -5.215
    period
    26
    plain
    CIA/alt_vertical
    cipher
    COMPASS/keyword
    key alphabet
    POSITION/keyword
    mode
    beau
    fragment
    HPIEIAFL...MMPLEASUNISBYAT
  2. score
    -5.23
    period
    26
    plain
    KRYPTOS/alt_vertical
    cipher
    DIGITAL/keyed_columnar
    key alphabet
    WEBSTER/keyword
    mode
    vig
    fragment
    YUNFORPW...RNUINBATEPANGFW
  3. score
    -5.249
    period
    26
    plain
    CIA/alt_vertical
    cipher
    COMPASS/keyword
    key alphabet
    SOMEWHERE/keyword
    mode
    beau
    fragment
    ISEDERFL...NNSLDRMTHEMAYRW
  4. score
    -5.253
    period
    26
    plain
    WORLDCLOCK/columnar
    cipher
    WILLIAMWEBSTER/columnar
    key alphabet
    INVISIBLE/keyword
    mode
    beau
    fragment
    EAXORTOR...IXATTEESGROATAH
  5. score
    -5.26
    period
    26
    plain
    SHADOWFORCES/alt_vertical
    cipher
    PALIMPSEST/alt_vertical
    key alphabet
    CLOCK/keyword
    mode
    beau
    fragment
    WVMENATV...KOVEDTHUYWINITA
  6. score
    -5.277
    period
    26
    plain
    KRYPTOS/keyed_columnar
    cipher
    TUTANKHAMEN/keyed_columnar
    key alphabet
    SOUTH/keyword
    mode
    beau
    fragment
    BEENTFST...OKENAYEDRVEABSD
  7. score
    -5.309
    period
    26
    plain
    CIA/alt_vertical
    cipher
    COMPASS/keyword
    key alphabet
    INTERPRETATION/keyword
    mode
    beau
    fragment
    HIEDEAFL...MMILDATUPETOYAR
  8. score
    -5.332
    period
    26
    plain
    MAGNETIC/alt_vertical
    cipher
    UNDERGRUUND/keyword
    key alphabet
    TWO/keyword
    mode
    vig
    fragment
    SEIMPDFT...THETTENBIQUEROC
  9. score
    -5.35
    period
    26
    plain
    ORDINATE/keyed_columnar
    cipher
    EAST/columnar
    key alphabet
    ILLUSION/keyword
    mode
    beau
    fragment
    BOVECSZF...HGORSAFTENLEDDO
  10. score
    -5.351
    period
    26
    plain
    DESPARATLY/alt_vertical
    cipher
    DESPERATELY/keyed_columnar
    key alphabet
    WILLIAMWEBSTER/keyword
    mode
    varbeau
    fragment
    REATOLHW...VSEBUSEFCOFANIT
  11. score
    -5.363
    period
    26
    plain
    CARNARVON/columnar
    cipher
    TUTANKHAMUN/keyed_columnar
    key alphabet
    SHADOW/keyword
    mode
    beau
    fragment
    WSRINJUS...MASITBISONRDLEX
  12. score
    -5.385
    period
    26
    plain
    TUTANKHAMUN/columnar
    cipher
    MAGNETIC/keyword
    key alphabet
    INVISIBLE/keyword
    mode
    varbeau
    fragment
    RECPGUEA...YMEGRALAIMSTALU
and 3 more
vocab matches
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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