Experiment 161

“F6.7: change, move, change with the two keyed stages on different tables (standard then KRYPTOS, or the reverse), key lengths 2-14 each, solved exactly”

F6.7 (pivot audit, issue #55, D5). 0080 tested a repeating key, a move, then a second repeating key, both on the same table. Here the two keyed stages use different tables: the standard alphabet first and the KRYPTOS alphabet second, or the reverse. With different tables the two keys no longer add, but each known letter still links one slot of the first key to one slot of the second by a one-to-one relation, so every connected group of slots has at most 26 consistent assignments: solved exactly. Moves: 0160's library (844 distinct: the four column readings at every width, K3's rule at every multiplier, forwards and inverted); key lengths 2-14 each; both orders of tables; each stage added or Beaufort-subtracted. Ten scrambled coppers.

revertedstatus
a new rootparents
3 mintime, all phases
0candidates
0/24known letters
unclocked
1

The experiment method

What the method does with the 24 known letters.

Two secret words, one used on the plain alphabetthe plain alphabet A to Z in the usual order.'s table and the other on the KRYPTOS table, with the letters moved in a grida grid Writing the message into rows of some width and reading it out in another order, column by column for instance, which shuffles the letters without changing them. between them. Because the tables differ, the two words cannot simply be added together, but each known letter still ties one letter of the first word to one letter of the second. Following those ties decides exactly whether any pair of words of lengths 2 to 14 fits, for each grid move, on the carved textthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. and on scrambled copies.

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 ACCENTconsistent settings, by the number of checks they pass: is K4's count above every copy's?012345678K4 above all ten copiesinside the copies' rangeinside at every level; at 8 checks K4 4, copies 0-4settings passing five or more checks: K4 and the ten scrambled copies (log scale)log10 count2.02.53.0K4 2.59K4 388, copies 300-504OUT: NO READING; TWO KEYS ON TWO TABLES ROUND A MOVE FIT K4 AS OFTEN AS SCRAMBLED COPIESEASTNORTHEASTBERLINCLOCK
the idea

A first key on the plain alphabet's table, a grid move, a second key on the KRYPTOS table (or the reverse): the two halves of the sculpture's alphabets used in turn. 0080 tried both keys on one table.

the check

Each known letter ties one letter of the first key to one of the second, one to one; following the ties decides every setting exactly: 844 moves, key lengths 2-14 each, on K4 and ten scrambled copies.

the bound

At every level of checks K4 sits inside the copies' range (5 or more: 388 against 300-504). Closed.

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. Encipher with a first word of length 5 on the plain-alphabet table.
  2. Write the result in rows of 9 and read down the columns.
  3. Encipher again with a second word of length 7 on the KRYPTOS table: the carved text.
  4. A known letter E at place 22 sits under first-word letter 22 mod 5 and, after the move, under second-word letter (its new place) mod 7.
  5. Guess the first-word letter: the E becomes a definite middle letter, and the carved letter then fixes the second-word letter.
  6. Follow every such tie; a contradiction for all 26 guesses rules the setting out.
the worksheet: the first steps by hand, on squared paper
ONE KNOWN LETTER, ONE TIE: PLAIN-ALPHABET TABLE FIRST, KRYPTOS TABLE SECONDfirst key lettermiddle letter (E + key)carved F, KRYPTOS tablesecond key letterA (0)EF - E12 - 11 = 1B (1)FF - F12 - 12 = 0C (2)GF - G12 - 13 = 25At place 22 the known E and the carved F tie the two keys: each guess for the first key's letter gives exactlyone letter for the second. Twenty-four ties, each between two slots, decide the setting.
4

Worked example, generated

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

first word on the plain-alphabet table, a grid move, second word on the KRYPTOS table

at a known place: guess the first-word letter v; the known letter plus v (plain alphabet) is the middle letter;
the carved letter minus the middle letter (KRYPTOS alphabet) is the second-word letter: one second letter per guess.
every known letter ties a first-word slot to a second-word slot this way; a contradiction for all 26 guesses rules the setting out.
5

Hypothesis, for a cryptanalyst

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

C1(a)/(c), C20(a) ('layer two'), C5(b) ('key word/s': two words), C27(c) (Sanborn's 'slightly different' table: the two halves of the work use the two alphabets). Model: y_i = A^-1(A(p_i) + s1 k1[i mod m]); carved c_{M(i)} = B^-1(B(y_i) + s2 k2[M(i) mod n]) with (A, B) = (standard, KRYPTOS) or (KRYPTOS, standard), s1, s2 in {+1, -1}, m, n 2-14. Each known letter gives k2[M(i) mod n] = s2 (B(c) - B(A^-1(A(p) + s1 k1[i mod m]))), a bijection between the two slot values; consistency decided by propagation over each component (26 trials per component). Checks = links - slots + components. Statistic fixed before the run: consistent settings with at least five checks on K4 against the coppers' range (0080's threshold), and the same count per check level.

6

Prediction

Written before the run; the result decides it.

No setting with five or more checks fits K4; counts at each check level inside the coppers' range. Zero candidates.

7

Method

  1. Build the 844 moves.
  2. For each text, move, table order, signs and key lengths m, n: the links (slot of k1, slot of k2) at the 24 known letters.
  3. Propagate each component from each of 26 values; consistent if one value closes every link.
  4. Count consistent settings by checks; compare K4 with the 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

844 moves x 169 key-length pairs x 8 table/sign settings: consistent with >= 5 checks K4 388 (coppers 300-504); by checks 1-4 K4 [15084, 3772, 1220, 524]

What was searched, as the harness recorded it.

family
change (table A), move, change (table B != A): two repeating keys of lengths 2-14 on different tables round one of 844 moves
moves
844
key lengths
2, 14
table orders
std then kry, kry then std
signs
4
consistent by checks
0
k4
11,816
coppers min
11,816
coppers max
11,816
1
k4
15,084
coppers min
14,812
coppers max
15,448
2
k4
3,772
coppers min
3,684
coppers max
4,052
3
k4
1,220
coppers min
1,088
coppers max
1,332
4
k4
524
coppers min
468
coppers max
552
5
k4
348
coppers min
276
coppers max
460
6
k4
16
coppers min
4
coppers max
32
7
k4
16
coppers min
0
coppers max
20
8
k4
4
coppers min
0
coppers max
4
k4 consistent with 5 or more checks
388
coppers with 5 or more
444, 300, 432, 344, 372, 388, 432, 468, 504, 360
k4 top
  1. move
    ccw84inv
    tables
    std then kry, signs +1+1
    m
    13
    n
    13
    checks
    9
  2. move
    ccw84inv
    tables
    std then kry, signs +1-1
    m
    13
    n
    13
    checks
    9
  3. move
    ccw84inv
    tables
    std then kry, signs -1+1
    m
    13
    n
    13
    checks
    9
  4. move
    ccw84inv
    tables
    std then kry, signs -1-1
    m
    13
    n
    13
    checks
    9
  5. move
    colr84inv
    tables
    std then kry, signs +1+1
    m
    13
    n
    13
    checks
    8
  6. move
    colr84inv
    tables
    std then kry, signs +1-1
    m
    13
    n
    13
    checks
    8
  7. move
    colr84inv
    tables
    std then kry, signs -1+1
    m
    13
    n
    13
    checks
    8
  8. move
    colr84inv
    tables
    std then kry, signs -1-1
    m
    13
    n
    13
    checks
    8
  9. move
    k3x23
    tables
    std then kry, signs +1+1
    m
    13
    n
    12
    checks
    7
  10. move
    k3x23
    tables
    std then kry, signs +1-1
    m
    13
    n
    12
    checks
    7
  11. move
    k3x23
    tables
    std then kry, signs -1+1
    m
    13
    n
    12
    checks
    7
  12. move
    k3x23
    tables
    std then kry, signs -1-1
    m
    13
    n
    12
    checks
    7
and 8 more
seconds
102
controls
10 shuffled coppers (seed 1607)
exhaustive
yes

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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