Experiment 106

“A one-to-one letter substitution with every move built so far: paths, mixed turns, triple turns and the type-1 library”

0019 tested a monoalphabetic substitution with 23,931 routes. Since then experiments 80-99 built far larger move sets: the type-1 library (27,852), grid paths (43,579), mixed-sense double turns (53,743) and every triple clockwise turn (1.7 million). A one-to-one substitution commutes with any move, so one test covers both orders: the known letters must land on carved letters that a single one-to-one table can explain.

revertedstatus
experiment 19parents
2 mintime, all phases
0candidates
0/24known letters
unclocked
1

The experiment method

What the method does with the 24 known letters.

The simplest two-step cipher swaps each letter for another by a fixed table and then moves the letters around. Experiment 19 tried this with about 24,000 ways of moving letters. Since then we have built ways of moving letters by the million. For each one we check whether a single swap table can turn the known lettersthe known letters Sanborn has confirmed that positions 22 to 34 of the message read EASTNORTHEAST and positions 64 to 74 read BERLINCLOCK. into the carved lettersthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. where they land: the same letter must always become the same letter.

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 ACCENTswap letters by one fixed table, then move them: the move here is snake rows of 10 read by columnsEASTNORTHEASTBERLINCLOCKBLSWSZKIBNVTPKDKJCGKAUCAwhere each known letter lands, and the carved letter thereE at places 22, 31, 65 lands on B, U, Z: one table would have to turn E into all threea swap table needs every known letter to land on one carved letter, and no two letters on the same onetype-1 library27,852 movesconsistent: K4 0, ten scrambled coppers 0grid paths42,978 movesconsistent: K4 0, ten scrambled coppers 0mixed double turns53,214 movesconsistent: K4 0, ten scrambled coppers 0triple clockwise turns1,711,697 movesconsistent: K4 0, ten scrambled coppers 01,835,741 moves in all: no table fits, on the copper or any scrambled copyOUT: NO READING; NO SWAP TABLE FITS ANY MOVEEASTNORTHEASTBERLINCLOCK
the cipher

The simplest two-step cipher swaps each letter for another by a fixed table, then moves the letters around. Experiment 19 tried about 24,000 moves; since then the project has built them by the million.

the check

For each move, the same known letter must always land on the same carved letter, and two different known letters never on the same one. E alone, three times among the cribs, is a strong test.

the bound

1,835,741 moves in four sets: not one admits a swap table, on K4 or on any 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. Pick a move, say snake rows of 10 read by columns.
  2. Find where each known letter lands and read the carved letter there.
  3. E occurs three times among the known letters (places 22, 31 and 65): all three must land on the same carved letter.
  4. And two different known letters must never land on the same carved letter.
  5. Repeat for every move in the four sets and on scrambled coppers.
the worksheet: the first steps by hand, on squared paper
SNAKE ROWS OF 10, READ BY COLUMNS: THE KNOWN LETTERS AND THE CARVED LETTERS WHERE THEY LANDA23 > 23: L, 32 > 83: CB64 > 37: WC70 > 95: C, 73 > 78: KE22 > 13: B, 31 > 92: U, 65 > 47: ZH30 > 91: AI68 > 77: DK74 > 68: TL67 > 67: V, 71 > 96: AN26 > 53: K, 69 > 86: GO27 > 63: B, 72 > 87: KR28 > 73: P, 66 > 57: IS24 > 33: S, 33 > 74: KT25 > 43: S, 29 > 82: J, 34 > 64: NEach row lists a known letter, theplaces it occupies, where the moveputs each, and the carved letterthere.A swap table needs each row to show asingle carved letter, different fromevery other row. Rows in accentalready show two or three: dead.
4

Worked example, generated

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

snake rows of 10, read by columns: the known letters and the carved letters where they land

letter  places (lands at: carved)
     A  23 (23: L), 32 (83: C)
     B  64 (37: W)
     C  70 (95: C), 73 (78: K)
     E  22 (13: B), 31 (92: U), 65 (47: Z)
     H  30 (91: A)
     I  68 (77: D)
     K  74 (68: T)
     L  67 (67: V), 71 (96: A)
     N  26 (53: K), 69 (86: G)
     O  27 (63: B), 72 (87: K)
     R  28 (73: P), 66 (57: I)
     S  24 (33: S), 33 (74: K)
     T  25 (43: S), 29 (82: J), 34 (64: N)

a single swap table needs every row to show one carved letter, different from every other row
5

Hypothesis, for a cryptanalyst

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

Family 9 (least covered, two experiments), open 'only for routes outside the set (spirals, diagonals, keyed routes)' (families.md); 0018 found substitution-then-transposition the only construction reproducing the width-21 repeats. Model: c = route(sigma(p)) = sigma(route(p)), sigma any permutation of 26 letters. Test: for the 24 known letters at their landing places, equal message letters must land on equal carved letters and different on different. Route sets: the type-1 library (K3's rule, one and two clockwise turns, plain and true-keyword columnar, forward and inverse); 0092's 30 x 29 path pairs at widths 2-96; 0099's mixed-sense double turns; 0083's triple clockwise turns at widths 2-96; all deduplicated. Ten shuffled coppers. Survivors decrypt wherever sigma is fixed and are scored.

6

Prediction

Written before the run; the result decides it.

No route of any set survives on K4, and none on the shuffled coppers, as in 0019. Zero candidates.

7

Method

  1. Build the four route sets and deduplicate (by a 64-bit hash of each route).
  2. For each route and text, map each known letter to the carved letter at its landing place; reject on a clash.
  3. Count survivors per set on K4 and ten shuffled coppers.
  4. Decrypt survivors where the table is fixed and score them.
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

Routes tested: {'type-1 library': 27852, 'grid paths': 42978, 'mixed double turns': 53214, 'triple clockwise turns': 1711697}. Consistent (K4 / controls): none on any text.

What was searched, as the harness recorded it.

family
one-to-one substitution (commutes with the move) with four route sets
routes by set
type-1 library
27,852
grid paths
42,978
mixed double turns
53,214
triple clockwise turns
1,711,697
stopped
None
consistent by set
k4 survivors
none
n k4 survivors
0
controls
10 shuffled coppers (seed 106), identical test

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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