Experiment 102

“The period-3 free-alphabet excess, against 400 scrambled coppers and 400 that keep K4's width-21 columns”

0100 left one cell above all 50 coppers: Quagmire IV at period 3 after a move, 12 distinct equation sets against 0-11. Here the four period-3 cells (one alphabet or a pair, key after or before the move) are counted against 400 plain shuffles, with a look-elsewhere correction across the four, and against 400 copies of K4 whose 21-wide grid has its columns shuffled, which keeps every pair of letters 21 apart and so K4's width-21 repeats.

revertedstatus
experiment 100parents
3 mintime, all phases
0candidates
0/24known letters
unclocked
1

The experiment method

What the method does with the 24 known letters.

In experiment 100 one count stayed higher on K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. than on fifty scrambled copies. K4 has a known oddity: letters 21 places apart repeat in pairs more than chance. Because 21 is a multiple of 3, that oddity could raise this count by itself. So we compare K4 with 400 ordinary scrambles and with 400 scrambles that keep the oddity, by moving whole columns of a 21-wide grid around.

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 ACCENTK4 repeats letter pairs 21 apart; 21 is a multiple of 3, so a fairer chance level keeps them: shuffle whole columns of a 21-wide gridK4 in rows of 21: 11 repeated pairsOBKRUOXOGHULBSOLIFBBWFLRVQQPRNGKSSOTWTQSJQSSEKZZWATJKLUDIAWINFBNYPVTTMZFPKWGDKZXTJCDIGKUHUAUEKCARa copy, columns shuffled (first 13 among themselves, last 8 too): 11KHBUUOXROLOBGSBIBWLOFRGLQKRPVQSFSNOJTSQWTQEJSZKAWKZLSUTDFWNBAIIPPYTKZMVTWNGFDCXJDZKTKKGHCUAUUAIREa pair of unknown alphabets with a 3-letter key, after a move: distinct ways it fits, out of 27,853 moves400 letter shufflesmean 4.81max 23p = 0.043400 shuffles of whole columnsmean 6.21max 26p = 0.10K4: 12the other three cells give K4 0, p 1.0; over all four, the chance that some cell does as well as K4's best under shuffles is 0.048keeping K4's pairs at 21 raises p from 0.043 to 0.10: the period-3 excess is not significantOUT: NO READING; THE PERIOD-3 EXCESS IS CHANCEEASTNORTHEASTBERLINCLOCK
the doubt

Experiment 100 left one count higher on K4 than on fifty scrambles. K4 also repeats letter pairs 21 apart more than chance, and 21 is a multiple of 3, which could raise a period-3 count by itself.

the test

So K4 is compared with 400 ordinary scrambles and with 400 copies that move whole columns of a 21-wide grid, which keeps every pair 21 apart.

the result

K4's 12 beats the ordinary scrambles with p 0.043, but against copies that keep the pairs p is 0.10, and allowing for four cells it is 0.048 even under scrambles. Not significant.

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. Write K4 in rows of 21; the last row has 13 letters.
  2. Shuffle the first 13 columns among themselves and the last 8 among themselves; every pair of letters 21 apart stays a pair.
  3. For each move, test whether some pair of alphabets with a 3-letter key fits the 24 known letters, and collect the distinct ways it fits.
  4. Compare K4's count with the counts on these copies and on ordinary scrambles.
the worksheet: the first steps by hand, on squared paper
K4 IN ROWS OF 21, AND ONE COPY WITH ITS COLUMNS SHUFFLED (13 SHORT-ROW COLUMNS AMONG THEMSELVES, 8 AMONG THEMSELVES)OKBHKBRUUUOOXXORGOHLUOLBBGSSOBLIIBFWBLBOWFFRLGRLVQQKQRPPRVNQGSKFSSSNOOTJWTTSQQSWJTQQSESJESKZZKZAWWAKTZJLKSLUUTDDIFAWWNIBNAFIBINPYPPYVTTKTZMMZVFTPWKNWGGFDDKCZXXJTDJZCKDTIKGKKGUHHCUUAAUUEUKACIARREThe last row holds 13 letters, so columns0-12 have five letters and 13-20 four: eachgroup is shuffled within itself. A letterand the one below it move together.Repeated pairs 21 apart: K4 11, the copy 11.The copy keeps K4's oddity but scrambleseverything else.
4

Worked example, generated

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

K4 in rows of 21, and one copy with its columns shuffled (13 short-row columns among themselves, 8 among themselves)

  OBKRUOXOGHULBSOLIFBBW
  FLRVQQPRNGKSSOTWTQSJQ
  SSEKZZWATJKLUDIAWINFB
  NYPVTTMZFPKWGDKZXTJCD
  IGKUHUAUEKCAR

  KHBUUOXROLOBGSBIBWLOF
  RGLQKRPVQSFSNOJTSQWTQ
  EJSZKAWKZLSUTDFWNBAII
  PPYTKZMVTWNGFDCXJDZKT
  KKGHCUAUUAIRE

letter pairs 21 apart that repeat: K4 11, the copy 11
5

Hypothesis, for a cryptanalyst

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

Follow-up of 0097 and 0100. Mechanism to test: carved places 21 apart share a key slot mod 3, and K4 has 11 repeated letter pairs 21 apart (0056), so a period-3 key after a move may fit K4 more often for that reason alone. Null A: 400 letter shuffles (seed 102). Null B: 400 column permutations of K4 written 21 wide, the 13 columns of the short last row permuted among themselves and the other 8 among themselves, so every vertical pair is kept. Cells: Quagmire III or IV, key after (A) or before (B) the move, period 3; type-1 library plus no move; distinct canonical equation sets; linear test mod 2 and mod 13 as in 0097. Report K4's p under each null and, under null A, the share of shuffles whose smallest p over the four cells is at most K4's.

6

Prediction

Written before the run; the result decides it.

Under plain shuffles K4's cell is near p 0.02, with a look-elsewhere p above 0.05; under the column permutations K4 is unremarkable (p above 0.2), so the excess comes from the width-21 repeats. Zero candidates.

7

Method

  1. Build the type-1 library and the two nulls.
  2. For each text, route and order, test the free-alphabet filter and the linear test at period 3 for both models, collecting distinct equation sets.
  3. Compute K4's p per cell under each null and the look-elsewhere p under null A.
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

III A: K4 0, shuffles mean 0.01 max 1 p 1.000, 21-column permutations mean 0.01 max 1 p 1.000; III B: K4 0, shuffles mean 0.0 max 0 p 1.000, 21-column permutations mean 0.0 max 0 p 1.000; IV A: K4 12, shuffles mean 4.81 max 23 p 0.043, 21-column permutations mean 6.21 max 26 p 0.100; IV B: K4 0, shuffles mean 0.0 max 0 p 1.000, 21-column permutations mean 0.0 max 0 p 1.000. Look-elsewhere over the four cells under shuffles: p 0.048.

What was searched, as the harness recorded it.

family
period-3 free-alphabet cells against two nulls
routes done
27,853
routes
27,853
nullA
400 letter shuffles (seed 102)
nullB
400 column permutations of K4 at width 21 (keep all 76 vertical pairs)
cells
III A
k4
0
nullA mean
0.01
nullA max
1
p nullA
1
nullB mean
0.01
nullB max
1
p nullB
1
III B
k4
0
nullA mean
0
nullA max
0
p nullA
1
nullB mean
0
nullB max
0
p nullB
1
IV A
k4
12
nullA mean
4.81
nullA max
23
p nullA
0.043
nullB mean
6.21
nullB max
26
p nullB
0.1
IV B
k4
0
nullA mean
0
nullA max
0
p nullA
1
nullB mean
0
nullB max
0
p nullB
1
k4 smallest p nullA
0.043
look elsewhere p nullA
0.048

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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