“F12.4: a pencil session: K4 written out at widths 7, 8, 13, 14, 21, 24 and 31, six patterns noted by eye, each then tested against 1,000 shuffles”
F12.4. Stein: 'the process of discovery is often intuitive as well as analytic.' Before any search code, K4 was written out at the widths that matter with the known letters marked and looked at; these six patterns were noted and are tested here exactly as written, each against 1,000 letter-preserving shuffles: (1) the most copies of one letter in one column at width 7 (K: 4 of 8 at places 32, 46, 53, 74); (2) K, the commonest letter, in two adjacent width-7 columns (7 of 8: places 3, 32, 46, 53, 74, 87, 94); (3) the number of repeated bigrams (10: HU, SO, FB, GK, SS, QS, EK, KZ, TJ, DI); (4) how many of their spacings share the factor 4 (5 of 10: 20, 28, 32, 44, 48), Kasiski's test; (5) five of the six S's within 12 places (33-44: SSOTWTQSJQSS); (6) one letter three times at a fixed spacing of 2 or 3 (U at 88, 90, 92). An observation outside every shuffle becomes a new item.
We wrote the carved lettersthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. out in rows of different widths, as Stein did with pencil and paper, and noted what caught the eye: the letter K lining up in sevens, five S's crowded together, three U's two apart, letter pairs that repeat. Each is then checked against a thousand shufflings of the same letters; the eye finds patterns in random lettersa shuffled control The same experiment run on the carved letters shuffled into a random order. too.
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.
the idea
Stein: 'the process of discovery is often intuitive as well as analytic.' K4 written out in rows of 7, 8, 13, 14, 21, 24 and 31, the known letters marked, and every pattern noted before any code.
the check
Six patterns: the letter K lining up in two columns of seven, five S's crowded together, repeated letter pairs and their spacings, three U's two apart; each counted on a thousand shufflings of K4's letters.
the bound
Nothing beats every shuffling; the strongest two (1 in 250) were picked out by eye among many possible patterns. No new item.
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.
Write K4 in rows of 7 and find the Ks: four sit in the fifth column, three in the fourth.
Write K4 in a line and mark letter pairs that occur twice: ten of them; measure the distances between the two copies.
Mark the S's: five fall between places 33 and 44. Mark the U's at 88, 90, 92.
Shuffle the 97 letters and count the same things; repeat a thousand times; a pattern is real only if no shuffle matches it.
the worksheet: the first steps by hand, on squared paper
4
Worked example, generated
The same steps run by the code on the real letters.
K4 in rows of 7 (K in capitals, everything else lower case):
o b K r u o x
o g h u l b s
o l i f b b w
f l r v q q p
r n g K s s o
t w t q s j q
s s e K z z w
a t j K l u d
i a w i n f b
n y p v t t m
z f p K w g d
K z x t j c d
i g K u h u a
u e K c a r
K at places 3, 32, 46, 53, 74, 78, 87, 94
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Stein 1999 (knowledge/sources/stein-1999-cracking-the-courtyard-crypto.txt): looking before attacking; F12.2 (0168) measured the fixed battery. These six are by-eye findings, so their selection is post hoc: the multiple-comparison count is the number of patterns a reader could have noticed, larger than six; a pattern counts only if outside every shuffle. Statistic definitions are in the method and fixed before the run.
6
Prediction
Written before the run; the result decides it.
None of the six lies outside every shuffle (eye-found patterns in 97 letters are usually chance). Zero candidates.
7
Method
Statistics: (1) max over letters and residues mod 7 of the letter's count in that residue; (2) for the commonest letter, its largest count in two adjacent residues mod 7, as a share; (3) repeated bigrams (occurrences beyond the first); (4) repeated-bigram spacings divisible by 4; (5) for each letter with at least 6 copies, the shortest window holding all but one (smaller is more clustered); (6) the most equal letters in an arithmetic run with step 2 or 3.
1,000 shuffles (seed 1614); one-sided p in the direction observed.
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
(1) most of one letter in one width-7 column: K4 4, p 0.204; (2) commonest letter's share in two adjacent width-7 columns: K4 0.875, p 0.004; (3) repeated bigrams: K4 10, p 0.04; (4) repeated-bigram spacings divisible by 4: K4 5, p 0.021; (5) shortest window holding all but one copy of a 6-copy letter: K4 12, p 0.004; (6) most equal letters at a fixed step of 2 or 3: K4 3, p 0.198
What was searched, as the harness recorded it.
family
observation: six by-eye patterns in K4 against 1,000 shuffles
observations
observation
(1) most of one letter in one width-7 column
k4
4
shuffles min
2
shuffles max
5
p one sided
0.204
outside every shuffle
no
observation
(2) commonest letter's share in two adjacent width-7 columns
k4
0.875
shuffles min
0.375
shuffles max
0.875
p one sided
0.004
outside every shuffle
no
observation
(3) repeated bigrams
k4
10
shuffles min
0
shuffles max
14
p one sided
0.04
outside every shuffle
no
observation
(4) repeated-bigram spacings divisible by 4
k4
5
shuffles min
0
shuffles max
7
p one sided
0.021
outside every shuffle
no
observation
(5) shortest window holding all but one copy of a 6-copy letter
k4
12
shuffles min
8
shuffles max
68
p one sided
0.004
outside every shuffle
no
observation
(6) most equal letters at a fixed step of 2 or 3
k4
3
shuffles min
1
shuffles max
4
p one sided
0.198
outside every shuffle
no
outside every shuffle
none
note
selected by eye, so post hoc; only an observation outside every shuffle would become an item
controls
1000 letter-preserving shuffles (seed 1614)
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.