“F1.2: design 2 carried to two free alphabets (Quagmire IV), its power measured on planted English at key lengths 8, 13 and 16 against copies that keep the known places”
F1.2, the second half of 0141, which crashed. Design 2 (parallel tempering in the set that keeps every known-letter check) over two independent alphabets, C(c) = P(p) + k, at the three lengths 0136 leaves under the quadgram bound (open bits 89, 112, 126 against 130). Controls changed for cost: 0141 drew fully shuffled copies that fit, but the exact two-alphabet decider takes minutes per shuffle; here each copy keeps the plant's carved letters at the 24 known places and shuffles the other 73, so it fits by construction and differs from the plant only in the order of the letters the English test reads. Every text starts from the plant's exact witness (0123's decider), randomised by 400 check-keeping swaps; a text whose search finishes no run is reported, not dropped.
The search that notices planted English under one scrambled alphabet is extended to two scrambled alphabets, one for the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. and one for the carved lettersthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page., and checked on planted English at three key lengths. Each planted message is compared with copies that keep the letters at the 24 known places and scramble the rest, so only the order of the other letters differs. If it notices the English often enough, it may judge the carved text at that length.
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
A variant of the sculpture's table uses two scrambled alphabets, one for the message and one for the carved letters. 0136 showed English could decide it at key lengths 8, 13 and 16. Design 2 is extended to both alphabets.
the check
Five planted English texts per length, each against five copies that keep the carved letters at the 24 known places and shuffle the other 73; the same search on all.
the bound
Planted texts beat all their copies 5 times in 5 at 13 and 4 in 5 at 16. At 8 the search, slower with 16 checks, ran last and did not finish: no verdict.
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.
Encipher a passage of English with two random alphabets and a random key of length 8, known words in place.
Make five copies that keep the carved letters at the 24 known places and shuffle the other 73.
Find one pair of alphabets that gives all 24 known letters; it works for the copies too, since their known places are the same.
Run sixteen searches side by side from that pair, swapping letters within either alphabet while every check holds, scoring the whole text as English.
The planted text is noticed if it beats all five copies; luck gives that one time in six.
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.
key length 23, Beaufort form: K4 in rows of 23; each column is one key slot
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
the seven checks every move keeps (place(carved) + place(known) equal within a column):
column 0: R+S (24) = M+C (70)
column 1: V+T (25) = Z+L (71)
column 2: Q+N (26) = F+O (72)
column 3: Q+O (27) = P+C (73)
column 4: P+R (28) = K+K (74)
column 21: F+E (22) = T+I (68)
column 22: L+A (23) = T+N (69)
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C27(c) (the 'slightly different' tableau), C1(b). Model: 0123's Quagmire IV, two unknown bijections P, C, key length L in {8, 13, 16}, checks 16, 11, 8. Search: replica exchange, 16 replicas, T 0.1 -> 0.002, 10 runs x 625 rounds x 1,000 moves per text (0139's effort), moves swap two places in one alphabet, repaired by a second swap when a check breaks; full-text quadgram mean. Power: 5 planted texts per length (Carter windows, seed 143), each against 5 copies keeping the 24 known places (seed 1431); null 1/6 per plant (0.83 of 5). Bar fixed before the run: at least 4 of 5 beat all their own copies. A passing length gets K4 against copies of K4 kept the same way in the next run; a failing length stays blocked (no power).
6
Prediction
Written before the run; the result decides it.
Power falls with the number of checks and the doubled freedom: at least 4 of 5 at length 8 (16 checks), fewer at 13 and 16. No planted text recovered. Zero candidates.
7
Method
5 planted Quagmire IV texts per length and 5 kept-place copies of each.
0123's decider gives each plant an exact witness; it starts the plant and its copies.
The compiled two-alphabet tempering search on all 90 texts; decryption checked against Python.
Per length: plants beating all their own copies.
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
Quagmire IV power: L8 1/5 (16 checks), L13 5/5 (11 checks), L16 4/5 (8 checks); runs per text 0-10
What was searched, as the harness recorded it.
family
two free alphabets (Quagmire IV), periodic key 8, 13, 16, no move: power of design 2 on planted English
search
parallel tempering, 10 runs x 16 replicas x 625 rounds x 1000 moves per text, T 0.1->0.002; start from the plant's exact witness (0123) randomised by 400 check-keeping swaps
not exhaustive
yes
runs done
min
0
max
10
texts with no finished run
27
c decryption checked
yes
copies
keep the carved letters at the 24 known places, shuffle the other 73 (fit by construction)
bar
>= 4 of 5 plants beat all 5 own copies (null 0.83)
by length
8
checks
16
found
1
passes bar
no
rows
score
-5.239
letters right
39
runs
4
own copies
-99, -99, -99, -5.821, -5.576
rank among own
1
found own
yes
recovered
no
score
-99
letters right
None
runs
0
own copies
-99, -99, -99, -99, -99
rank among own
1
found own
no
recovered
no
score
-99
letters right
None
runs
0
own copies
-99, -99, -99, -99, -99
rank among own
1
found own
no
recovered
no
score
-99
letters right
None
runs
0
own copies
-99, -99, -99, -99, -99
rank among own
1
found own
no
recovered
no
score
-99
letters right
None
runs
0
own copies
-99, -99, -99, -99, -99
rank among own
1
found own
no
recovered
no
13
checks
11
found
5
passes bar
yes
rows
score
-4.675
letters right
41
runs
10
own copies
-4.93, -4.831, -4.811, -4.738, -4.682
rank among own
1
found own
yes
recovered
no
score
-4.733
letters right
45
runs
10
own copies
-4.993, -4.989, -4.987, -4.928, -4.809
rank among own
1
found own
yes
recovered
no
score
-4.719
letters right
35
runs
10
own copies
-4.927, -4.921, -4.898, -4.854, -4.756
rank among own
1
found own
yes
recovered
no
score
-4.516
letters right
39
runs
10
own copies
-4.831, -4.827, -4.822, -4.71, -4.707
rank among own
1
found own
yes
recovered
no
score
-4.58
letters right
47
runs
10
own copies
-5.016, -4.997, -4.978, -4.832, -4.788
rank among own
1
found own
yes
recovered
no
16
checks
8
found
4
passes bar
yes
rows
score
-4.562
letters right
39
runs
10
own copies
-4.694, -4.677, -4.635, -4.616, -4.615
rank among own
1
found own
yes
recovered
no
score
-4.541
letters right
35
runs
10
own copies
-4.73, -4.7, -4.659, -4.629, -4.531
rank among own
2
found own
no
recovered
no
score
-4.553
letters right
32
runs
10
own copies
-4.754, -4.689, -4.656, -4.637, -4.588
rank among own
1
found own
yes
recovered
no
score
-4.567
letters right
42
runs
10
own copies
-4.682, -4.627, -4.619, -4.619, -4.615
rank among own
1
found own
yes
recovered
no
score
-4.365
letters right
52
runs
10
own copies
-4.645, -4.605, -4.57, -4.561, -4.465
rank among own
1
found own
yes
recovered
no
controls
per plant, 5 kept-place copies (seed 1431)
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.