“F1.5 design 2: parallel tempering in the set that keeps the known letters, measured on planted English against scrambled copies of itself (one free alphabet, Beaufort form, key length 23)”
F1.5, step 2, design 2. Design 1 (0137) failed its validity check (0138): against shuffles of themselves only 6 of 12 planted texts beat all six copies (bar 9). The climb never recovers a planted text; the true key is a narrow basin (about 12 check-keeping swaps wide, dry runs) in a landscape of false optima. Design 2 replaces independent annealing restarts with parallel tempering: 16 replicas at temperatures 0.1 to 0.002 that exchange states, the standard remedy for rugged landscapes, at the same compute per text (10 runs x 16 replicas x 625 rounds x 1,000 moves = 10^8 moves). Bar measured as in 0138, each plant against its own shuffles.
A second way of searching for hidden Englisha planted message A real English passage, with the 24 known letters written in at their places, enciphered by the method under test with a random key. under one scrambled alphabet. Instead of starting the search a thousand times from scratch, sixteen searches run side by side, some bold and some cautious, and swap places when a bold one finds something promising. We again test it on planted English, comparing each planted message only with scrambled copies of itself. If it cannot tell them apart well, we stop trying to build such a search and record the cells as undecidable with today's tools.
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
Design 1 noticed planted English only at even odds. Design 2 runs sixteen searches side by side at different boldness, swapping states, the usual remedy when the true answer sits in a narrow pit among many false ones.
the check
8 planted texts at length 23, each against 6 shuffles of its own letters that still fit the known letters; the same compute per text as design 1.
the bound
6 of 8 beat all their own copies (luck gives 1.1; bar 6): design 2 passes. Still no planted text recovered; it notices English it cannot read.
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 a random alphabet and a random 23-letter key, the Beaufort way, with the known words in place.
Make six shuffles of its carved letters that could still give the known letters.
Start sixteen searches on the same text, each at its own boldness (temperature), each moving only between alphabets that keep the known letters right.
After every round, let neighbouring searches swap their current alphabets when the cooler one would gain.
Keep the best score seen; do the same on the six shuffles.
The planted text counts as noticed if it beats all six shuffles; luck gives that one time in seven.
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), C1(b) as 0137. Cell: one unknown alphabet, Beaufort form, key length 23 (7 checks), 75 open bits against 130 bits of quadgram evidence (0136). Search: replica exchange Monte Carlo over the alphabet in the set where every known-letter check holds (0137's moves and start), free key values as moves, full-text quadgram mean, geometric ladder T 0.1 -> 0.002, neighbour exchanges after every round. Dry run on 8 plants before this record (scratch): no plant recovered, best -4.71 to -4.91, 31-46 letters right. Plants: 8 Carter windows (seed 139, 0120's generator); own coppers: 6 shuffles of each plant's ciphertext that fit length 23 exactly (0119's decider). Null rate of a plant beating all 6: 1/7. Bar fixed before the run: design 2 passes if at least 6 of 8 plants beat all 6 of their own coppers. If it fails, F1.5 is blocked by its stop rule (two designs failed; issue #50).
6
Prediction
Written before the run; the result decides it.
No plant recovered; fewer than 6 of 8 plants beat all 6 of their own coppers (about the 50% of design 1), so design 2 fails the bar and F1.5 is blocked by its stop rule. Zero candidates.
7
Method
Draw 8 planted texts at length 23 and 6 fitting shuffles of each.
Run the compiled parallel-tempering search on all 56 texts at equal effort.
Per plant: found if its best is above all 6 of its own coppers; rank; letters right.
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
plants beating all 6 own coppers: 6/8 (null 1.1); beating all 0137 K4 coppers: 8/8; recovered 0; bar passed
What was searched, as the harness recorded it.
family
power check of 0137's climb: one unknown alphabet, Beaufort form, key length 23; each plant against shuffles of itself
search
parallel tempering, 10 runs x 16 replicas x 625 rounds x 1000 moves per text, T 0.1->0.002
plants
8
own coppers per plant
6
shuffles tried
110
restarts done
min
10
max
10
c decryption checked
yes
null rate found
0.143
null expected found
1.14
bar
design 1's power at 23 stands if >= 6 of 8 plants beat all 6 of their own coppers
plants found against own
6
passes bar
yes
plants recovered
0
plants found against 0137 k4 coppers
8
rows
score
-4.764
letters right
36
true score
-4.261
restarts
10
own coppers
-5.104, -5.023, -5.02, -5.001, -4.953, -4.931
rank among own
1
found own
yes
rank among k4 coppers 0137
1
recovered
no
score
-4.85
letters right
39
true score
-4.379
restarts
10
own coppers
-5.145, -5.063, -5.046, -4.989, -4.964, -4.94
rank among own
1
found own
yes
rank among k4 coppers 0137
1
recovered
no
score
-4.71
letters right
36
true score
-4.37
restarts
10
own coppers
-5.046, -5.037, -4.996, -4.924, -4.871, -4.852
rank among own
1
found own
yes
rank among k4 coppers 0137
1
recovered
no
score
-4.934
letters right
38
true score
-4.554
restarts
10
own coppers
-4.985, -4.976, -4.934, -4.929, -4.889, -4.885
rank among own
5
found own
no
rank among k4 coppers 0137
1
recovered
no
score
-4.694
letters right
41
true score
-4.244
restarts
10
own coppers
-5.108, -5.039, -5.034, -5.02, -4.942, -4.893
rank among own
1
found own
yes
rank among k4 coppers 0137
1
recovered
no
score
-4.805
letters right
37
true score
-4.532
restarts
10
own coppers
-5.202, -5.163, -5.057, -5.052, -5.034, -4.95
rank among own
1
found own
yes
rank among k4 coppers 0137
1
recovered
no
score
-4.731
letters right
42
true score
-4.192
restarts
10
own coppers
-5.144, -5.019, -5.003, -4.935, -4.932, -4.88
rank among own
1
found own
yes
rank among k4 coppers 0137
1
recovered
no
score
-4.795
letters right
34
true score
-4.152
restarts
10
own coppers
-5.071, -5.042, -5.025, -4.896, -4.861, -4.772
rank among own
2
found own
no
rank among k4 coppers 0137
1
recovered
no
controls
per plant, 6 shuffles of its own ciphertext that fit length 23 exactly (0119's decider, seed 139)
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.