“D1: design 2's power against its budget: the tempering climb at full length and at a tenth, every number of runs 1-10, on clean and Sanborn-style plants at F1.1 L23 and F1.2 L13, each against its own copies”
D1 (issue #77), first measurement. Design 2 (F1.5) costs 20-30 min per setting: 10 independent tempering runs (16 replicas x 625 rounds x 1000 moves) on K4, 12 copies and a power test. Two cuts are measured here on the same plants: fewer runs (each run's best is recorded, so power at 1-10 runs comes from one pass) and runs a tenth as long (62 rounds, a second pass). Plants: clean Carter (0139's and 0143's rule) and A6.2's Sanborn-style classes (0226), at F1.1's Beaufort L23 (0140's compiled climb) and F1.2's L13 (0144's).
The best tool we have for judging the hardest cases is slow: for each setting it runs ten long searches on K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. and on a dozen scrambled copiesa shuffled control The same experiment run on the carved letters shuffled into a random order.. Here we hide test messages, run the tool, and note after every one of the ten searches, and with searches a tenth as long, whether the hidden message was already picked out. If it usually is, the tool can be made much cheaper without missing more, and settings we had to skip for cost can be judged.
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
The decider for the hardest cells runs ten long searches per text. If a hidden message is usually found in the first runs, or in short ones, it can be cut.
the check
259 texts (37 planted messages, clean and Sanborn-style, and 6 scrambled copies of each) climbed twice, every run's best written down.
the bound
At length 23 one full run finds as many as ten; at 13 nothing under nine does. With copies climbed one at a time, 3.5 times cheaper, short of ten. The ten-run power itself came out lower than recorded: messy 6 of 12 at 23, clean 2 of 5 at 13.
2
Experiment lineage
What this experiment was built on, from the lineage page: 15 experiments before it, back to the root of its line. Its number is in bold.
keptreverted, in its family's colour×error or timeoutreverted under today's rulesbuilt on a parent in the same familybuilt on a parent in another family
3
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 under Result and bounds below.
4
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Hide a test message under a shuffled alphabet and a key of 23 numbers.
Make six scrambled copies of its ciphertext that the same key length still fits.
Run the tempering search ten times on each of the seven texts, writing down the best score after each run.
After run 1, is the hidden message's best above all six copies' bests? After run 2? ... After run 10?
Repeat with runs a tenth as long.
Over many hidden messages, the share found after r runs is the tool's power at that budget.
the worksheet: the first steps by hand, on squared paper
5
Worked example, generated
The same steps run by the code on the real letters.
D1 measures how fast design 2 finds a planted message. For one plant and its six copies:
run 1 2 3 ... 10
plant best of runs 1..r
copies best of runs 1..r, each
found at r when the plant's best is above every copy's best.
Repeated with runs a tenth as long; power at each budget is the share of plants found.
6
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
F1.5 design 2 (parallel tempering in the set of keys that keep the 24 known letters; 0139-0146) decided F1.1 L23, L26 and F1.2 L8, L13, L16 at measured power; F1.4's free-alphabet residue (about 1,900 settings), F1.7's fitting lags (about 100), F6.1 (about 443,000) and F6.2 3-14 are blocked by its cost. A tempering run either reaches the basin of the planted reading or not; if most plants are found in the first runs, or in short runs, the decider can be cut without losing power. Separately and exactly, copies can be climbed one at a time, stopping at the first that beats the target: the decision 'target above every copy' is unchanged, and under the null the target is exchangeable with its copies, so the expected number climbed is H_12 = 3.1 instead of 12 (no run needed; stated here). Test: per plant, found at budget (rounds, r) when the best of its first r runs is strictly above the best of the first r runs of each of its 6 own copies (null 1/7). Pre-registered: the reference is the full budget (625 rounds, 10 runs) measured in this run; a cheaper budget qualifies when its power is at least the reference's on clean and on Sanborn-style plants at both lengths; D1 is reached when the cheapest qualifying budget times the sequential-copies factor is at least ten times cheaper per setting. Also reported: design 2's power on 12 fresh Sanborn-style plants at L13, beside 0226's 9 of 12 (the reopened F1.2 L13 cell).
7
Prediction
Written before the run; the result decides it.
Power saturates early: at full length 3 runs reach the reference power at L23 and 5 at L13; runs a tenth as long lose power (about two thirds of the reference at L23, half at L13). With sequential copies, 3 full runs give about 3.3 x 3.1 = 10 times cheaper per setting at L23: D1 reached at L23, not at L13. Design 2 on fresh Sanborn-style plants at L13: 9-11 of 12. Zero candidates.
8
Method
L23: 8 clean plants (0120's make_plants rule) and 12 Sanborn-style (0226's class texts, arm 0: 4 xstops, 4 K1-K3 windows, 4 with three letters changed), each enciphered in the Beaufort form with a random alphabet and key of 23; 6 own copies each, shuffles that 0120's exact decider fits at 23.
L13: 5 clean plants (0144's plant4) and 12 Sanborn-style (arm 1), two random alphabets and a key of 13; witness from 0123's decider under a 20 s alarm (0226's rule); 6 kept-place copies each, the plant's witness as start.
Every text climbed twice with 0140's and 0144's compiled tempering, same replicas, moves and temperatures: 10 runs of 625 rounds and 10 runs of 62 rounds, each run's best score recorded with its wall time.
Power at every (rounds, r), r = 1-10, by class and length; cost per text from the measured times.
9
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
reference power L23 clean (6, 8), messy (6, 12); L13 clean (2, 5), messy (8, 12); cheapest qualifying budget (625, 9); per-setting factor with sequential copies 3.5
What was searched, as the harness recorded it.
item
D1
decider
F1.5 design 2: 0140's (L23, one alphabet, Beaufort) and 0144's (L13, two alphabets) compiled tempering
plants
23
clean
8
sanborn style
12
13
clean
5
sanborn style
12
own copies
6
null per plant
1/7
rounds
625, 62
runs
10
reference
23
clean
6, 8
messy
6, 12
cost
1
13
clean
2, 5
messy
8, 12
cost
1
power table
23/625/1
clean
6, 8
messy
7, 12
cost
0.1
23/625/2
clean
7, 8
messy
8, 12
cost
0.2
23/625/3
clean
6, 8
messy
7, 12
cost
0.3
23/625/4
clean
6, 8
messy
8, 12
cost
0.4
23/625/5
clean
6, 8
messy
7, 12
cost
0.5
23/625/6
clean
6, 8
messy
8, 12
cost
0.6
23/625/7
clean
6, 8
messy
8, 12
cost
0.7
23/625/8
clean
6, 8
messy
7, 12
cost
0.8
23/625/9
clean
6, 8
messy
7, 12
cost
0.9
23/625/10
clean
6, 8
messy
6, 12
cost
1
23/62/1
clean
4, 8
messy
6, 12
cost
0.01
23/62/2
clean
5, 8
messy
6, 12
cost
0.02
23/62/3
clean
4, 8
messy
8, 12
cost
0.03
23/62/4
clean
4, 8
messy
7, 12
cost
0.04
23/62/5
clean
4, 8
messy
8, 12
cost
0.05
23/62/6
clean
5, 8
messy
8, 12
cost
0.059
23/62/7
clean
5, 8
messy
9, 12
cost
0.069
23/62/8
clean
5, 8
messy
10, 12
cost
0.079
23/62/9
clean
5, 8
messy
8, 12
cost
0.089
23/62/10
clean
5, 8
messy
8, 12
cost
0.099
13/625/1
clean
0, 5
messy
8, 12
cost
0.1
13/625/2
clean
1, 5
messy
9, 12
cost
0.2
13/625/3
clean
1, 5
messy
9, 12
cost
0.3
13/625/4
clean
1, 5
messy
9, 12
cost
0.4
13/625/5
clean
1, 5
messy
8, 12
cost
0.5
13/625/6
clean
1, 5
messy
8, 12
cost
0.6
13/625/7
clean
1, 5
messy
8, 12
cost
0.7
13/625/8
clean
1, 5
messy
8, 12
cost
0.8
13/625/9
clean
2, 5
messy
8, 12
cost
0.9
13/625/10
clean
2, 5
messy
8, 12
cost
1
13/62/1
clean
1, 5
messy
10, 12
cost
0.01
13/62/2
clean
4, 5
messy
11, 12
cost
0.02
13/62/3
clean
3, 5
messy
11, 12
cost
0.03
13/62/4
clean
1, 5
messy
10, 12
cost
0.04
13/62/5
clean
0, 5
messy
10, 12
cost
0.05
13/62/6
clean
1, 5
messy
10, 12
cost
0.059
13/62/7
clean
1, 5
messy
11, 12
cost
0.069
13/62/8
clean
1, 5
messy
11, 12
cost
0.079
13/62/9
clean
2, 5
messy
11, 12
cost
0.089
13/62/10
clean
2, 5
messy
11, 12
cost
0.099
power by class full budget
23/clean
6, 8
23/xstops
2, 4
23/k123
2, 4
23/sub3
2, 4
13/clean
2, 5
13/xstops
2, 4
13/k123
3, 4
13/sub3
3, 4
qualifying budgets
625, 9
625, 10
cheapest qualifying
625, 9
sequential copies factor
3.17
sequential copies note
exact: stop climbing copies at the first that beats the target; same decision; expected copies under the null H_12 = 3.10
cost factor per setting
3.5
d1 reached
no
seconds per text
13/625
207
13/62
24.7
23/625
167.4
23/62
18.9
f12 l13 sanborn style full budget
8, 12
f12 l13 with 0226
0226: 9 of 12
texts
259
climbs
518
compute seconds
6,714
exhaustive
no
expected total time
about 47,700 core-seconds (140 texts at about 121 s for L23, 119 at about 259 s for L13, both passes), 100 min on 8 cores
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 2026-11-05 17:14 UTC; updated after every experiment.