“F13.2: a classifier trained on 17 cipher families' own 97-letter ciphertexts (no known words), its power on held-out texts, and K4 named against 2,000 shuffles of itself”
F13.2 (issue #85), the first F13 run. 0168 measured K4 on 71 statistics one at a time against shuffles and found nothing outside them; F7 (0018, 0027) built ciphers by family and compared single statistics. Here the statistics are combined: 17 generators (one per family or cell of the map, keys drawn at random inside each family's space, plaintext from Carter's book with no known word, half of it Sanborn-style) make 4,000 ciphertexts each; every text is measured by 0168's 71 statistics, A13's 14 tests and 70 classic cipher-identification statistics (kappa at shifts 1-60, digraphic and even-pair I.C., delta I.C., repeats); a multinomial logistic classifier is trained on 3,000 per family and its power measured on 1,000 held-out per family, written from the other end of the book. Then K4's posterior for each family is ranked against 2,000 shuffles of K4, which keep its letter counts, so a family is named only for structure beyond the counts. The search never reads the 24 known letters. Rerun of 0230, which errored before any text was made: its worker function could not be sent to the pool (the harness loads attack.py under another module name); fixed as 0229 does, the method unchanged.
Before attacking a cipher, codebreakers often ask what kind it is: some kinds leave fingerprints, such as letters repeating at a fixed spacing. Here we build a sorting machinea classifier A program that learns to tell kinds of things apart from examples. (a classifier): we make 4,000 fake K4sthe workshop An experiment that builds thousands of pretend K4s by each suspected method and measures them, to learn which methods produce text that looks like the real one. with each of 17 kinds of cipher, measure 155 things about each, and teach the machine to tell the kinds apart. We test it on fakes it has never seen, to know how often it is right, and then show it K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page.. Because K4's letter counts alone could fool it, K4 counts as looking like a kind only if it looks more like that kind than 2,000 shuffles of its own letters do.
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
F13.2: from its statistics alone, which kind of cipher does K4 look like? No known letter is read.
the check
A classifier trained on 17 families' fakes is right 28% of the time on fresh ones (chance 6%): sure for alphabet swaps, transpositions and short keys, near chance among the flat families.
the bound
Against 2,000 shuffles of itself K4 names no family by the rule; one cell (ciphertext autokey) fell under the corrected line with no power behind it, so it was replicated (0232).
2
Experiment lineage
What this experiment was built on, from the lineage page: 5 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.
Take 97 letters of English and encipher them with one kind of cipher and a random key.
Measure the result: how evenly letters are spread, how often a letter recurs 1, 2, 3 ... 60 places later, repeated pairs and triples, doublets.
Do this thousands of times for each of 17 kinds, and fit weights that turn the measurements into a guess of the kind.
Check the guesses on fresh fakes: the share right is the machine's power.
Measure K4 and 2,000 shuffles of K4's letters; a kind is named only if K4 scores higher for it than nearly every shuffle.
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.
F13.2 measures a ciphertext and asks which kind of cipher made it. For K4 (no known letter read):
index of coincidence 0.0361 (random letters 0.0385, English 0.066)
kappa at shifts 1-10 0.062 0.042 0.043 0.054 0.033 0.033 0.100 0.022 0.034 0.057
doublets 6, longest repeat 2, distinct letters 26
Each of 17 cipher kinds makes 4,000 such texts; a classifier learns the kinds from 155 such numbers,
is scored on texts it never saw, then reads K4 and 2,000 shuffles of K4's letters.
6
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Cipher-type identification (the ACA's and NCID's practice; Sinkov's statistics) asks which generator a ciphertext is typical of. F13.1 (reports/f13-solvability-map.md) lists the families English alone could decide; F13.2 asks whether K4's own statistics point at any of them, without the known letters. Classes: monoalphabetic, columnar transposition (width 2-30), substitution then transposition (F9), periodic key on any of six alphabet pairs (standard, KRYPTOS, mixed; Quagmire I-IV) in three forms at lengths 2-12, 13-26 and 27-60 (F1, F1.1, F1.2), progressive key (F1.9), ciphertext and plaintext autokey with primers 1-30 (F1.7), running key from English (F1.3), Gromark base 10 (F5), Hill 2x2 and 3x3, plain or affine (F8), trifid 27-cell cube with no 27th symbol in the output (F4), Chaocipher (F10.1), a move then the table and the table then a move (F6), and uniform random letters (the one-time pad, the null). Features: 0168's 71 (segment chi-squares, I.C. at 1-48 alphabets, repeats at widths 7, 21, 31: the width-7 doublet column and width-21 repeats among them, 04-structure.md), A13's 14 (tools/a13_structure.py), and 70 more. Tests C4(a)-(b) (a mask leaves a type signature?), C1(a) (move then table), C11a ('interval 7') and F7's fingerprints as features rather than single tests. Pre-registered: 34 cells (17 families x two feature sets: the item's named 85 and all 155); K4 names a family when its posterior for that family is above all but a share p < 0.05/34 = 0.00147 of 2,000 shuffles of K4, and that family's positive control (12 held-out plants per family, each against 1,000 of its own shuffles, the same rule) finds at least 6 of 12. A named family is a candidate, replicated with a retrained classifier and fresh shuffles before anything else.
7
Prediction
Written before the run; the result decides it.
Held-out accuracy well above chance (1/17) overall, near 100% for monoalphabetic, transposition, substitution then transposition and Hill; high for short periodic keys; but the flat families (long periodic keys, running key, autokeys, Gromark, Chaocipher, the move-and-table pairs, random letters) confused with each other near chance among themselves. K4 is put among the flat families; against its shuffles no family is named (p above 0.00147 in all 34 cells). Plants of the distinctive families are found against their own shuffles; plants of the flat families are not. Zero candidates.
8
Method
Plaintexts: 97-letter windows of Carter's Tomb of Tut-ankh-Amen (the plants' source), half clean, half Sanborn-style (full stops as X, three letters changed); training from the first 80% of the book, held-out texts and plants from the last 20%. No known word is written in.
17 generators, keys at random inside each family's space; 3,000 training and 1,000 held-out texts per family, in jobs of 100 with their own seeds.
155 features per text: 0168's all_stats (frozen), A13's battery, and kappa at shifts 1-60, digraphic and even-pair I.C., delta I.C. on both alphabets, doublets, longest repeat, distinct letters, top count, English letter log-likelihood.
Multinomial logistic regression (numpy, L2 1e-3, Adam 3,000 steps, standardized features), one on the named 85 features and one on all 155. Power: held-out confusion matrix, recall per family, AUC of each family against random letters.
K4 and 2,000 shuffles of K4 through both models; per family the share of shuffles at or above K4's posterior.
Positive control: 12 held-out plants per family, each against 1,000 of its own shuffles, the same rule.
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
held-out accuracy named 0.26, all 0.284 (chance 0.059); K4 top (all): [('ciphertext autokey', 0.162), ('running key', 0.104)]; families named against shuffles: none (smallest p 0.001, alpha 0.00147)
What was searched, as the harness recorded it.
item
F13.2
search reads known letters
no
self check
K1 reproduced by the periodic substitution (KRYPTOS table, PALIMPSEST); Chaocipher matches Rubin's vector; columnar, Hill 2x2/3x3 affine and trifid round-trip
families
monoalphabetic, transposition, substitution then move, periodic 2-12, periodic 13-26, periodic 27-60, progressive key, ciphertext autokey, plaintext autokey, running key, Gromark, Hill, trifid, Chaocipher, move then table, table then move, random letters
texts per family
train
3,000
held out
1,000
plaintext
Carter 1923, half clean, half full stops as X with three letters changed; train first 80%, held-out last 20%; no known words
features
named (0168's 71 + A13's 14)
85
all (plus 70 classic identification statistics)
155
classifier
multinomial logistic, L2 0.001, Adam 3000 steps, standardized
chance accuracy
0.059
power
named
held out accuracy
0.26
train accuracy
0.272
recall
monoalphabetic
0.851
transposition
0.913
substitution then move
0.489
periodic 2-12
0.435
periodic 13-26
0.127
periodic 27-60
0.113
progressive key
0.16
ciphertext autokey
0.078
plaintext autokey
0.09
running key
0.046
Gromark
0.097
Hill
0.436
trifid
0.11
Chaocipher
0.124
move then table
0.173
table then move
0.148
random letters
0.033
auc against random letters
monoalphabetic
1
transposition
1
substitution then move
1
periodic 2-12
0.894
periodic 13-26
0.652
periodic 27-60
0.541
progressive key
0.519
ciphertext autokey
0.553
plaintext autokey
0.624
running key
0.582
Gromark
0.578
Hill
0.805
trifid
0.757
Chaocipher
0.545
move then table
0.727
table then move
0.675
confusion
monoalphabetic
monoalphabetic
851
transposition
78
substitution then move
52
periodic 2-12
17
trifid
2
transposition
monoalphabetic
39
transposition
913
substitution then move
32
periodic 2-12
5
trifid
10
move then table
1
substitution then move
monoalphabetic
79
transposition
417
substitution then move
489
periodic 2-12
5
trifid
8
move then table
1
table then move
1
periodic 2-12
monoalphabetic
24
transposition
8
substitution then move
8
periodic 2-12
435
periodic 13-26
29
periodic 27-60
22
progressive key
20
ciphertext autokey
13
plaintext autokey
24
running key
7
Gromark
29
Hill
124
trifid
72
Chaocipher
22
move then table
110
table then move
52
random letters
1
periodic 13-26
substitution then move
1
periodic 2-12
84
periodic 13-26
127
periodic 27-60
75
progressive key
87
ciphertext autokey
52
plaintext autokey
55
running key
18
Gromark
59
Hill
101
trifid
63
Chaocipher
82
move then table
95
table then move
84
random letters
17
periodic 27-60
monoalphabetic
1
periodic 2-12
52
periodic 13-26
90
periodic 27-60
113
progressive key
125
ciphertext autokey
70
plaintext autokey
47
running key
35
Gromark
67
Hill
71
trifid
51
Chaocipher
105
move then table
73
table then move
73
random letters
27
progressive key
monoalphabetic
1
periodic 2-12
39
periodic 13-26
67
periodic 27-60
94
progressive key
160
ciphertext autokey
69
plaintext autokey
52
running key
44
Gromark
80
Hill
62
trifid
34
Chaocipher
130
move then table
69
table then move
73
random letters
26
ciphertext autokey
periodic 2-12
29
periodic 13-26
63
periodic 27-60
85
progressive key
125
ciphertext autokey
78
plaintext autokey
62
running key
33
Gromark
87
Hill
69
trifid
52
Chaocipher
126
move then table
89
table then move
76
random letters
26
plaintext autokey
monoalphabetic
2
transposition
3
periodic 2-12
74
periodic 13-26
74
periodic 27-60
79
progressive key
101
ciphertext autokey
71
plaintext autokey
90
running key
41
Gromark
51
Hill
76
trifid
60
Chaocipher
71
move then table
101
table then move
81
random letters
25
running key
periodic 2-12
47
periodic 13-26
83
periodic 27-60
110
progressive key
88
ciphertext autokey
66
plaintext autokey
61
running key
46
Gromark
72
Hill
60
trifid
45
Chaocipher
96
move then table
103
table then move
99
random letters
24
Gromark
monoalphabetic
2
periodic 2-12
61
periodic 13-26
77
periodic 27-60
98
progressive key
113
ciphertext autokey
65
plaintext autokey
55
running key
26
Gromark
97
Hill
68
trifid
37
Chaocipher
86
move then table
92
table then move
92
random letters
31
Hill
monoalphabetic
3
substitution then move
4
periodic 2-12
104
periodic 13-26
49
periodic 27-60
51
progressive key
33
ciphertext autokey
27
plaintext autokey
46
running key
14
Gromark
31
Hill
436
trifid
52
Chaocipher
49
move then table
52
table then move
39
random letters
10
trifid
monoalphabetic
13
transposition
16
substitution then move
11
periodic 2-12
120
periodic 13-26
54
periodic 27-60
52
progressive key
45
ciphertext autokey
39
plaintext autokey
51
running key
18
Gromark
38
Hill
131
trifid
110
Chaocipher
56
move then table
102
table then move
137
random letters
7
Chaocipher
periodic 2-12
34
periodic 13-26
63
periodic 27-60
114
progressive key
140
ciphertext autokey
83
plaintext autokey
61
running key
31
Gromark
84
Hill
61
trifid
36
Chaocipher
124
move then table
77
table then move
64
random letters
28
move then table
monoalphabetic
4
transposition
9
substitution then move
4
periodic 2-12
191
periodic 13-26
64
periodic 27-60
66
progressive key
65
ciphertext autokey
40
plaintext autokey
46
running key
21
Gromark
57
Hill
53
trifid
81
Chaocipher
50
move then table
173
table then move
64
random letters
12
table then move
monoalphabetic
3
transposition
13
substitution then move
21
periodic 2-12
57
periodic 13-26
65
periodic 27-60
57
progressive key
83
ciphertext autokey
62
plaintext autokey
63
running key
31
Gromark
70
Hill
59
trifid
93
Chaocipher
74
move then table
89
table then move
148
random letters
12
random letters
substitution then move
2
periodic 2-12
46
periodic 13-26
68
periodic 27-60
98
progressive key
151
ciphertext autokey
63
plaintext autokey
63
running key
38
Gromark
70
Hill
69
trifid
32
Chaocipher
108
move then table
89
table then move
70
random letters
33
all
held out accuracy
0.284
train accuracy
0.302
recall
monoalphabetic
0.925
transposition
0.951
substitution then move
0.761
periodic 2-12
0.428
periodic 13-26
0.116
periodic 27-60
0.067
progressive key
0.038
ciphertext autokey
0.081
plaintext autokey
0.104
running key
0.038
Gromark
0.064
Hill
0.435
trifid
0.159
Chaocipher
0.262
move then table
0.15
table then move
0.141
random letters
0.112
auc against random letters
monoalphabetic
1
transposition
1
substitution then move
1
periodic 2-12
0.895
periodic 13-26
0.649
periodic 27-60
0.538
progressive key
0.516
ciphertext autokey
0.547
plaintext autokey
0.623
running key
0.582
Gromark
0.585
Hill
0.809
trifid
0.761
Chaocipher
0.557
move then table
0.726
table then move
0.68
confusion
monoalphabetic
monoalphabetic
925
transposition
21
substitution then move
37
periodic 2-12
13
Hill
1
trifid
3
transposition
monoalphabetic
17
transposition
951
substitution then move
25
periodic 2-12
1
trifid
6
substitution then move
monoalphabetic
82
transposition
133
substitution then move
761
periodic 2-12
7
trifid
9
move then table
4
table then move
4
periodic 2-12
monoalphabetic
24
transposition
4
substitution then move
8
periodic 2-12
428
periodic 13-26
28
periodic 27-60
14
progressive key
3
ciphertext autokey
13
plaintext autokey
25
running key
13
Gromark
19
Hill
119
trifid
101
Chaocipher
38
move then table
90
table then move
54
random letters
19
periodic 13-26
periodic 2-12
78
periodic 13-26
116
periodic 27-60
51
progressive key
23
ciphertext autokey
49
plaintext autokey
73
running key
13
Gromark
39
Hill
111
trifid
72
Chaocipher
136
move then table
88
table then move
81
random letters
70
periodic 27-60
monoalphabetic
1
periodic 2-12
52
periodic 13-26
78
periodic 27-60
67
progressive key
40
ciphertext autokey
54
plaintext autokey
67
running key
35
Gromark
48
Hill
66
trifid
55
Chaocipher
218
move then table
70
table then move
63
random letters
86
progressive key
monoalphabetic
1
periodic 2-12
40
periodic 13-26
77
periodic 27-60
43
progressive key
38
ciphertext autokey
65
plaintext autokey
71
running key
43
Gromark
46
Hill
60
trifid
42
Chaocipher
253
move then table
54
table then move
74
random letters
93
ciphertext autokey
transposition
1
periodic 2-12
38
periodic 13-26
68
periodic 27-60
62
progressive key
22
ciphertext autokey
81
plaintext autokey
80
running key
29
Gromark
58
Hill
70
trifid
50
Chaocipher
216
move then table
67
table then move
77
random letters
81
plaintext autokey
monoalphabetic
1
transposition
3
substitution then move
1
periodic 2-12
73
periodic 13-26
75
periodic 27-60
36
progressive key
22
ciphertext autokey
70
plaintext autokey
104
running key
35
Gromark
46
Hill
77
trifid
69
Chaocipher
142
move then table
84
table then move
84
random letters
78
running key
periodic 2-12
45
periodic 13-26
75
periodic 27-60
68
progressive key
19
ciphertext autokey
70
plaintext autokey
76
running key
38
Gromark
50
Hill
60
trifid
68
Chaocipher
174
move then table
94
table then move
87
random letters
76
Gromark
periodic 2-12
57
periodic 13-26
80
periodic 27-60
59
progressive key
26
ciphertext autokey
59
plaintext autokey
66
running key
34
Gromark
64
Hill
73
trifid
51
Chaocipher
182
move then table
80
table then move
84
random letters
85
Hill
monoalphabetic
3
periodic 2-12
105
periodic 13-26
50
periodic 27-60
37
progressive key
10
ciphertext autokey
22
plaintext autokey
58
running key
11
Gromark
17
Hill
435
trifid
62
Chaocipher
74
move then table
44
table then move
38
random letters
34
trifid
monoalphabetic
9
transposition
12
substitution then move
10
periodic 2-12
120
periodic 13-26
50
periodic 27-60
36
progressive key
14
ciphertext autokey
41
plaintext autokey
65
running key
20
Gromark
33
Hill
122
trifid
159
Chaocipher
82
move then table
75
table then move
116
random letters
36
Chaocipher
periodic 2-12
37
periodic 13-26
54
periodic 27-60
65
progressive key
37
ciphertext autokey
71
plaintext autokey
60
running key
29
Gromark
45
Hill
60
trifid
41
Chaocipher
262
move then table
71
table then move
61
random letters
107
move then table
monoalphabetic
4
transposition
2
substitution then move
8
periodic 2-12
189
periodic 13-26
73
periodic 27-60
40
progressive key
19
ciphertext autokey
49
plaintext autokey
58
running key
19
Gromark
43
Hill
49
trifid
90
Chaocipher
97
move then table
150
table then move
67
random letters
43
table then move
monoalphabetic
4
transposition
5
substitution then move
22
periodic 2-12
55
periodic 13-26
58
periodic 27-60
39
progressive key
24
ciphertext autokey
63
plaintext autokey
71
running key
31
Gromark
47
Hill
54
trifid
107
Chaocipher
133
move then table
83
table then move
141
random letters
63
random letters
transposition
2
substitution then move
2
periodic 2-12
48
periodic 13-26
68
periodic 27-60
55
progressive key
29
ciphertext autokey
76
plaintext autokey
67
running key
32
Gromark
34
Hill
63
trifid
52
Chaocipher
222
move then table
72
table then move
66
random letters
112
k4 top posteriors
named
ciphertext autokey, 0.163
running key, 0.102
periodic 27-60, 0.095
random letters, 0.085
all
ciphertext autokey, 0.162
running key, 0.104
plaintext autokey, 0.101
Chaocipher, 0.095
k4 shuffles argmax
named
Chaocipher, 552
progressive key, 443
periodic 27-60, 310
ciphertext autokey, 173
random letters, 163
all
Chaocipher, 895
random letters, 358
periodic 27-60, 167
ciphertext autokey, 122
Hill, 119
cells
34
alpha per cell
0.001
k4 shuffles
2,000
positive control
12 held-out plants per family, each against 1000 own shuffles, the K4 rule
k4 cells
named/monoalphabetic
k4 posterior
0
shuffles mean
0
shuffles at or above
1,939
p
0.97
plants found
8, 12
named/transposition
k4 posterior
0
shuffles mean
0
shuffles at or above
74
p
0.037
plants found
0, 12
named/substitution then move
k4 posterior
0
shuffles mean
0
shuffles at or above
261
p
0.131
plants found
0, 12
named/periodic 2-12
k4 posterior
0.013
shuffles mean
0.026
shuffles at or above
1,307
p
0.654
plants found
3, 12
named/periodic 13-26
k4 posterior
0.039
shuffles mean
0.072
shuffles at or above
1,935
p
0.968
plants found
0, 12
named/periodic 27-60
k4 posterior
0.095
shuffles mean
0.1
shuffles at or above
1,194
p
0.597
plants found
0, 12
named/progressive key
k4 posterior
0.07
shuffles mean
0.106
shuffles at or above
1,926
p
0.963
plants found
0, 12
named/ciphertext autokey
k4 posterior
0.163
shuffles mean
0.092
shuffles at or above
1
p
0.001
plants found
0, 12
named/plaintext autokey
k4 posterior
0.081
shuffles mean
0.068
shuffles at or above
415
p
0.208
plants found
0, 12
named/running key
k4 posterior
0.102
shuffles mean
0.082
shuffles at or above
181
p
0.091
plants found
0, 12
named/Gromark
k4 posterior
0.057
shuffles mean
0.079
shuffles at or above
1,795
p
0.898
plants found
0, 12
named/Hill
k4 posterior
0.078
shuffles mean
0.047
shuffles at or above
280
p
0.14
plants found
4, 12
named/trifid
k4 posterior
0.048
shuffles mean
0.037
shuffles at or above
293
p
0.147
plants found
0, 12
named/Chaocipher
k4 posterior
0.084
shuffles mean
0.106
shuffles at or above
1,715
p
0.858
plants found
0, 12
named/move then table
k4 posterior
0.029
shuffles mean
0.044
shuffles at or above
1,469
p
0.735
plants found
0, 12
named/table then move
k4 posterior
0.056
shuffles mean
0.043
shuffles at or above
133
p
0.067
plants found
0, 12
named/random letters
k4 posterior
0.086
shuffles mean
0.099
shuffles at or above
1,583
p
0.792
plants found
0, 12
all/monoalphabetic
k4 posterior
0
shuffles mean
0
shuffles at or above
1,786
p
0.893
plants found
8, 12
all/transposition
k4 posterior
0
shuffles mean
0
shuffles at or above
1,050
p
0.525
plants found
0, 12
all/substitution then move
k4 posterior
0
shuffles mean
0
shuffles at or above
1,812
p
0.906
plants found
0, 12
all/periodic 2-12
k4 posterior
0.013
shuffles mean
0.026
shuffles at or above
1,264
p
0.632
plants found
2, 12
all/periodic 13-26
k4 posterior
0.039
shuffles mean
0.071
shuffles at or above
1,885
p
0.943
plants found
0, 12
all/periodic 27-60
k4 posterior
0.083
shuffles mean
0.097
shuffles at or above
1,418
p
0.709
plants found
0, 12
all/progressive key
k4 posterior
0.06
shuffles mean
0.091
shuffles at or above
1,913
p
0.957
plants found
0, 12
all/ciphertext autokey
k4 posterior
0.162
shuffles mean
0.089
shuffles at or above
10
p
0.005
plants found
0, 12
all/plaintext autokey
k4 posterior
0.102
shuffles mean
0.071
shuffles at or above
166
p
0.083
plants found
0, 12
all/running key
k4 posterior
0.104
shuffles mean
0.083
shuffles at or above
229
p
0.115
plants found
0, 12
all/Gromark
k4 posterior
0.064
shuffles mean
0.07
shuffles at or above
1,213
p
0.607
plants found
0, 12
all/Hill
k4 posterior
0.069
shuffles mean
0.049
shuffles at or above
400
p
0.2
plants found
3, 12
all/trifid
k4 posterior
0.038
shuffles mean
0.033
shuffles at or above
600
p
0.3
plants found
0, 12
all/Chaocipher
k4 posterior
0.095
shuffles mean
0.123
shuffles at or above
1,674
p
0.837
plants found
0, 12
all/move then table
k4 posterior
0.029
shuffles mean
0.043
shuffles at or above
1,381
p
0.691
plants found
0, 12
all/table then move
k4 posterior
0.049
shuffles mean
0.044
shuffles at or above
580
p
0.29
plants found
0, 12
all/random letters
k4 posterior
0.094
shuffles mean
0.11
shuffles at or above
1,538
p
0.769
plants found
0, 12
named families
none
smallest p
0.001
exhaustive
no
compute seconds
173
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.