“F13.4a: a periodic key on the sculpture's 8 table classes, key lengths 1-36, solved from the ciphertext alone (quadgram climb, MIX8m rescoring), K4 against 200 climbed shuffles, plants at seven lengths”

1. Guess a key length, say 7, and write the carved letters in 7 columns.
2. Pick one of the eight ways of using the sculpture's table.
3. For column 1 try all 26 shifts and keep the one that makes the whole text read best; then column 2, and so on, going round until nothing improves.
4. Start again from a few random keys and keep the best reading.
5. Do it for every length up to 36 and every way of using the table, and compare K4's best with the best that shuffles of K4's letters reach.

The same climb on K1's 63 carved letters, key length 10, the KRYPTOS table, no known letter:

  shifts found  PALIMPSEST
  reading       BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION

On K4 the climb runs for every length 1-36 and all 8 ways of using the table, and K4's best is compared with
the best that 200 shuffles of K4's letters reach.

F1 with the sculpture's tables (K1, K2: Quagmire III on KRYPTOS with PALIMPSEST and ABSCISSA; 01-facts.md) is the first family in rank; C8(a), C27(c), C28. Every verdict on it rests on the known letters sitting at 22-34 and 64-74 of the final text, letter for letter (A2) and without slips (A1). F13.1 (reports/f13-solvability-map.md) puts a periodic key on a fixed table decidable by English alone to length 36 (125 bits at 26, under the 173 the quadgram scorer carries; 189 with MIX8m, 0233). The classic hand method (Stein; Friedman's Military Cryptanalysis) is exactly this: one shift per column, chosen by how well the decryption reads. Pre-registered: one statistic per text, S = max over L of (best MIX8m log-probability at L minus the shuffles' mean at L) / their sd; K4 flags at p < 0.05 against 200 shuffles (one test). Power per planted length: found when S is above all 10 own copies' S (null 1/11); a length is decided when at least 6 of its 8 plants are found (0120's bar as used by A6.2). The item closes for the lengths decided and is blocked above, by the measured power.

Plants found 8 of 8 at lengths 5-15, most at 20, falling to a few at 30-36 (columns of 2-3 letters): decided to about 20-26. K4's statistic inside its shuffles (p above 0.05), its best readings English-like junk with no known letter in place beyond chance (the harness's gate 2 on the 36 submitted readings: at most 3 of 24). So F13.4a closes for the decided lengths and is blocked above them.

1. Texts: K4; 200 shuffles of K4; 56 plants (lengths 5, 10, 15, 20, 26, 30, 36; 8 each, 4 clean and 4 with X stops; random class and shifts) and 10 shuffles of each plant: 817 texts.
2. Per text, per class (8) and length (1-36): coordinate ascent on the shifts, 30 random restarts, each pass trying all 26 shifts of every column in random order, scored by the harness's quadgram table.
3. The 288 best readings rescored by MIX8m (0233: KN8 on the manuals mixed with the quadgram table, weight 0.55); per length the best over classes.
4. z per length against K4's shuffles; S = the largest z; K4 ranked among its shuffles; each plant among its own copies.
5. K4's best reading at each length submitted as a candidate (key: class and shifts), so the harness checks the known letters only after the search; gate 4's controls are the shuffles' best readings, scored as the harness scores.

All 36 candidates, lowest loss first.

K4 statistic 2.15 at length 20, p 0.617 against 200 shuffles; plant power L5 8/8, L10 8/8, L15 8/8, L20 7/8, L26 6/8, L30 5/8, L36 2/8; decided lengths [5, 10, 15, 20, 26]

What was searched, as the harness recorded it.

item

F13.4a

search reads known letters

no

classes

std/std/vig, std/std/beau, std/kry/vig, std/kry/beau, kry/std/vig, kry/std/beau, kry/kry/vig, kry/kry/beau

key lengths

1, 36

restarts

30

climb

coordinate ascent on the shifts, quadgram table; best per (class, length) rescored by MIX8m (0233)

texts

817

k4 copies

200

k4 statistic

2.147

k4 best length

20

k4 p

0.617

copies statistic max

5.383

copies statistic median

2.31

k4 rank per length copies at or above

1

136

2

194

3

179

4

51

5

8

6

77

7

11

8

156

9

168

10

107

11

61

12

122

13

38

14

43

15

73

16

126

17

168

18

137

19

138

20

7

21

53

22

27

23

135

24

175

25

38

26

62

27

76

28

17

29

18

30

16

31

83

32

8

33

94

34

140

35

14

36

176

plant power

5

8, 8

10

8, 8

15

8, 8

20

7, 8

26

6, 8

30

5, 8

36

2, 8

plant exact recovery

5

8, 8

10

8, 8

15

7, 8

20

0, 8

26

0, 8

30

0, 8

36

0, 8

decided lengths at 6 of 8

5, 10, 15, 20, 26

k4 best readings

20

MIMESONTENSNVSATOMCLEELERMUSTHGOESALAYNURTEDISLIOUTPMZUBORHENEVIONPORINTHASYTHEPHAUSEWANDAMESAMEF

7

ESSHHBLERMQMOCEWLPROMTWONINFIUNIPADFLYUPWUDBUIDHMCDJIMMORACKJRAWFPNOCWLYPIFKOJIBENTORRSQUMBUPSSYF

10

WWASSMUCBNCGRTMJFTWHEABSTONDMTOFITMRTHLYRLITCIWNRGBEAMSBFOROVAROWNSHOSHAFLUEAYUDBESEGEHICAIPULAYO

exhaustive

no

compute seconds

91