“F1.1 at key length 26 decided with design 2: K4 against 12 scrambled copies of itself (one free alphabet, Beaufort form)”
F1.1 Beaufort 26, rerun alone after 0141 crashed (its two-alphabet part ran out of time while drawing fitting shuffles, and a text with no finished search broke the summary; no result survived). Same test as 0141's first part: 0140 found design 2 has power at 26 (5 of 6 planted texts beat all 6 of their own copies), so K4 runs against 12 shuffles of itself that fit at 26.
The search that tells planted English from its own scrambled letters runs on the carved textthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. for the last undecided case of one scrambled alphabet: a 26-letter key, where the known lettersthe known letters Sanborn has confirmed that positions 22 to 34 of the message read EASTNORTHEAST and positions 64 to 74 read BERLINCLOCK. give only one check. The carved text is compared with scrambled copies of itself; if it were English enciphered this way it would usually come first.
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
At length 26 the known letters give one check, yet design 2 noticed planted English against its own letters 5 times in 6 (0140). So K4 runs against scrambled copies of itself here too.
the check
12 shuffles of K4 that still fit at 26; the same search on all 13. K4 scores -4.99, copies -5.05 to -4.69.
the bound
K4 ranks 12 of 13: the Beaufort-26 cell is closed at the measured strength. With 0140, one scrambled alphabet on both sides with no move is closed at every key length.
2
Best candidate against the known letters
Laid out as the copper carries K4: OBKR ends the line that finishes K3, then three lines of 31. Left, as carved, the 24 known places in accent. Right, the candidate: a known place it gets right is an accent cell, one it misses is outlined. This is the candidate with most known letters right; none passed every gate.
in: the copper, always the same
as carved, 97 letters; the 24 known places in accent
ECDMRIPFEIMEHNLSSTTRTVDOHW?OBKR
UOXOGHULBSOLIFBBWFLRVQQPRNGKSSO
TWTQSJQSSEKZZWATJKLUDIAWINFBNYP
VTTMZFPKWGDKZXTJCDIGKUHUAUEKCAR
OBKR ends the line that finishes K3, then three lines of 31
out: the candidate
every place read; known places in accent, misses outlined
ECDMRIPFEIMEHNLSSTTRTVDOHW?QINA
RCEOUSEAZEYNONENGEASTNORTHEASTE
DTUDECRSABSOSCIVEFUSSHKRLDRABER
LINCLOCKCLARINRUNGONTAGTOLEMASC
checked: the known letters in place, and the reading turns back into the copper
3
How the score is made
The loss of the best candidate, part by part. Zero is solved.
Known letters missed
0 of 24, ten points each
0.00
English
the 73 free letters score -5.23; English text scores -3.6
1.63
Key
213 bits to write it down (key words are cheap, arbitrary letters 4.7 bits each); each 60 beyond 60 costs a point
2.54
Loss
of 240, the worst possible
4.17 1.7%
4
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Write K4 in rows of 26; each column is one key slot; one column holds two known letters, whose sums must agree.
Search alphabets that keep that sum, sixteen searches side by side, scoring the whole text as English.
Do the same on 12 shuffles of K4 that still allow the known letters.
If K4 is anywhere inside the pack, the cell is closed at the measured strength.
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.
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)
best alphabet on K4: UTVXRSWEPNHFLZDAOQBJICKGYM
key values: [7, 12, 5, 19, 4, 11, 10, 6, 23, 15, 7, 1, 5, 12, 14, 21, 10, 20, 25, 1, 3, 18, 1, 9, 3, 0]
place 22: carved F at 11, key 18: 18 - 11 = 7 -> E
place 64: carved N at 9, key 1: 1 - 9 = 18 -> B
6
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C27(c), C1(b). One unknown alphabet on both sides, Beaufort form x(c_i) + x(p_i) = k[i mod 26], 1 check (0119). Search: 0139's compiled parallel tempering in the set where the check holds, 10 runs x 16 replicas x 625 rounds x 1,000 moves per text, full-text quadgram mean. K4 vs 12 shuffles of K4 fitting at 26 (0119's decider, seed 142). Rule fixed before the run: K4 above all 12 stops the queue for a replication; otherwise the cell closes sampled at the measured power (5 of 6 at 6 copies, 0140).
7
Prediction
Written before the run; the result decides it.
K4 inside its copies (rank 2-13); the Beaufort-26 cell closes sampled at power about 0.8. No reading.
K4's rank; its best reading returned with the copies' English scores as controls.
9
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
1candidates returned
0passed every gate
24/24known letters, best
1.7%lowest loss
nonechampion before
All 1 candidates, lowest loss first.
1failed at baseline24/24 known lettersloss 1.7%
ECDMRIPFEIMEHNLSSTTRTVDOHW?QINA
RCEOUSEAZEYNONENGEASTNORTHEASTE
DTUDECRSABSOSCIVEFUSSHKRLDRABER
LINCLOCKCLARINRUNGONTAGTOLEMASC
Beaufort form, one alphabet UTVXRSWEPNHFLZDAOQBJICKGYM on both sides, key length 26
L26: K4 -4.990, rank 12 of 13 (-5.051 to -4.688); stop False.
What was searched, as the harness recorded it.
family
one free alphabet, Beaufort form, key length 26: K4 vs 12 of its own fitting copies (design 2)
search
parallel tempering, 10 runs x 16 replicas x 625 rounds x 1000 moves per text, T 0.1->0.002; two-alphabet runs start from an exact witness (0123) randomised by 400 check-keeping swaps