“One carved letter wrong, through a K3-style move and a repeating key”
0031, 0050 and 0068 allowed one wrong carved letter only for keys with no move. Here every route of the type-1 library (K3's rule, one or two quarter turns, plain and true-keyword columnar, 27,852 distinct) is joined to a repeating key of length 1-26 before or after the move, and a setting counts as consistent if all known letters agree once at most one of them is set aside as a carving error.
Sanborn made at least one mistake carving K2the earlier messages The three solved parts of the sculpture.. If he made one in K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page., a correct method could fail our test at exactly one of the 24 known lettersthe known letters Sanborn has confirmed that positions 22 to 34 of the message read EASTNORTHEAST and positions 64 to 74 read BERLINCLOCK.. So we rerun the grid moves of experiments 80 to 85 with a short repeating secret word, and this time accept any setting that fits all known letters but one. Allowing one miss also lets more chance settings through, so scrambled coppers tell us how many to expect.
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 error
Sanborn made at least one carving mistake in K2. If K4 has one too, a correct method could fail at exactly one of the 24 known letters, so here one miss is allowed.
the check
Group the known letters by key slot after the move; within a slot they must share one key value. With a turn of 8 and a key of 9 they disagree 14 times; one carving error excuses one.
the bound
27,852 moves, keys of 1 to 26 letters before or after, 8 tables: the shortest key that fits with one miss is 20 letters after the move and 24 before, as on scrambled coppers (19-21 and 24-25).
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.
Pick a move, say a clockwise quarter turn of a grid 8 wide, and a key length, say 9.
For each known letter, find where the move puts it and the key value that turns it into the carved letter there.
Group the known letters by key slot: carved place mod 9.
In each group, count the letters that disagree with the group's most common value.
A total of 0 fits outright; a total of 1 fits if that one carved letter is a carving error.
Repeat for every move, key length 1-26, both orders and every table rule, and on ten scrambled coppers.
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.
clockwise quarter turn of a grid 8 wide, then a key of length 9; sculpture's alphabet, Vigenere
place letter lands at copper key value slot (mod 9)
22 E 71 Z 14 7
23 A 83 C 2 1
24 S 95 C 3 4
25 T 10 H 10 0
26 N 22 F 19 3
27 O 34 S 1 6
64 B 90 U 13 8
65 E 5 U 10 4
66 R 17 I 14 7
disagreements at period 9: 2 (2 means two or more)
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Type 7 of directions.md, 'one letter off through types 1 and 2'. K2 carries a carving error Sanborn confirmed (the dropped S, corrected in 2006; 01-facts.md) and K1-K3 carry deliberate misspellings (C10, C17). A wrong carved letter outside the 24 crib images is invisible to crib tests; one on a crib image breaks exactly one equation. So: route library as in 0090 (forward and inverse, deduplicated); repeating key of period 1-26 after the move (slot = carved place mod p) or before it (slot = message place mod p); 8 tableau consistency classes. Within each key slot the forced values must agree; the number of disagreements is the sum over slots of (letters in slot - largest agreeing group). Zero is the plain test (0080-0085 bounds); one is one carving error. Counts per period compared with ten shuffled coppers.
6
Prediction
Written before the run; the result decides it.
With one miss allowed, the smallest consistent period on K4 is no lower than on the scrambled coppers, and the count at every period lies inside their range, give or take one period. No setting below period 14. Zero candidates.
7
Method
Build the route library.
For each route, class and text, compute the key value forced at each known letter and its slot for each period and order.
Count the disagreements per period; record periods with zero and with one.
Repeat on ten shuffled coppers.
List K4's settings with one disagreement below period 14, and which known letter is set aside.
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
27,852 routes x 8 classes x 2 orders, periods 1-26, one miss allowed. Smallest period with at most one miss: K4 {'A': 20, 'B': 24}, controls {'A': [21, 20, 20, 20, 19, 20, 20, 20, 21, 21], 'B': [24, 25, 24, 24, 24, 25, 24, 24, 24, 24]}. K4 one-miss settings below 14: 0. Outside control range: {'A misses<=0': [25], 'A misses<=1': [22], 'B misses<=0': [], 'B misses<=1': [24]}.
What was searched, as the harness recorded it.
family
type-1 route library, then or before a periodic tableau key, at most one known letter set aside