“F3.3: EAST NORTHEAST and its parts read as numbers (bearing 67.5 degrees, compass points of 32 and 16, mils) as the number half of a two-part key, with an unknown word, exact”
F3.3 (A14(b)). Same decider as 0175, new readings: the known words' directions as numbers. EAST NORTHEAST as the bearing 67.5 degrees (6 7 5; 0 6 7 5; 67 5; 675; 67 30 as degrees and minutes; 1200 mils), as compass point 6 of 32 or 3 of 16 (and 7, 4 counting from 1), EAST as 90 degrees, point 8 of 32, 4 of 16, NORTHEAST as 45 degrees, 4 of 32, 2 of 16; the pair EAST, NORTHEAST and the triple ENE, E, NE in each scale. Each sequence forward and reversed, every start, both signs, an unknown word of 1-24 letters, 12 table rules. Single numbers are a word shifted by a constant, which 0005's sweep already covers; they are run as a check of the decider.
The known words are directions. A direction is also a number: east-northeast is 67.5 degrees on a compass, or the 6th of 32 compass points. Perhaps such a number is half of the keythe secret word The word or string a cipher needs besides the method. and a secret word the other half. For every way of writing these numbers we ask 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. what the secret word would be, and compare with scrambled copies.
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 known words are directions, and a direction is also a number: east-northeast is 67.5 degrees, or the 6th of 32 compass points. Such a number could be half of the key, a secret word the other half.
the check
Every way of writing the directions as numbers, repeated from every start, added or subtracted, with a secret word of 1 to 24 letters on each of 12 table rules; the 24 known letters must agree on the word.
the bound
Nothing fits K4 or any of 20 scrambled copies; a planted text is found. F3.3 closed.
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.
Write 6 7 5 (east-northeast is 67.5 degrees) again and again under the message, from some start.
On the sculpture's table the known E at place 22 over the carved F asks for key value 1.
Subtract the number under place 22: the rest is the secret word's letter for that slot.
Places that share a slot of the word must leave the same rest.
Every start, sign, word length and table rule; then scrambled copies.
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.
6 7 5 (67.5 degrees) from the first digit, Vigenere on the KRYPTOS table, word length 7
place known carved key num word value slot
22 E F 1 6 21 0
23 A L 10 7 3 1
24 S R 21 5 16 2
25 T V 18 6 12 3
26 N Q 1 7 20 4
27 O Q 15 5 10 5
28 R P 2 6 22 6
29 T R 23 7 16 0
30 H N 5 5 0 1
31 E G 2 6 22 2
32 A K 19 7 12 3
33 S S 0 5 21 4
34 T S 2 6 22 5
64 B N 11 6 5 0
65 E Y 17 7 10 1
66 R P 2 5 23 2
67 L V 5 6 25 3
68 I T 15 7 8 4
69 N T 11 5 6 5
70 C M 9 6 3 6
71 L Z 8 7 1 0
72 O F 7 5 2 1
73 C P 20 6 14 2
74 K K 0 7 19 3
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
A14(b) (direction words as numbers, knowledge/12-assumptions.md, for information), C5(b) ('key word/s'), C6 (Scheidt's two-part keys), C15 (K2's 'six point five' bearing language). Model as 0175: carved = T(plain, k_i), k_i = w[i mod a] + s d[(i + o) mod m], 12 rules; the 24 known letters force k; w's slots must agree. Statistic: live settings by checks and dictionary words among forced words, K4 against 20 coppers.
6
Prediction
Written before the run; the result decides it.
No setting with 5 or more checks fits K4, as on the coppers; no dictionary word forced. Zero candidates.
7
Method
Build the direction readings.
For each text, table rule, reading, start and sign: the word's value at each known place.
For each word length 1-24: slot agreement; fully forced words looked up in the dictionary, every rotation.
K4 against 20 coppers; one planted text as a builder check.
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
live settings with >=4 checks: K4 0 (coppers 0-0); dictionary words 4+: K4 0 (coppers 0-0); plant found True
What was searched, as the harness recorded it.
family
word plus the direction words read as numbers, k = w[i mod a] + s d, 12 table rules, exact
readings
ENE 67.5 degrees: 6 7 5
6, 7, 5
ENE 67.5 degrees: 6 7 5, reversed
5, 7, 6
ENE 067.5: 0 6 7 5
0, 6, 7, 5
ENE 067.5: 0 6 7 5, reversed
5, 7, 6, 0
ENE 67 5
67, 5
ENE 67 5, reversed
5, 67
ENE 675
675
ENE 67 degrees 30 minutes
67, 30
ENE 67 degrees 30 minutes, reversed
30, 67
ENE 6 7 3 0
6, 7, 3, 0
ENE 6 7 3 0, reversed
0, 3, 7, 6
ENE 1200 mils: 1 2 0 0
1, 2, 0, 0
ENE 1200 mils: 1 2 0 0, reversed
0, 0, 2, 1
ENE 12 0 0
12, 0, 0
ENE 12 0 0, reversed
0, 0, 12
ENE point 6 of 32
6
ENE point 7 of 32 (from 1)
7
ENE point 3 of 16
3
ENE point 4 of 16 (from 1)
4
E 90 degrees: 9 0
9, 0
E 90 degrees: 9 0, reversed
0, 9
E 90
90
NE 45 degrees: 4 5
4, 5
NE 45 degrees: 4 5, reversed
5, 4
NE 45
45
E, NE degrees: 90 45
90, 45
E, NE degrees: 90 45, reversed
45, 90
E, NE digits: 9 0 4 5
9, 0, 4, 5
E, NE digits: 9 0 4 5, reversed
5, 4, 0, 9
E, NE of 32: 8 4
8, 4
E, NE of 32: 8 4, reversed
4, 8
E, NE of 32 from 1: 9 5
9, 5
E, NE of 32 from 1: 9 5, reversed
5, 9
E, NE of 16: 4 2
4, 2
E, NE of 16: 4 2, reversed
2, 4
E, NE of 16 from 1: 5 3
5, 3
E, NE of 16 from 1: 5 3, reversed
3, 5
ENE, E, NE of 32: 6 8 4
6, 8, 4
ENE, E, NE of 32: 6 8 4, reversed
4, 8, 6
ENE, E, NE of 16: 3 4 2
3, 4, 2
ENE, E, NE of 16: 3 4 2, reversed
2, 4, 3
ENE, E, NE degrees: 67.5 90 45 as 6 7 5 9 0 4 5
6, 7, 5, 9, 0, 4, 5
ENE, E, NE degrees: 67.5 90 45 as 6 7 5 9 0 4 5, reversed