“A key word over the columns and a second key over the rows: the message in rows of seven, each letter shifted by its column's letter and its row's letter”
0032 gave each row of the grid one key letter; repeating keys give each column one. Here both at once: the key at a place is its column's letter of one word plus its row's letter of a second key, on a grid of width 2-48. Within a row the row letter cancels, so a column whose letter steps against its neighbour's makes doubled letters in that column only: the one construction found here that lines doublets up in sevens by design. Tested exactly from the 24 known letters, on the copper as carved and after each of 0080's 26,000 moves (keyed columns read the right way, issue #26), in both orders.
Write the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. in rows of seven under KRYPTOS. Shift each letter along the tablethe table The right-hand half of the sculpture, 26 rows of the alphabet each shifted one place further, starting from the word KRYPTOS. by its column's letter of KRYPTOS, and also by a letter chosen for its row from a second key. It is easy to do by hand and needs two key words, as Scheidt said. It also explains an oddity: inside a row the row's shift is the same for both letters of a pair, so doubled lettersthe doublets Places where a carved letter is immediately followed by the same letter. can only appear where two neighbouring column letters differ in a particular way, and they pile up in the same column, as five of K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page.'s six doubled letters do. 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. test every width exactly, with and without a scrambling step before or after.
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 key
Each letter is shifted by its column's letter of one key word and by its row's letter of a second key. Inside a row the row letter is the same for neighbours, so doubled letters can only collect in particular columns, as K4's do in rows of seven.
the check
Two known letters in one row differ by the difference of their column letters; the same two columns one row down must differ by the same amount. In rows of 7 the first such pair already disagrees.
the bound
Every width 2-48, both tables, with no scrambling and after or before 27,754 scramblings: nothing fits beyond what scrambled coppers show.
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 the copper in rows of 7. Place 22 is in row 3, column 0; place 23 in row 3, column 1; places 29 and 30 in row 4, columns 0 and 1.
On the sculpture's alphabet with Vigenere, copper minus message gives the key at each place: F - E = 1 at 22, L - A = 10 at 23, R - T = 23 at 29, N - H = 5 at 30.
Each key is a column letter plus a row letter. Places 22 and 23 share their row, so their difference, 1 - 10 = 17, is the difference of the column letters 0 and 1.
Places 29 and 30 share the next row and the same two columns, so 23 - 5 = 18 must be the same difference.
17 is not 18: width 7 with this table is dead, whatever the two key words are.
Width 7 has 14 such checks in all; test every width 2-48, both tables and signs, with no move and after each of 0080's moves in both orders, 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.
no move; rows of 7; key = column letter + row letter; sculpture's alphabet, s = +1
place known copper column row copper - known = column + row
22 E F 0 3 1
23 A L 1 3 10
29 T R 0 4 23
30 H N 1 4 5
64 B N 0 9 11
65 E Y 1 9 17
71 L Z 0 10 8
72 O F 1 10 7
24 known letters, 7 column slots and 4 row slots: 14 checks
places 22 and 29 share column 0; places 23 and 30 share column 1; 22, 23 share row 3; 29, 30 share row 4:
(22) - (23) must equal (29) - (30): 1 - 10 = 17, 23 - 5 = 18
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Type 2 of directions.md ('7-block constructions... keyed by KRYPTOS or another 7-letter word'), the prior-work database's seven-based sub-variant 4 ('KRYPTOS as a numeric key for something other than column order or an additive key: row order in a 14x7, or a per-row shift of a width-7 grid (Bean-style row shifts)'). Mechanism for the width-7 doublet column (0056, 0065): with key a[j mod w] + b[j div w], two adjacent letters in one row share b, so C[j] = C[j+1] iff P[j+1] - P[j] = a[c] - a[c+1], which depends only on the column c; doublets collect in the columns where a steps, i.e. at fixed residues mod w. Clues C5(b) ('key word/s'), C8(a) (KRYPTOS as the K4 key in a new way), C1(a) and C3 ('matrix', 'spatial systems'), C11a ('interval 7'). Model on one alphabet A (standard or KRYPTOS), sign s = +1 or -1 (s = -1 when exactly one of the two keys is applied Beaufort-wise): C[j] = s P + a[col] + b[row]; each known letter is an edge between column slot and row slot, consistency by spanning tree, checks = edges - (slots touched - components). Grid positions are carved places (move, then grid key: order A) or message places (grid key, then move: order B). Moves: none, plus 0080's set (K3 rule, one or two quarter turns, plain and keyword columnar, forward and inverse; keyword columnar now read in true key order). Widths 2-48, rows as many as needed (the row key is free, so a repeating row word is a special case). Exact; ten shuffled coppers through the identical search.
6
Prediction
Written before the run; the result decides it.
On the copper as carved (no move), no width passes all its checks; width 7 has about 14 checks and fails. After moves, consistent settings at every number of checks lie inside the range of the ten shuffled coppers, and no setting with five or more checks survives on K4. Zero candidates.
7
Method
For each width, assign every known letter its column slot and row slot (by carved place or by message place).
Grow a spanning tree over the slots and test every other known letter against it, on both alphabets and both signs.
Do this with no move and after each of 0080's moves, in both orders.
Count consistent settings by number of checks on K4 and ten shuffled coppers.
Print K4's settings with five or more checks, with the slot letters they fix.
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
No move: widths consistent on K4: none (width 7 has 14 checks). With moves: 27,754 routes x widths 2-48 x 2 orders, 2,313,108 structures x 4 cases. K4 consistent with >= c checks, c = 1..8: [25753, 1102, 30, 4, 0, 0, 0, 0]; controls max [26510, 1209, 51, 6, 1, 0, 0, 0], min [25550, 1009, 28, 0, 0, 0, 0, 0]. Levels outside the control range: []. K4 cases with 5+ checks: 0.
What was searched, as the harness recorded it.
family
key = column letter of one key + row letter of another on a grid of width 2-48, no move or after/before 0080's moves