“A key word over the columns plus a shift that changes every m letters, the carved lines of 31 among them”
0087 tied the second shift to the rows of the same grid. Here the second shift changes every m letters for any m from 2 to 50 and any starting offset, independent of the column word's length w (2-31). Among these is the sculpture's own layout: K4 starts four letters before the end of a 31-letter carved line and fills three more, so a shift per carved line is m = 31 with offset 27. Doublets still pile up by column wherever the block shift stays constant.
Keep the column word of experiment 87, but let the second shift change every so many letters, not at the end of each row: for instance once per carved line of the sculpture, which holds 31 letters. Within a stretch where the second shift stays the same, doubled lettersthe doublets Places where a carved letter is immediately followed by the same letter. can still only appear in certain columns of the word. 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 word length, stretch length and starting point exactly.
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
A word over the columns plus a shift that changes every so many letters, for instance once per carved line: the sculpture's K4 sits on lines of 31 letters.
the check
Two known letters in the same column of the word and the same stretch need the same key; with a 7-letter word and the carved lines, places 22 and 29 already disagree.
the bound
Word lengths 2-31, stretches 2-50 at every offset, both tables: no combination with two checks survives on the copper.
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.
On the sculpture K4 begins four letters before the end of a 31-letter carved line, so its places 1-4 end one line, 5-35 fill the next, 36-66 the next and 67-97 the last.
Take a key word of 7 letters over the columns (place p uses letter (p - 1) mod 7) plus one shift for each carved line.
Places 22 and 29 both use column 0 and both lie on the line of places 5-35, so they need the same total key.
On the sculpture's alphabet with Vigenere, F - E = 1 at place 22 and R - T = 23 at place 29: different, so a 7-letter word with one shift per carved line is dead on this table.
Repeat for every word length 2-31, every stretch length 2-50 and starting point, both tables and signs, and 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.
the carved lines: K4 starts 4 letters before the end of a 31-letter line (offset 27)
line 1: places 1-4, line 2: 5-35, line 3: 36-66, line 4: 67-97
word of length 7 over the columns, one shift per carved line; sculpture's alphabet, s = +1
place known copper column line copper - known
22 E F 0 2 1
29 T R 0 2 23
64 B N 0 3 11
71 L Z 0 4 8
7 column slots, 3 line slots, 24 known letters: 15 checks
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Type 2 of directions.md, continued from 0087: the doublet-column mechanism key = a[j mod w] + b[(j + o) div m] with the block length m free of w (a slowly changing tableau row, a new row of the table every m letters, or a new shift per line of text). C27(b) (the BERLIN worksheet laid out on 31-character lines he counted on; 01-facts.md: K4 fills the last four characters of K3's eleventh line and three full 31-character lines), the prior-work database ('the literal physical artifacts (the 31-character carved lines...) have not been used as a route or grid in any published attempt'), C5(b), C8(a), C11a. One alphabet (standard or KRYPTOS), sign +1 or -1, no move. Each known letter is an edge between column slot j mod w and block slot (j + o) div m; consistency by spanning tree. Bounds: w = 2-31, m = 2-50, o = 0..m-1 (the column key's own offset is a relabelling and drops out). Exact; ten shuffled coppers.
6
Prediction
Written before the run; the result decides it.
No combination with three or more checks survives on K4 beyond the shuffled-copper rate; the carved-line case (m = 31, offset 27) is dead at every word length. Zero candidates.
7
Method
For each word length w, block length m and offset o, give each known letter its column slot and block slot.
Grow a spanning tree over the slots and test the other known letters, on both alphabets and both signs.
Count consistent combinations by number of checks on K4 and ten shuffled coppers.
Print K4's survivors with three or more checks and the carved-line case.
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
31,994 (w, m, offset) structures x 4 cases. K4 consistent with >= c checks, c = 1..8: [1, 0, 0, 0, 0, 0, 0, 0]; controls max [230, 1, 0, 0, 0, 0, 0, 0], min [0, 0, 0, 0, 0, 0, 0, 0]. Outside: []. Carved lines (m = 31, offset 27): widths alive none. K4 survivors with 3+ checks: 0.
What was searched, as the harness recorded it.
family
key = a[j mod w] + b[(j + o) div m], one alphabet, either sign, no move
w
2, 31
m
2, 50
offsets
all 0..m-1
structures with checks
31,994
structures by checks
1
1,434
2
1,295
3
352
4
1,177
5
1,285
6
3,214
7
2,000
8
2,728
9
1,986
10
3,373
11
1,276
12
1,272
13
1,272
14
1,271
15
1,269
16
1,267
17
1,263
18
1,251
19
1,238
20
1,109
21
662
carved lines m31 o27
2
checks
20
consistent
none
3
checks
19
consistent
none
4
checks
18
consistent
none
5
checks
17
consistent
none
6
checks
16
consistent
none
7
checks
15
consistent
none
8
checks
14
consistent
none
9
checks
13
consistent
none
10
checks
12
consistent
none
11
checks
11
consistent
none
12
checks
10
consistent
none
13
checks
9
consistent
none
14
checks
9
consistent
none
15
checks
7
consistent
none
16
checks
6
consistent
none
17
checks
5
consistent
none
18
checks
5
consistent
none
19
checks
7
consistent
none
20
checks
9
consistent
none
21
checks
9
consistent
none
22
checks
7
consistent
none
23
checks
6
consistent
none
24
checks
4
consistent
none
25
checks
2
consistent
none
31
checks
1
consistent
none
k4 at least
1
1
2
0
3
0
4
0
5
0
6
0
7
0
8
0
controls at least
1
89, 0, 108, 90, 0, 230, 90, 3, 20, 109
2
0, 0, 0, 0, 0, 0, 1, 0, 0, 0
3
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
4
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
5
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
6
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
7
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
8
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
check levels outside control range
none
k4 survivors 3 plus
none
n k4 3 plus
0
controls
10 shuffled coppers (seed 88), identical search
How this experiment sits among the others is on the lineage page; its family's open hypotheses are on the families page.
Rendered from the record on 2026-10-18 12:26 UTC; updated after every experiment.