“Two key words, two passes through the tableau: the cribs as linear equations mod 26”
New root in family 3. The key is the sum of two short repeating keys, one per pass, so the 24 cribs become linear equations in a + b unknowns and consistency is decided exactly.
revertedstatus
a new rootparents
3 mintime, all phases
0candidates
0/24known letters
1
The experiment method
What the method does with the 24 known letters.
Suppose the artist ran the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. through the sculpture's tablethe table The right-hand half of the sculpture, 26 rows of the alphabet each shifted one place further, starting from the word KRYPTOS. twice, with a different secret word each time. Two pushes along the alphabet add up to one push, so the two words act like one long key made by addingVigenere The three rules of arithmetic a table can use: add the key letter to the message letter, subtract the message letter from the key letter, or subtract the key letter from the message letter. them letter by letter. 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. give 24 facts about that sum. If the two words are short, say 7 and 8 letters, 24 facts are more than enough to tell whether any pair of words can produce them, and if so, what the words are. We check every pair of lengths and read off the words where the facts agree.
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 slots
Two secret words, used one after the other on the table, add up: each place uses one slot of the 7-letter word and one of the 8-letter word, and each known letter forces their total.
the loop
Places that share a slot tie the other slots together; when a chain of ties comes back to a slot, the totals must agree. For lengths 7 and 8 they first disagree at place 64.
the bound
Every pair of lengths from 2 to 30 was tried, plain and carved alphabets standard or the sculpture's: no pair with total length below 25 survives, and no survivor is made of puzzle words.
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.
Take lengths 7 and 8 and the KRYPTOS alphabet for everything, Vigenere both passes.
Position 22 needs a total key letter that sends E to F: R, index 1. Position 22 uses slot 0 of the 7-letter word (21 mod 7) and slot 5 of the 8-letter word (21 mod 8), so x0 + y5 = 1.
Position 29 uses slot 0 again and slot 4: x0 + y4 = its forced value.
Subtract: y5 - y4 is now fixed.
Walk all 24 positions this way; every slot gets tied to the others through shared positions.
When a loop closes, the values must agree, or the pair 7 and 8 is dead.
If they all agree, pick x0 freely; every other letter follows.
Twenty-six choices of x0 give twenty-six word pairs; see whether either word is one the puzzle knows.
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.
lengths 7 and 8, KRYPTOS alphabet throughout, Vigenere both passes: equations from the first cribs
pos plain cipher total key index x slot (pos-1 mod 7) y slot (pos-1 mod 8)
22 E F R 1 0 5
23 A L D 10 1 6
24 S R U 21 2 7
29 T R W 23 0 4
30 H N O 5 1 5
64 B N E 11 0 7
65 E Y L 17 1 0
positions 22 and 29 share x slot 0, so y5 - y4 equals the difference of their totals; the chain of such ties must close consistently.
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Scheidt's habit of combining two key components (knowledge/people/scheidt.md, C6) and Sanborn's 'double' (C1 reading c, composed tableau passes) suggest two keywords X and Y applied in two passes. Two passes through the same tableau compose to one periodic key t[i] = x[i mod a] + s y[i mod b] mod 26 with s = +1 or -1 depending on the modes, of period lcm(a, b). 0005 excluded periods 1-26 and 30-52, so only pairs with lcm in {27, 28, 29} or 53 and above remain; within them the question is whether the forced total key factors into two short words. For each pair 2 <= a < b <= 30, each plain and cipher alphabet in {standard, KRYPTOS}, each sign of the plaintext (Vigenere-like or Beaufort-like) and each s, the 24 forced values give 24 equations x_u - y'_v = t over Z26, checked by a weighted union-find; with a + b - 1 effective unknowns there are 25 - a - b redundant checks, each passing by chance with probability 1/26. Survivors are enumerated (26 to the power of the number of components) and X, Y matched against the vocabulary and K1-K3 windows under both key alphabets and both signs; matches are decrypted and submitted. Bounds: complete for two-pass periodic keys with lengths 2-30 under the standard and KRYPTOS alphabets.
6
Prediction
Written before the run; the result decides it.
Length pairs with a + b above about 20 survive by chance under some settings, because they have few redundant checks. Pairs with a + b of 15 or less survive in at most a handful of settings. No surviving pair yields X or Y in the vocabulary or K1-K3 windows; zero candidates pass.
7
Method
For each plain alphabet, cipher alphabet and plaintext sign, compute the forced total key value t at each crib position.
For each length pair (a, b) with lcm not in 1-26 or 30-52, and each sign s, build nodes for the a slots of X and the b slots of Y and add the edge x[i mod a] - s y[i mod b] = t[i] for each crib.
Reject on any inconsistent cycle.
Count components; enumerate the free values when there are at most three components.
Match X and Y against the vocabulary and K1-K3 windows under the standard and KRYPTOS key alphabets; decrypt and submit matches.
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
4896 cases; 3498 consistent; 0 word matches submitted.
What was searched, as the harness recorded it.
family
two periodic keys composed through two tableau passes
lengths
2 <= a < b <= 30, lcm outside 1-26 and 30-52
pairs
306
alphabets
plain and cipher in {std, kry}; key words read in std or kry
cases
4,896
survivors
3,498
survivors by a plus b
25
18
26
16
27
50
28
34
29
96
30
80
31
160
32
148
33
176
34
192
35
144
36
144
37
192
38
176
39
160
40
128
41
160
42
144
43
144
44
128
45
112
46
112
47
112
48
96
49
96
50
80
51
80
52
64
53
64
54
48
55
48
56
32
57
32
58
16
59
16
smallest surviving pairs
none
vocab or k1k3 matches
0
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.