“Every move of the type-1 library, then a table built on one alphabet in an unknown order, key lengths 1-26, decided exactly”
F6.1 (one free alphabet after or before each move), first exact test, order A (move, then the table); order B follows as 0130 because both do not fit one 30-minute budget. 0097 tested this only with a relaxation that can refute but not confirm, at key lengths 3, 7 and 21, and only in the added (Vigenere-like) form; that made it weak. Here 0119's exact decider (mod 13 and mod 2, exhaustive where the solution space is small, a depth-first search with a node limit elsewhere, every fit re-checked) runs on every one of the 27,852 moves, key lengths 1-26, both table forms (added and Beaufort). Controls: 12 scrambled coppers on a fixed sample of 800 moves, with K4 counted on the same sample.
Sanborn said he wrote the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. into a grida grid Writing the message into rows of some width and reading it out in another order, column by column for instance, which shuffles the letters without changing them. and read it out another way (a 'matrix'), then used the big lettered table. Earlier tests fixed 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.'s alphabet to the plain A-Z or the KRYPTOS one. Here the table's scrambled alphabet may be any of the possible orders, and for each of about 28,000 ways of moving the letters, each key length up to 26 and two ways of reading the table, arithmetic on 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. decides whether any alphabet and key could work at all. We do the same on scrambled copies of the carved textthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. to see how often that happens by chance.
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
Sanborn wrote of matrix codes and then going back to the table, and said his table was slightly different from the carved one. Here every move of the type-1 library comes first, then a table on one alphabet in any of its 26! orders.
the check
For each move, key length 1-26 and form, the 24 known letters give 24 equations, solved exactly mod 13 and mod 2: either no one-to-one alphabet fits, or one is found and checked.
the bound
No move admits an alphabet below key length 6. Above that, K4 fits as often as scrambled coppers: above all twelve in 7 of 52 cells, while a copper manages 0-8 against the rest.
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 7 wide, and write where each of the 24 known letters lands in the carved text.
Pick a key length, say 9, and the order 'move first': each known letter's slot is its landing place mod 9.
Write one line per known letter: place-in-alphabet of the carved letter there = place of the known letter + key value of the slot (all unknown).
If two known letters in one slot sit under the same carved letter but differ, or the same known letter under two carved letters, stop: dead.
Otherwise solve the 24 lines mod 13 and mod 2; if two different letters are always forced onto the same place, dead.
Else look for one alphabet and key that satisfy every line; if found, check it, and the setting fits.
Repeat for every move, key lengths 1-26, the Beaufort form (carved place = key minus known place), and on 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.
move: turn cw 7 (write the message in rows of 7, read the columns bottom to top); then the table, key length 9
place known lands at carved slot (landing place mod 9)
22 E 11 U 1
23 A 25 V 6
24 S 39 Q 2
25 T 53 K 7
26 N 67 V 3
27 O 81 T 8
28 R 94 K 3
29 T 10 H 0
30 H 24 R 5
31 E 38 T 1
32 A 52 J 6
33 S 66 P 2
34 T 80 X 7
64 B 5 U 4
65 E 19 B 0
66 R 33 S 5
67 L 47 Z 1
68 I 61 N 6
69 N 75 W 2
70 C 88 U 6
71 L 4 R 3
72 O 18 F 8
73 C 32 K 4
74 K 46 K 0
form V: a slot sends one known letter to two carved letters (or two to one): dead
form B: a slot sends one known letter to two carved letters (or two to one): dead
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C1(a) (Sanborn, CNN 2005, knowledge/sources/cnn-2005-sanborn-interview-transcript.txt: 'I used a matrix code, and then we can possibly use this code to decipher with... double matrixes and triple matrixes... and then went back to this table to do the ultimate'), C27(c) (his table 'slightly different from the one on Kryptos'), C2(a). Model: plaintext p moved by a permutation pi of the type-1 library (K3's rule a + b i mod 97 at all 9,312 settings, one quarter turn cw/ccw at widths 2-96, two cw turns at every width pair, plain columnar both ways, keyed columnar from the vocabulary and theme words, each forward and inverse: 27,852 distinct maps, as 0097), and one unknown bijection A on both sides of a periodic table with key k of length L. Order A only (move, then table): A(c_j) = s A(m_j) + k[j mod L], slot = carved place j; order B is 0130. Form V: s = +1 (Quagmire III with free order; variant Beaufort is V with k negated); form B: s = -1 (Beaufort). The 24 known letters give 24 equations over Z26; exact decision as 0119 (refute when two letters coincide mod 13 and mod 2, or three mod 13; enumerate the mod-13 space up to scaling at rank <= 5; else 300 random points as a witness hunt, then depth-first search with pruning, 200,000 nodes, 'undecided' reported). A per-slot filter (each slot one-to-one) runs first; it is implied by the model, so it loses nothing. Zekios (2026, research note combined_methods_and_sevens.md) did any-alphabet keys only to period 12 and only for double rotations.
6
Prediction
Written before the run; the result decides it.
K4 has fitting settings at key lengths of about 7 and up in both forms, at the rate of the scrambled coppers: in no more cells (form, length) is K4 above all 12 coppers than the most any single copper manages against the rest. Key lengths 1-5 have no fit. If K4 beats that null count, the queue stops for a replication (cells where K4 fits and no copper does are listed, and count in it). Zero candidates; fits that remain are at the coppers' rate and only an English climb could judge them, which 0120 found powerless, so they are blocked, not open.
7
Method
Build the 27,852 moves of the type-1 library.
For each move, key length 1-26 and form, write the 24 equations (slot, known letter, carved letter at the place the move sends it).
Drop settings that fail the per-slot test; decide the rest exactly (dead, fit with a re-checked witness, or undecided at the node limit).
The same on 12 scrambled coppers over a fixed random sample of 800 moves.
Per cell (form, length): K4's fits on the sample against the coppers'; count cells where K4 is above every copper and compare with the same count for each copper against the rest.
Validate on planted texts (random move, form, length, alphabet and key must decide 'fit').
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
K4 on 27,852 of 27,852 moves; smallest key length with a fit {'AV': 6, 'AB': 6}; fits at L<=8: 312. Sample of 800 moves: K4 above every copper in 7 of 52 cells, coppers against the rest 0-8; cells where only K4 fits: []. Stop queue: False.
What was searched, as the harness recorded it.
family
one unknown alphabet on both sides (Quagmire III / Beaufort with a free order), periodic key 1-26, after a type-1 move (order A)
moves
27,852
k4 moves done
27,852
cells
order A (move, then table) x 2 forms x key lengths 1-26
exhaustive
exact decision per setting (0119's decider; undecided counted where the node limit was hit)